The unusual interactions between polymer grafted cellulose nanocrystal aggregates

Using computer simulations we study how a corona of polymer molecules grafted to cellulose nanocrystal aggregate (CNA) particles in ﬂ uences the interaction between pairs of parallel CNAs. The resulting distance and orientation (face-to-face versus edge-to-edge) dependence is very rich and counterintuitive. Although the unperturbed polymer corona assumes cylindrical symmetry relatively quickly as the degree of polymerisation increases, the polymer mediated interactions between the grafted particles are strongly orientation dependent. Rather unexpectedly we ﬁ nd that the forces in the face-to-face orientation are much larger than in the edge-to-edge con ﬁ guration although in the latter case the distance between the particle surfaces is much smaller. The reason for this e ﬀ ect is that overall the face-to-face orientation leads to larger chain con ﬁ nement. Interestingly, we ﬁ nd that the deviations of the polymer mediated interactions from cylindrical symmetry are larger in the case of longer grafted molecules compared to shorter ones. When the distance between the CNAs becomes larger and the overlap of the polymer coronas becomes small, the orientation dependence of the mediated interaction vanishes and the particles behave as cylindrical rods. However, this is only a crossover point where the behaviour of the system inverts to slightly larger forces in the edge-to-edge compared to the face-to-face con ﬁ guration. Thus, even though the polymer density around the CNAs is nearly perfectly cylindrically symmetric the polymer mediated interactions are strongly orientation dependent, revealing the polygon character of the CNA cross-section.


Introduction
The physical and geometrical properties of cellulose nanocrystals (CNC) have attracted recent interest of the research communities as new applications are discovered for these naturally occurring nanoparticles. 1,2 It is well known that CNCs have high aspect ratios (length-to-width), L/w spanning a range that varies with the CNC source, between 10 for cotton and ca. 70 for tunicate. 1,3,4 The subject to debate, however, is the exact geometry of CNC cross-sections.
CNCs are extracted from native cellulose microbrils via acid hydrolysis, which breaks the disordered regions and leaves the crystalline regions intact. Therefore, the CNC cross-section is oen interpreted to resemble the cross-section of the original cellulose microbril. Unfortunately, there is little consensus over the microbril cross-section. Early accounts 5 suggest a rectangular shape which has been later supported by electron microscopy imaging of very large microbrils. 6 More recently, a hexagonal cross-section has been suggested. 7,8 In addition, the validity of both the rectangular and the hexagonal model has been rightly questioned. 9 The subject of the nanocrystalor microbrilshape is not trivial since the cross-section impacts the type, size and orientation of the main crystal faces. This in turn is important because the different faces have very different physical-chemical properties, including hydrophobicity and hydrogen bonding ability 10,11 all of which determine how CNCs interact and interface with other materials.
The size of the microbrils that constitute the origin of CNCs is initially determined by biosynthesis. Despite constant progress, 12 the processes that control the structure of microbrils perpendicular to their axis remain elusive. The primary cellulose producing units, terminal protein complexes (TCs), are reported to consist of 6 Â 6 cellulose synthases that could in principle produce 36 cellulose chains simultaneously, 7 but there is also evidence that the primary crystalline unit could consist of 24 cellulose chains. 9 The arrangements and geometries of the TCs also depend on their biological origin.
In the cell walls, the microbrils are oen assembled in larger structures, resulting in larger CNC structures, which are here referred to as cellulose nanocrystal aggregates. It is very oen that experimental work reports CNAs in the literature rather than CNCs. 3 When considering the shape of CNAs, one has to consider that they are prepared by hydrolysis with concentrated sulphuric acid. Taking into account that sulphuric acid even degrades the sidewalls of carbon nanotubes, it is likely that edges and corners of the CNCs and CNAs are also subjected to extensive erosion and that rearrangements may occur. Indeed, a recent study on commercial acid hydrolysed grades of cellulose reported cross-sectional shapes that were uncharacteristic for biological CNCs or CNAs. 13 To make matters even more complicated CNCs seem to be twisted. 2,14 The direct visual proof is difficult, but more indirect evidence has existed for quite some time. The rst indication of a twist came with the discovery of chiral nematic phases (e.g. ref. 2 and 15-17). It was proposed that the origin of the chiral phase of CNCs might be a twist of the crystal. Although many questions remain there is now compelling evidence that the twist does exist 9 and that it may originate from internal stresses. These stresses are caused by weaker hydrogen bonding on the surfaces of the crystals, especially in the case where they are broken by sulfatation or other functionalisations. This results in slightly larger intermolecular distances and stretching of the cellulose chains, which the crystal accommodates by twisting. It is unknown, however if and how this twist is inherited by the CNAs from its underlying CNCs. If the origin of the chiral nematic phases is the twist of the constituting particles, then the CNAs should be twisted too, because they are the ones most oen used in experiments reporting chiral phases (e.g. ref. 15).
This intense debate inspires the question: are the exact shape and twist of CNAs important for their technical application? In this paper we focus on the importance of edges, i.e. deviations of the particle shape from cylindrical symmetry. While this study is inspired by cellulose nanocrystal aggregates, rod shaped nanocrystals with nm-sized and polygon-shaped cross-sections have also been produced from various inorganic materials. 18,19 It is also likely that the cross-section of the closely related natural chitin nanocrystals 20,21 could be polygonal.
For this discussion, it is important to consider that CNCs and CNAs are almost never used in their native state, because they are essentially insoluble in all relevant solvents. Since cellulose particles can be sourced from biomass, sustainability and environmental friendliness are great driving forces for their utilisation. In such a case water is the rst-choice solvent. As CNCs and CNAs easily aggregate in water, their aqueous suspensions must be stabilised. Most commonly they are electrostatically stabilised 2,4,22 by surface charges, which are introduced, e.g. during sulfatation. Alternatively water-soluble polymers can be graed to the particles. 15,[23][24][25] The third option, used to a lesser extent, is adsorption of amphiphilic molecules, such as surfactants 26,27 or copolymers. 28 All these methods create long-distance repulsions between the CNAs. This raises the question whether or not the underlying non-cylindrical shape of the particles matters for these interactions or if the particles effectively become cylindrical rods. Here we focus on the interactions caused by graed polymers. They are particularly interesting as their interaction range can ultimately be limited by the length of the graed molecules. 29 As the length scale of the steric repulsion, which is of the order of the size of the graed chains, is well in the range of the small dimensions of CNCs and CNAs, an interesting interplay between these length scales is expected.
Here we report on mesoscale computer simulations to investigate the interplay between the cross-sectional geometry of the CNAs and the length of the graed molecules. Similar to brushes graed on patterned planar surfaces 30,31 the polymer brushes graed to the CNA faces must be expected to "spill over" at the edges. This should smooth out any non-cylindrical features and eventually result in a cylindrical polymer corona. While we nd that this is indeed the case, the polymer mediated forces between the graed CNAs are strongly orientation dependent.
Our results indicate that the edges of CNCs and CNAs play important roles in the interparticle interactions. This must be expected to affect their self-or directed-assembly. Such effects are relevant in coating and structuring with CNCs/CNAs. It is also relevant to the association behaviour of CNCs and thus affects the rheology, dispersion and other phenomena relevant to the application of CNCs/CNAs. This contribution intends for the rst time to reveal such aspects that are otherwise elusive to experimentation.

Model and simulation
Since the exact shape of CNAs is quite elusive and varies between different cellulose-producing species, we focus on fundamental aspects, in particular the existence of edges along the particle surface, while foregoing other details such as the specic surface chemistry.
Because of the detailed insight computer simulations provide, they are very well suited and widely used to study graed polymers. 32,33 Here the graed polymer molecules are represented by chains of beads. Beads k and l, which are nearest neighbours in the same chain, are bonded via a harmonic bond potential where 3 bond is the depth of the potential well, r bond is the bond length, r kl ¼ ||r kl ||, r kl ¼ r k À r l and r k and r l are the positions of k and l, respectively. The solvent, water, is treated implicitly and the graed polymer is assumed to be soluble. This situation can be modelled by polymer beads interacting with each other via the repulsive Weeks-Chandler-Andersen (WCA) potential f(r ij ). (2) where r cut ¼ 2 1/6 is the cut-off-radius, 3 is the well depth and s is the length parameter of the Lennard-Jones (LJ)(12,6) potential in 2.
Graing is modelled by placing anchor beads at random positions along the surface of the crystal at a xed distance from the surface that coincides with the minimum of the CNA/polymer interaction. During the simulation the anchor beads are not allowed to move, but they interact with all other polymer beads. Initially the polymer chains are grown as almost straight chains perpendicular to the surfaces. The slight randomness of the bead positions aids the initial equilibration. Initially the CNAs are placed far enough apart to avoid overlap of polymer chains graed to different CNAs. Then the system is relaxed, aer which the particles are slowly moved to a given distance. Then the system is fully equilibrated before results are determined.
While the model is very simple it seems important to choose a sensible graing density. One common method to gra polymers to CNAs is to rst react some of the hydroxyl groups with sulphuric acid to form sulphate esters. Then a polymer chain with a cationic terminal functionality is attached via a strong ionic interaction. To obtain a rough estimate of the graing density we assume that a polymer chain is attached to each sulphate ester group. Then the graing density can be estimated from the efficiency of the sulphate ester formation. In ref. 34 this is estimated to be 0.62% of all hydroxyl functions of the CNAs leading to a graing density of z0.3 nm À2 .
To translate this graing density into the model, a physical length scale needs to be chosen, i.e. a value for the length parameter s needs to be chosen. If s ¼ 1 nm then the model graing density is 0.3s À2 . The choice of s ¼ 1 nm is sensible because it is similar to the Kuhn length of typical polymers, such as poly ethylene-oxide. † The exact cross-section of CNCs and CNAs is intensely debated as pointed out in the introduction. However, in all possible geometries well dened crystal faces are connected by edges rendering the particles non-cylindrical. Here we focus on the existence of these edges, which can be modelled by representing the CNAs as quadratic prisms. Their aspect ratio is usually large, which suggests their treatment as innite in the long dimension. This eliminates any effects from edges and corners at both ends, which is sensible considering that these regions are comparatively small and even less well understood than the cross-section.
The simplest way to represent such a crystal is to view it as continuum matter assuming that the internal structure of the CNAs is not relevant for the graed polymers. The interaction with the polymer beads is then found by integration over the CNA's volume. Such a procedure makes it possible to represent the edges of the crystal well. We do this numerically by placing beads representing the solid on a simple cubic lattice and then sum over all positions. The solid beads are assumed to have the same size as the polymer beads and interact with them via the Lennard-Jones (LJ)(12,6) potential in eqn (2). Since the summation is quite costly, we calculate a ne 2D grid of the potential before the simulation. During the simulation the interaction between the polymer beads and the crystal is determined by bilinear interpolation between the four nearest grid points.
Unfortunately, it is largely unknown how different polymers interact with CNAs. Clearly, this would depend on the polymer, which crystal faces are exposed and what their specic properties are. However, in this study we focus on the inuence of the CNAs shape on the graed polymers. Therefore the interactions between the CNAs and the chains anchored (graed) on them are chosen to be repulsive with only a minimal attraction at short distances (Table 1). The potential is represented in Fig. 1.
The system is simulated using standard Dissipative Particle Dynamics (DPD). In addition to the conservative forces discussed above, DPD requires random forces and dissipative forces

Cellulose nanocrystals
Side length of quadratic cross-section ¼ 13.0 Distance between centres, wherer ij ¼ r ij /||r ij ||, q ij is a random variable with limits À1 and 1, and zero mean (see ref. 35 for the utilized random number generator), x and u R (r ij ) are the strength parameter and the weight function of the random force, g and u D (r ij ) are the strength parameter and the weight function of the dissipative force, v ij ¼ v j À v i , v i is the velocity of bead i and r c ¼ 2.5s is the cut-off of the dissipative and the random force. The method allows the simulation of a canonical ensemble. In the canonical ensemble the dissipative and the random forces are connected by the uctuation dissipation theorem leading to where k B is Boltzmann's constant and T is the temperature that can be freely chosen. Thus, the random and the dissipative forces together constitute the DPD thermostat. Here we use the weight functions originally published in ref. 36.
It is important to recognise that F R ij is a stochastic force which requires slight modications of the integration algorithm. 36 All model and simulation parameters are given in Table 1.
For simplicity we employ the customary reduced quantities: lengths are given in units of the LJ length parameter s, the energy is scaled with the well depth of the bead/bead LJ interaction 3, the temperature scale is given in terms of 3/k B and time is represented in units of ffiffiffiffiffiffiffiffiffiffiffiffiffi where m is the mass of a bead.

Shape of the grafted polymer shell
The local densities in Fig. 2 visualise the shape of the polymeric shell around the CNAs for two different polymers: 8 beads long and 22 beads long. The densities are averaged along the axis of the CNA since no structural variations are expected in this direction. The short 8-bead chains lead to a polymer layer that still resembles the square cross-section of the CNA. While the local density is affected by the shape of the CNA, it is immediately obvious that the memory of this shape is more and more lost the further one moves away from the surface. In the case of the 22-bead chains most of the density appears to have circular symmetry except for the inner most region close to the CNA's surface. We also observe some degree of layering near the CNA faces that is much weaker along the edges (see below). Such packing effects are typical for bead spring-models graed to at surfaces 37,38 and spherical particles 39,40 and can also be observed in hard-sphere uids near so repulsive walls. 41 Bulk polymer chains are known to follow scaling laws that are identical to those of self-avoiding random walks. This indicates that exible polymer molecules lose any memory of their chain orientation rather quickly. Extrapolating this to polymers graed to irregular particles, one would expect that the polymer layer becomes more and more spherical the further the polymer corona extends from the particle. Indeed this has been observed in simulations of polymer graed nanocrystals. 42 Experimentally it was found that polymer brushes graed on small gold particles (which are non-spherical) are shorter compared to brushes of the same molecules graed to planar surfaces, which means that the molecules also ll the space over the edges and corners. 43 A similar lateral "spillover" has been observed for laterally nite brushes on at surfaces. 30,31 This suggests that in the present case the polymer corona around the innitely long CNAs, modelled by square prisms, should assume cylindrical symmetry.
To investigate to which extent the graed layer deviates from cylindrical symmetry, i.e., retains a memory of the geometry of the nanoparticle it is graed to, we follow concentric circles of  radius r around the axis of the CNA and determine extrema in the local density and its average. The results are shown in Fig. 3. Initial differences between the curves are expected due to the geometry of the CNAs and the layering. Aer this initial region all three curves converge for the 22-bead chains. It is quite intriguing that aer a large region of cylindrical symmetry spanning from r z 12 to 20 the density starts to deviate from cylindrical symmetry again. The 8-bead chains follow the same tendency but seem to be too short to have a region of cylindrical symmetry. This result becomes even more surprising when we determine the location of the extrema (Fig. 4). In the inner region we observe effects of the quadratic cross-section of the CNA and of layering. It is important not to misinterpret this as a local density, instead the dots indicate the location of extrema along concentric circles. Beyond this initial region maxima are located in front of the crystal faces, while along the edges the density is minimal. This is an expected curvature effectthere is more space along the edges and it grows as one moves further away from the nanocrystal. However, the differences between the maximal and minimal local density values are very small.
All the more intriguing is therefore the inversion of the positions of the extrema as one moves further out (Fig. 4). The differences in the density (Fig. 3) might appear small, but have a noticeable impact on the interaction between polymer graed CNAs as we show below.
These results suggest that the most important and most interesting congurations for a pair of graed nanocrystals are the face-to-face and the edge-to-edge conguration (Fig. 5). Density proles for these two directions, i.e. perpendicular to the face and diagonal (45 to the previous), are plotted in Fig. 6. Near the crystal faces we observe weak oscillations in the density. It is interesting that the highest peak is not located in the very weak minimum of the crystal/bead interaction, instead this is the location of the very low rst maximum in the density. It appears that the ordering is due to the graing, i.e. the bonding between the rst chain bead and the immobile anchor bead that is placed in the potential minimum. It also appears that the chains are pulling on the anchor-beads, possibly because the lateral connement by other graed molecules causes congurational entropy penalties. This seems to lead to some preferential orientation of the rst few segments of the chains perpendicular to the surface. The preferential orientation creates some bead/bead, bead/anchor-bead and consequently, bead/surface correlations, which are reected in the density prole. The oscillations decay quickly as, except for the bonds, there are no bead/bead attractions. In the diagonal direction remnants of the rst two oscillations (the wall peak and the highest maximum) are also visible.  From this point on all densities decay monotonously. The decay is steep for the 8-bead molecules, but more gentle for the 22-bead chains. The density proles for the 8-bead molecules clearly show that the polymeric corona is not yet cylindrical. The density prole of the 22-bead molecules has a very large region over which the density has perfect cylindrical symmetry. However, as discussed above, in the outer regions deviations occur with the density in the diagonal direction reaching out further compared to the perpendicular direction. It is interesting that near the particle surface the local density is lower in the case of the longer molecules. This would be consistent with the suggested pulling.

Grafted polymer-mediated interactions between the CNAs
The key focus of this study is to determine whether or not the graed CNAs behave as cylindrical rods or if their behaviour reects aspects of the geometry of the CNAs' cross-section. While the local densities indicate nearly cylindrical symmetry, it is the mutual interactions of graed CNAs that will determine their behaviour. Here these interactions are steric repulsions originating from the overlap of the polymer coronas of pairs of graed CNAs.
This overlap causes deformation of the polymer layer. In Fig. 7 the deformation is visualised by plotting the difference between the deformed and an unperturbed polymer corona. As expected, this difference increases with decreasing distance between the CNAs. While deformations are largest near the contact between the two coronas, it is interesting that the entire polymer coating is affected. The importance of deformation has also been observed for simulated atomic force microscopy on structured polymer brushes. 31 Any deformation of the unperturbed polymer corona leads to a restoring force. This force should be expected to be stronger for stronger deformations. In Fig. 8 the steric repulsion forces are presented for both chain lengths considered here, namely, 8 and 22 beads in the face-to-face conguration and the edge-to-edge conguration. Because we consider the CNAs to be innitely long we report the force per unit length, i.e., the force per 1s of CNAs. As expected from the monotonously increasing deformation, all forces increase monotonously with decreasing distance between the CNAs.
The forces are shorter ranged but increase faster with decreasing distance for the CNAs modied with the shorter gras. The steeper increase in the force is plausible because the local density also increases faster for the shorter molecule (Fig. 6). This steeper increase of the local density leads to stronger deformation at the same overlap in the case of the shorter molecules compared to the longer ones.
This argument is interesting as it also predicts a higher force for the edge-to-edge conformation compared to the face-to-face conformation. Indeed, this is found for both molecules and small overlaps (insets in Fig. 8). It has to be noted, however, that this difference in the force is very small.
As the distance between the CNAs is decreased the face-to-face and edge-to-edge force curves cross and the behaviour is inverted. Now the repulsion in the edge-to-edge conformation is weaker compared to the face-to-face arrangement. Comparing the deformations plotted in Fig. 7(c) and (d) it is immediately obvious that in the edge-to-edge conguration the chains are deformed but not very conned. This is dramatically different in the face-toface arrangement, where the chains graed onto the CNA face pointing towards the other crystal are strongly conned between the opposing faces. Similar effects have been observed and  At very small distances in the face-to-face cases the forces increase dramatically. Both length of graed molecules lead to nearly identical forces which can be expected because at small distances the non-graed ends of the molecule are squeezed out of the gap between the crystals and therefore, the region between the opposing faces must be expected to be very similar in both cases. Interestingly, there is no sign of force oscillations that are normally associated with layering (Fig. 5). However, this is consistent with our assumption of a preferential perpendicular orientation of molecule segments near the anchor bead through pulling by the rest of the molecule. Under strong connement the molecules can no longer pull perpendicularly to the surfaces and consequently, the layering disappears.
The forces for the edge-to-edge conguration increase steeply in the same region because the layers of anchor-beads get very close. The resulting indication of cylindrical symmetry is purely coincidental and will not occur for other CNA geometries. Moreover, the forces and energies required to reach these small distances are very large and are unlikely to play a role in any application.
In Fig. 9 the potential of mean-force (PMF) is shown. As in the case of the force the PMF presented here is the PMF per 1s of CNA. The PMF is equal to the work required to overcome the repulsive interactions (from an innite distance).
Alternative to the interpretation presented for the forces, i.e. comparing the strength of the force at equal distances between the particles, we could ask how close two particles can come to each other at a given "collision" energy, i.e. PMF. This alternative interpretation reveals the apparent shape of the graed CNAs.
In the case of the shorter 8-bead chain the PMFs for the faceto-face and the edge-to-edge conguration are nearly identical. Thus, the apparent shape is that of a cylinder. This is surprising as the local density is clearly non-cylindrical (Fig. 3). The reason for this behaviour is largely related to the steepness of the density proles (Fig. 6) and consequently, of the forces (Fig. 8) and also to the aforementioned geometrical coincidence.
In the case of the longer graed molecules we observe that at small interaction energies ((1kT/s) the graed CNAs are slightly larger in the edge-to-edge conguration compared to the face-to-face conguration. This relationship is inverted for larger interaction energies (T5kT/s); now the graed crystals are larger in the face-to-face conguration compared to the edge-to-edge arrangement. This is exactly opposite of what one would expect for the ungraed particles. The difference can be large, up to z4s at 30kT/s. Thus, the longer molecules amplify the differences between the face-to-face and the edge-to-edge conformation.
Which forces or energies between the graed CNAs are relevant depends on the situation and is hard to estimate. In a stable dispersion an upper limit of these interaction energies can be extracted from the energy barriers required to prevent aggregation. If aggregation is prevented, then no particle in the system has an energy higher than the barrier. For electrostatically stabilised CNCs treated as cylinders with a radius of 2 nm the required barrier was estimated to be around 5kT. 22 This is very low and assuming that the graed CNAs have similar energies, it would mean that the two polymeric coronas barely touch each other even for very short particles. However, in dense systems such as deposited lms, the forces pushing the CNAs together might be signicantly higher. Fig. 8 Force per unit length of nanocrystal generated by steric repulsion between grafted molecules of 8 bead length (top) and 22 bead length (bottom) as a function of the distance between the CNA centres. The face-to-face conformation (blue and red) and the edge-to-edge conformation (yellow and green) are compared. In both cases a crossover from stronger edge-to-edge forces to stronger face-to-face forces can be observed. We have used dissipative particle dynamics simulations of chain-of-beads models to investigate if the polygonal character of the cross-section of cellulose nanocrystal aggregates is inherited by the corona of graed polymer molecules and possibly also by the polymer mediated interactions between the graed particles. While this work is inspired by cellulose nanocrystals, our results are relevant also for other nanocrystals with polygon cross-section. We nd that the local density of the polymer corona around isolated CNAs assumes cylindrical symmetry already at small distances from the particle surface. Thus, even graing with relatively short molecules smoothed out the non-cylindrical surface fairly effectively. Interestingly, we observe a small but systematic deviation from this behaviour in the outermost reaches of the polymer corona. Here the local density of the polymer is slightly higher along the edges of the CNAs compared to other directions even though the inner region is already cylindrically symmetric. Except for this small deviation the graed particles "look" essentially like cylindrical rods, i.e. their outer structure is essentially cylindrically symmetric.
However, the polymer mediated forces behave very differently. For most interparticle distances they are strongly orientation dependent. Rather unexpectedly we nd that at the same centre-to-centre distance the forces in the face-to-face orientation are much larger than in the edge-to-edge conguration although in the latter case the distance between the particle surfaces is smaller. This is a strong effect and it means that under the same compression the graed particles can come closer in the edge-to-edge orientation compared to the face-toface orientation. This is opposite to the behaviour of the pristine particles. The reason for this effect is that overall the faceto-face orientation leads to larger chain connement. This affects longer molecules stronger than shorter ones and therefore, we nd that deviations from cylindrical symmetry are stronger for the longer molecules.
At larger distances between the graed particles, where the overlap of the polymer coronas becomes small, the behaviour of the system changes to what one would expect from the unperturbed polymer densities. Here we nd slightly higher forces in the edge-to-edge compared to the face-to-face arrangement, which is consistent with the slightly higher local polymer density along the edges in the outermost region of the polymer corona. This behaviour of the force is exactly opposite to what we nd at shorter interparticle distances. As this crossover suggests, we also nd a small region where the forces in the two orientations are the same.
In summary, at large forces between the particles the edgeto-edge orientation generates the least resistance, while at small forces the face-to-face orientation is favourable. Between these two situations is a crossover point. Around this point the particles behave essentially as cylindrical rods.
These effects elucidated using simple models suggest that the non-cylindrical symmetry of CNAs and other nanoparticles has important implications on the interactions between their graed polymer coronas. This is consistent with the experimental observation of chiral nematic phases (e.g. ref. 2 and 15-17), which cannot be created by cylindrical rods. Of course, in chiral nematic phases the CNAs are not perfectly aligned which leads to more complex behaviour compared to that revealed in our study, but our results already demonstrate that the non-cylindrical structure of the CNAs "transpires" through the polymer corona. Our results are particularly important for applications exploiting densely packed and possibly aligned CNAs as in thin lms where deformations of the polymer corona are expected to be large (e.g. ref. 16, 17 and 44-48). The interactions with planar surfaces in these cases are particularly interesting because they lead to larger chain connement than in any CNA/CNA interaction.