Article pubs.acs.org/Langmuir
Dendrimer Nanofluids in the Concentrated Regime: From Polymer Melts to Soft Spheres Georgia A. Pilkington,† Jan S. Pedersen, and Wuge H. Briscoe* School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom ABSTRACT: Understanding dendrimer structures and their interactions in concentrated solutions is important to a wide range of applications, such as drug delivery and lubrication. However, controversy has persisted concerning whether, when confined to proximity, dendrimers would entangle as observed for polymer systems, or act as deformable spheres. Furthermore, how such behavior may be related to their size-dependent molecular architecture remains unclear. Using small-angle X-ray scattering (SAXS), the intermolecular interactions and structures in aqueous nanofluids containing three generations of carboxyl-terminated poly(amidoamine) (PAMAM) dendrimers (G0.5, Rg = 9.3 Å; G3.5, Rg = 22.6 Å; G5.5, Rg = 39.9 Å, where Rg is the radius of gyration) over a mass fraction range 0.005 ≤ x ≤ 0.316 have been studied. In the highly concentrated regime (x ≥ 0.157), we observe that the solution properties depend on the dendrimer generation. Our results suggest that the smaller G0.5 dendrimers form a highly entangled polymer melt, while the larger dendrimers, G3.5 and G5.5, form densely packed and ordered structures, in which the individual dendrimers exhibit some degree of mutual overlap or deformation. Our results demonstrate the tunability of interdendrimer interactions via their molecular architecture, which in turn may be harnessed to control and tailor the physical properties of dendrimer nanofluids.
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INTRODUCTION Dendrimers are highly branched macromolecules with a central core surrounded by successive layers of repeat units, known as generations (denoted as G). These are grown from the central core in a stepwise assembly, leading to a tree-like structure, hence the name “dendrimer”, which originates from the Greek word “dendron”, meaning tree. With a high degree of structural and chemical homogeneity, and tunable size, molecular mass, and surface functionality, dendrimers have been found to inherently possess some distinct physical and chemical properties compared to linear polymers, and have attracted considerable attention in a wide range of applications in the past 30 years, particularly as delivery vectors for drugs and genes1,2 Among the most widely studied dendrimers are the poly(amidoamine) (PAMAM) family, originally synthesized by Tomalia et al.3 Using this method PAMAM dendrimers of up to 10 generations can be synthesized, with a size increment of ∼1 nm per generation.4 PAMAM dendrimers can also be further functionalized with different terminal surface groups, including sodium carboxylate groups (−COONa), known as half-generation PAMAM, e.g., G0.5, G1.5, G2.5, etc., and hydrophobic groups, such as alkyl chains, making them dispersible in different solvents. Depending on the degree of branching (or dendrimer generation), the shape of the dendrimers has been found to vary significantly. For example, due to their more open and star-like structure, PAMAM dendrimers of lower generations have been previously shown, both experimentally and through theoretical simulations, to adopt a more planar and elliptical shape; whereas higher © XXXX American Chemical Society
generation dendrimers have been shown to become increasingly compact, centrosymmetrical, and particle-like.5 Intermolecular interactions between dendrimers in solution (dendrimer nanofluids6) will intricately depend on their molecular architecture and the surrounding medium, e.g., their solubility, the solution pH and salt concentration. In particular, dendrimer architectural details are likely to become increasingly important in concentrated or confined dendrimer solutions, where intermolecular interactions dominate the fluid properties. However, from a limited number of related studies, a unified view of the interactions and behavior of dendrimers in concentrated solutions has yet to emerge. Using a cone and plate rheometer, Uppuluri et al.7 showed that ethylenediamine solutions of G0−G6 PAMAM dendrimers exhibited Newtonian behavior over a concentration range of 30−75% w/w (mass fraction x = 0.3−0. 75), with the solution viscosity systematically increasing with increasing dendrimer size. It was concluded that the dendrimers did not interpenetrate or form transient networks, as typically observed for concentrated solutions of long chain linear or randomly branched macromolecules.8 However, a strong dependence of the solution viscosity on dendrimer concentration and temperature, as well as a lack of hysteresis between repeat loadings, indicated that the dendrimers possessed a substantial degree of flexibility and thus could deform when highly confined. Received: December 15, 2014 Revised: February 24, 2015
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three generations of carboxylic acid terminated PAMAM dendrimers with a low (G0.5), intermediate (G3.5), and high (G5.5) degree of branching, over the mass fraction range of 0.001 ≤ x ≤ 0.315. As an example, the structure of G0.5 PAMAM is shown in Figure 1, which consists of a
An apparent lack of entanglement in dendritic systems has also been reported in a number of structural studies using small angle scattering techniques. For instance, using small angle neutron scattering (SANS) Topp et al.9 showed that the spatial arrangement of G3 and G4 poly(propylene imine) (PPI) dendrimers was consistent with that expected for the packing behavior of hard spheres for dendrimer mass fractions of up to x = 0.8. It was further shown by complementary small-angle Xray scattering (SAXS) measurements that the dendrimers remained nominally spherical above a predicted mass fraction for random close packing of the dendrimers, but reduced in size due to deformation. More recently, SANS results obtained in mixtures of G4 PPI dendrimers with protonated and deuterated end groups also showed that the shape of the dendrimers was unaffected by interdendrimer interactions up to a volume fraction of ϕ = 0.23.10 Furthermore, Rietveld et al.11 suggested that a reduction in the osmotic compressibility of G1−G5 PPI dendrimers in deuterated methanol at the dendrimer concentration above its critical overlap concentration was consistent with dendrimer shrinkage in this regime, as supported by field gradient nuclear magnetic resonance (FG NMR) measurements, which did not show any interpenetration or network formation between the dendrimers in the solutions. In another investigation of the interactions between G2, G4, and G6 of PAMAM dendrimers in aqueous solutions using electron paramagnetic resonance (EPR) and fluorescence depolarisation, Jockusch et al.12 also showed that dendrimer mobility was independent of its volume fraction in the concentration range 0.01−5% (w/w), indicating that no significant entanglement or attractive interaction was present. However, a dramatic decrease in the dendrimer mobility above 30% (w/w) was observed but attributed to the increased solution viscosity, rather than dendrimer interpenetration or entanglement. In contrast, a number of investigations have presented evidence for dendrimer interpenetration or mutual overlap in concentrated solutions. For instance, Bodnar et al.13 showed that the shear viscosities of highly concentrated solutions of acetyl functionalized G4 and G5 PPI dendrimers were much lower than predicted for a system of charged hard spheres. Furthermore, by fitting an effective hard sphere model to corresponding SANS intensity profiles, it was shown that the interactions between the dendrimers were much less repulsive than expected for dispersions of charged spheres, suggesting that some degree of attraction between dendrimers, possibly through mutual interpenetration or clustering, was present. Similarly, Rosenfeldt et al.14 reported that the concentration dependence of the effective diameter of unfunctionalized G4 PPI dendrimers became nonlinear at a volume fraction of ϕ = 0.237, indicative of some attractive interactions or mutual overlap between the dendrimers. Further molecular dynamics (MD) simulations15 showed that interdendrimer interpenetration was present in melt solutions of G2−G5 PPI dendrimers. However, the degree of overlap between the dendrimers was found to decrease significantly with increasing dendrimer size and predicted to be limited to those of G5 or lower. Overall, there exists discrepancy regarding whether dendrimers, when they are confined and come into close proximity, would entangle, or instead deform and retain their individual shape. It is thus important to further study how both the interactions and structures of dendrimers may correlate with their size-dependent molecular architecture as they approach overlap. Here we report a SAXS study of solutions containing
Figure 1. Structure of sodium carboxyl G0.5 poly(amido,amine) (PAMAM) dendrimer.
tetrafunctional ethylamine core, surrounded by layers of tertiary amine branches and terminated with n sodium carboxyl groups, where n scales with the generation G number as n ∼ 2G+2.5. This manuscript is organized as follows. First, we briefly present the procedures and models for our SAXS data analysis. Second, we show characterization of the dendrimers structures and shapes in the dilute regime. Third, we present SAXS results obtained in solutions of the different generation dendrimers in the intermediate to semidilute regime, showing that the interactions between the dendrimers depend on their size and architecture. In particular, we present evidence that in the highly concentrated regime (x ≥ 0.157) the structure of the dendrimer solutions is similar to that of a polymer melt for G0.5 dendrimers, and exhibits a highly ordered system of soft, deformable spheres for G3.5 and G5.5 dendrimers. Our results may help to unify the conflicting views on dendrimer interactions in concentrated regime, that is, whether they interpenetrate or deform. In fact, we argue they may do both, depending on their molecular architecture.
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MATERIALS AND METHODS
Materials. Aqueous dispersions of generations G0.5 (theoretical molecular weight Mw = 1269 g mol−1), G3.5 (Mw = 12 927 g mol−1) and G5.5 (Mw = 52 900 g mol−1) PAMAM starburst dendrimers were purchased from Dendritech, Inc. (Midland, MI). Each dendrimer generation consisted of a tetrafunctional ethylenediamine core [>NCH2CH2N 0.005 for G3.5 and G5.5, an additional contribution of a structure factor S(q) peak can be seen for all the dendrimer generations studied (Figure 5). The appearance of an S(q) peak is a commonly observed feature of repulsive polyelectrolyte and colloidal systems and is related to the first maximum in the radial distribution function g(r) of the structures in the solution. As previously described by Guinier and Fournet,24 only the first maximum of this function is typically observed for liquid systems (such as the dendrimer solutions here) due to the broader distribution of the average distances between the scattering centers in the solution, compared to that of a crystalline solid, which leads to the smearing out of higher order correlation peaks. In the case of the concentrated solutions of carboxyl PAMAM dendrimers, the observation of an S(q) peak in the scattering intensity can be attributed to partial ionization of the dendrimer terminal carboxylate (−COO−Na+) groups, which gives rise to long-ranged, electrostatic interactions between the dendrimers. This consequently leads to liquid-like ordering of the dendrimers in a local close-packed face-centered cubic (fcc) arrangement.32
Figure 4. Kratky plot of I(q,x) × (qRg)2 versus qRg for dilute solutions of generations G0.5, G3.5, and G5.5 carboxyl-terminated PAMAM dendrimers, at a mass fraction x indicated in the legend. The form factor of a homogeneous sphere is shown for comparison (dashed curve) and the position of the expected maximum at qRg ∼√3 for a system of hard spheres is indicated (dotted line). The scattering curves have been offset in the y-axis for clarity. The inset shows a I(q) versus q log−log plot from a solution of G0.5 at x = 0.001, with the slope of the fitted straight line −1/(2v) = 1.255 ± 0.013 giving an volume scaling exponent of v ≈ 0.5 (cf. eq 8).
versus qRg plots of the scattering intensities collected for dilute solutions for each of the dendrimer generations. Here an x-axis of qRg is used in place of q so that the profiles for different generations (i.e., different Rg) can be directly compared. For comparison, the dashed bell-shaped curve in Figure 4 shows the calculated profile using eq 5 for a dilute solution of monodisperse spheres (Rg = 100 Å), which exhibits an asymptotic q−4 decay on both sides of a well-defined maximum at qRg ∼ 1.7 (i.e., √3), a value evident from a simple rearrangement of eq 5.25 For G5.5 dendrimer, a bell-shaped curve is observed, similar to that expected for solid spheres. However, the intensity peak is notably broader and the peak maximum slightly shifted to a higher q, indicative of a disordered structure of spheres. For G3.5, we similarly observe a bell-shaped curve with a well-defined maximum shifted slightly to a higher q value. However, the magnitude of the peak is significantly reduced (i.e., flattened) compared to that for G5.5. This suggests that the G3.5 dendrimers adopt a nominally spherical shape but a less well-defined structure in solution compared to G5.5. Such observations are in line with E
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Figure 6. Plot of the average center-to-center distance, dav, between dendrimers in the intermediate concentration regime for the G0.5, G3.5 and G5.5 of dendrimers, as a function of dendrimer mass fraction, x. The solid curves are the power law fits dav ∼ x‑β with the exponents β, indicated in the figure. Such power law dependences are consistent with the behavior of a system with short-range liquid-like order which gives a decay of β ∼ 0.32. The horizontal dashed lines represent the predicted hard sphere overlap distance d* for each dendrimer generation, approximated as d* ∼ 2RHS. The vertical dotted lines represent the critical overlap concentrations c*corresponding to the d* of G3.5 and G5.5 (c* for G0.5 is not shown), as indicated in the figure. The power law fits give c* values of 0.17 and 0.15 for G3.5 and G5.5, respectively.
and theoretical36,37 results for charged dendrimer solutions, characteristic of a liquid-like system with short-range order. Also indicated in Figure 6 are the predicted overlap distances d* (horizontal dashed lines) for the dendrimers. Due to the semiflexible nature of the dendrimers and observed hard sphere like packing, we approximate d* as d* = 2RHS. The dendrimer critical overlap concentrations c*, which correspond to d* according to the power fits, are also shown for reference for both G3.5 and G5.5. This approximation has also been made in previous work by Ramzi et al.38 The c* value for G0.5 is not shown as it is considerably larger. The significance of these parameters will be discussed further in the following sections. Typically, the S(q) contribution to the overall scattering intensity can be extracted from I(q) by dividing it with the scattering intensity obtained from a dilute solution I(q)dilute, where S(q) is assumed to be ∼1 (cf. eq 2), as this removes the contribution from the scattering structures P(q). For this analysis to be correct the form factor P(q) of the scattering structures, determined by their size and shape, must be independent of the concentration. However, for soft, penetrable objects such as polymer chains and dendrimers, the validity of this expression may be compromised due to possible overlap or deformation of the molecules in the concentrated regime. As a result, the P(q) obtained from dendrimer solutions in the dilute regime may not accurately describe their conformation in the concentrated regime. Therefore, the employment of the above assumption could give rise to unphysical features in the calculated structure factor. For this reason we have chosen not to perform this type of S(q) analysis. Instead we use a simple method previously used by Topp et al.,9 where I(q) is normalized by the maximum intensity Imax and plotted as a function of the q normalized by
Figure 5. Scattering intensities I versus q from solutions of generations (a) G0.5, (b) G3.5 and (c) G5.5 PAMAM dendrimers. I has been normalized by the dendrimer mass fractions x as indicated in legend. A higher order feature in the scattering profiles of G3.5 and G5.5 is labeled as PII.
For an fcc lattice, the position of the S(q) peak, qmax, is related to the average center-to-center distance dav between the particles by the application of a modified Bragg equation dav = 1.22(2π /qmax )
(9) 1/2
where the prefactor 1.22 (i.e., (3/2) ) is obtained from inserting the relation d(hkl) = a/√2 for an fcc lattice into the Bragg relation λ = 2a sin θ / (h2 + k 2 + k 2)
(10)
where a is the lattice constant, and h, k and l are the Miller indices of the Bragg plane. Using eq 9, the average interdendrimer distance dav has been obtained for each dendrimer generation as a function of mass fraction x, as shown in Figure 6, showing an asymptotic decay. Power law fits to dav ∼ x‑β from the plots (solid curves in Figure 6) yield values of β = 0.31−0.32 for all the dendrimers. Such behavior is comparable to that observed for 3D packing of spheres for which β = 1/3 from simple packing considerations. This result is also consistent with previous experimental33−35 F
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Langmuir the corresponding qmax (cf. Figure 7). In presenting the scattering curves in this way, the S(q) peaks of the scattering
region plateaus, leading to a shoulder-like scattering profile in Figure 5a, rather than a pronounced S(q) peak. Previously, similar scattering behavior has been reported for star polymers with a small number of arms and attributed to the entanglement of the flexible polymer chains.29,39,40 However, due to the hybrid nature of dendrimers between traditional polymers and colloidal particles, the interpretation of such scattering phenomena is more complex and as a result a number of possible interpretations have been presented. For G0.5, we observe a marked diminishment in the S(q) peak above a mass fraction of x = 0.050, which is below the predicted c* of the dendrimers (Figure 6). One might suggest that this could be due to clustering or aggregation of dendrimers as a result of interpenetration of the dendrimers, given the open dendrimer structure and the possible attraction between negatively charged dendrimer terminal carboxyl groups and positively charged internal tertiary amine groups (with a pKa of 3−63,36,41−43) at a neutral pH, at which our measurements were taken. However, as discussed above, the average dendrimer-dendrimer separation distance dav scales with the dendrimer concentration with the exponent β ∼ 0.32, suggesting that the dendrimers were not clustering, but rather, were in a liquid-like packing. As such, a simple explanation for the diminishing S(q) peak at x > 0.050 is that the molecular arrangement of the G0.5 PAMAM can be well described by a Gaussian star with an open structure. Accordingly, we suggest that two length scales, arising from competing interdendrimer interactions, are present in concentrated solutions of G0.5 PAMAM dendrimers. In the concentration regime (0.01 ≤ x ≤ 0.1), a structure factor S(q) is present in the high q range of q ∼ 0.05−0.12 Å−1 and shifts to higher q with increasing concentration, due to a decreasing interdendrimer distance dav with increasing concentration. However, as dav approaches d*, increasing overlap between the dendrimers eventually lead to a homogeneous system, analogous to a system of repulsive polymer chains with a uniform segment distribution and a P(q) arising from the segment distribution of the polymer chains.44 Previously, Ramzi et al.,38 observed that the SANS S(q) peak in highly concentrated solutions of G4 PPI dendrimers significantly diminished above a critical (hydrodynamic) overlap concentration c* of the dendrimers, attributing it to dendrimer interpenetration. However, in another study by Likos et al.45 a similar diminishment in the SANS S(q) peak from the concentrated solutions of G4 PPI dendrimers functionalized with urea46 was well described by a “soft” interaction potential, for which minimum interpenetration of the dendrimer branches was assumed. Instead, it was attributed to an anomalous structure factor peak47 appearing when the dendrimer concentration rose above a critical overlap density C*, which was approximated as C* = R−3 g,∞, rather than due to the mutual interpenetration of the dendrimers. 4. Concentrated Solutions of G3.5 PAMAM. Qualitatively the shape of the SAXS profiles for G3.5 PAMAM is notably different from those of G0.5, and for all the concentrations studied an S(q) peak was observed in the q range of q ∼ 0.012−0.11 Å−1 (cf. Figure 5b). With increasing dendrimer concentration, the qmax of the S(q) peak is shifted to higher q values and the corresponding dav ∼ x−0.31 (i.e., β ∼ 0.31), as expected for systems with liquid-like ordering. With the exception of the highest concentration (x = 0.227), the shift in qmax is also accompanied by narrowing of the peak with increasing dendrimer concentration, as shown in the I/Imax
Figure 7. Normalized scattering intensity profiles, I/Imax, plotted as a function of the normalized scattering vector q/qmax for solutions containing different mass fractions of (a) G0.5, (b) G3.5, and (c) G3.5 PAMAM dendrimers.
intensity profiles for each dendrimer concentration can be directly overlaid. Hence, any variation in the curve shape or magnitude is highlighted, and therefore any changes in the interactions between the dendrimers in solution can be more easily seen. In the following sections, the physical meanings of such deviations observed in the scattering intensities obtained from the concentrated solutions of the dendrimers studied (cf. Figure 5) and amplified using this method (cf. Figure 7) will be discussed for each of the dendrimer generations studied. 3. Concentrated Solutions of G0.5 PAMAM. For repulsive systems, the presence of an S(q) is also typically accompanied by a depression in the scattering intensity in the low q region due to excluded volume effects related to the finite-size and consequential mutual impenetrability of the scattering structures. This gives rise to an S(q) peak, as observed for the mass fractions of G0.5, x = 0−0.050, in the low q range of q ∼ 0.02−0.05 Å−1 in Figure 5b. However, at higher G0.5 concentrations of, x ≥ 0.010, the intensity in this low q G
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Langmuir versus q/qmax plot for G3.5 in Figure 7b. This signifies narrowing of the distribution in dav in the dendrimer solutions and thus an overall increase in ordering. However, at the highest G3.5 mass fraction (x = 0.227), the S(q) peak broadens noticeably and decreases in magnitude. Such a behavior is similar to that observed for G0.5 mass fractions x > 0.01, suggesting some mutual overlap of the dendrimers. Referring to Figure 6, the occurrence of possible overlap between the G3.5 dendrimers at x = 0.227 correlates well with their predicted overlap concentration c*. Such a correlation has also been previously reported for concentrated solutions G4 PPI dendrimers by Topp et al.9 who showed that the magnitude of the SANS S(q) peak decreased at very high concentrations (x > 0.6) of the dendrimers. However, this was attributed to an increase in incoherent scattering due to the large fraction of hydrogen present. In the same study, complementary SAXS measurements also revealed a distinct higher order feature in scattering intensity profiles at high q at all dendrimer concentrations studied, which was assumed to be related to the sphere-like form factor of the dendrimers. Hence, it was concluded that, even when concentrated above their predicted concentration for random close packing, the size and shape of the G4 PPI dendrimers remained similar and nominally spherical. This suggests that the dendrimers would deform with increasing concentration rather than interpenetrate with one another. In our case, we observe a much milder higher order feature (indicated as PII in Figure 5b) in the scattering profiles for G3.5, as compared with that observed in PPI dendrimer systems of the same generation.9 This is likely due to the longer branching units for PAMAM (seven bonds) compared that of PPI dendrimer (four bonds), which would have led to a more compact structure and a higher surface charge density for the PPI dendrimers. However, the presence of this peak suggests that the G3.5 dendrimers remained nominally spherical in this concentration regime, albeit with a less well-defined interface than that observed for G4 PPI dendrimers. Due to the mildness of the PII feature for G3.5, we have restrained from analytically determining the dendrimer size. However, numerical model fits to the scattering intensity profiles at x = 0.10, i.e., before significant overlap of the dendrimers, reveal a ∼25% decrease in the radius of the dendrimer core R compared to that in dilute solution. This suggests that the dendrimers underwent some deformation, as well as the mutual overlapping of the dendrimers, at this concentration. We thus conclude that, in the intermediate overlap regime 0.05 ≤ x ≤ 0.10, below the critical concentration c*, G3.5 dendrimers exhibited similar behavior to that expected for charged hard spheres, which is markedly different from that observed for G0.5. This maybe rationalized by the higher surface density of dendrimer terminal groups on G3.5. However, above c*, where the dendrimers are assumed to arrange into a random closed packing, the dendrimers are found to undergo some interpenetration and possibly also deformation, although they remain nominally spherical and as individual entities. Such dual behavior can be attributed to (1) the penetrable interface of the dendrimers surfaces which, despite the higher degree of surface group density compared to G0.5, could still facilitate some interdigitation between the outer dendrimer chains; and (2) at the same time, the increased steric crowding of the dendrimer surface groups limits their
interpenetration and instead leads to dendrimers deforming in order to pack more efficiently. 5. Concentrated Solutions of G5.5 PAMAM. Similar to G3.5 (cf. Figure 5c,b), the SAXS profiles for G5.5 show a pronounced S(q) peak in the q range ∼0.01−0.1 Å−1 at x > 0.1 (cf. Figure 5c). With increasing x, the qmax of the S(q) peak also shifts to higher q, indicative of the decreasing interdendrimer separation, while the width of peak progressively decreases due to the increased ordering of the dendrimers in the solution with increasing dendrimer number density. Also as observed for G3.5, the corresponding dav scales with x exponentially with an exponent β ∼ 0.32, as expected for a system of liquid like ordering. In addition, a distinct higher order feature (a secondary peak) at q ∼ 0.14 Å−1 in the G5.5 SAXS profiles is observed for all the concentrations (cf. PII in Figure 5c). As discussed above, this secondary maximum can be attributed to a contribution from the a sphere-like P(q) due to more compact, particle-like G5.5 dendrimers packed in an ordered structure.9 In this high q region (q > 0.1 Å−1), the scattering intensity profiles for G5.5 concentrations 0.005 ≤ x ≤ 0.1 almost overlay with each other, indicating that the G5.5 dendrimers retain a similar internal structure throughout this concentration range. However, at the highest G5.5 concentration x = 0.157, the secondary P(q) peak is shifted from q ∼ 0.141 Å−1 to 0.152 Å−1 (cf. Figure 8), indicating a decrease in the dendrimer size. From
Figure 8. Semilogarithmic plot of the scattering intensity, I(q), versus q from solutions of G5.5 PAMAM dendrimers. The scattering curves have been offset in the y-axis for clarity.
our numerical model fits to I(q) we find that this shift corresponds to a decrease in R by ∼33%. Referring to Figure 6, the average interdendrimer separation dav at which this occurs, is slightly smaller (dav = 87.8 Å) than the predicted critical overlap distance d* for the G5.5 dendrimers. However, we consider this difference to be within the experimental error. We therefore conclude that G5.5 PAMAM dendrimers behaved as expected for charged hard spheres in the intermediate overlap regime. However, at concentrations close to the predicted overlap concentration c* the dendrimers deformed in order to pack more efficiently in solution. In this conformation, a densification of the dendrimer core was also observed, which is probably facilitated by the expulsion of some solvent. H
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SUMMARY AND CONCLUSIONS Using SAXS we have characterized the intramolecular structures of generations G0.5, G3.5, and G5.5 of carboxyl terminated PAMAM dendrimers in dilute aqueous solutions. We find, in line with previous observations for amineterminated PAMAM dendrimers, that with increasing generation the higher degree of branching in the dendrimers molecular architecture leads to a transition from the more open, star polymer-like structure for the lowest generation (G0.5) to a more globular, compact structure for highest generation (G5.5). Across the solutions of the dendrimers in the intermediate regime to the semidilute regime we find that such structural differences between the dendrimer generations give rise to significantly different behaviors, particularly when the dendrimers approach their predicted overlap distance, d*. For the solutions of the lowest generation of dendrimer studied, G0.5, we find two competing length scales present: (1) the spatial distribution of the dendrimers in the solutions, which give rise to a structure factor S(q) peak in the scattering intensity, and (2) the correlation length between the dendrimer branch chains, which gives the contributions in the low q region. These length scales vary as a function of dendrimer concentration: the former increases with increasing dendrimer concentration and then sharply decreases above a certain critical concentration, above which the latter begins to dominate the scattering intensities. In solutions of the intermediate dendrimer generation G3.5, we find that the spatial ordering of the dendrimers gives rise to a pronounced S(q) peak, which was present for all concentrations investigated and varies with concentration as expected for the liquid-like packing of charged hard spheres. However, above the predicted critical overlap concentration c*, we find that the S(q) peak becomes markedly broadened and decreases in intensity, signifying a loss of order in the system. From numerical model fits to the scattering intensities we also find that some (∼25%) deformation of the dendrimers also occurs before c*. In the case of the highest dendrimer generation G5.5, we find that the dendrimers behave as predicted for solutions of charged hard spheres for all the solution concentrations investigated, which is demonstrated by a sharp S(q) peak becoming more pronounced and shifting to higher q positions with increasing concentration. However, at the highest concentration investigated, which is close to, but smaller than, the predicted c* for spheres of similar size, we observe a significant decrease in the dendrimer size by ∼33% accompanied by an increase in their core density. Such observations suggest that in this highly concentrated regime the G5.5 dendrimers deformed in order to pack more efficiently rather than overlapping, as observed for the lower dendrimer generations, which in turn gave rise to the observed simultaneous increase in dendrimer core density. In conclusion, we have demonstrated the interactions between charged dendrimers in solution are intricately dependent on their intramolecular characteristics. For the lowest generation we find that its open, star-like structure facilitated significant interpenetration or entanglement between the dendrimer branches leading to the subsequent formation of a homogeneous solution, with a structure similar to that of a polymer melt. However, for larger dendrimers we observe less interpenetration between the dendrimers, probably due to the
increasing steric crowding of the outer branches, and the dendrimers packed more like deformable, soft spheres. Such results are important as they demonstrate the possibility to systematically tune the interactions between dendrimers in concentrated solutions, and in turn the solution physical properties, through the molecular architecture of the dendrimers. We hope such results will offer useful insights to the application of dendrimers where the interdendrimer interactions and their solution properties are important considerations.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +44 (0) 117 3318256. Present Address †
Chemical and Biomolecular Engineering Department, Johns Hopkins University, Baltimore Maryland 21218, United States. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by a Short Term Scientific Mission (STSM) from the COST Action CM1101 [ECOST-STSMCM1101-100813-034386]. W.H.B. acknowledges funding from the Engineering and Physical Science Research Council (EPSRC EP/H034862/1), the European Research Council (ERC), Taiho Kogyo Tribology Research Foundation (TTRF), and the Marie Curie Initial Training Network (MC-ITN) NanoS3. B. Plazzotta and J. Lyngsø at the University of Aarhus are thanked for their help and advice during the SAXS measurements. G.A.P. was supported by a DTA studentship awarded by the School of Chemistry, University of Bristol (UoB), and acknowledges a travel bursary from the UoB Alumni Association.
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