Poly-l-Lactic Acid Nanotubes as Soft Piezoelectric Interfaces for Biology: Controlling Cell Attachment via Polymer Crystallinity.

It has become increasingly evident that the mechanical and electrical environment of a cell is crucial in determining its function and the subsequent behavior of multicellular systems. Platforms through which cells can directly interface with mechanical and electrical stimuli are therefore of great interest. Piezoelectric materials are attractive in this context because of their ability to interconvert mechanical and electrical energy, and piezoelectric nanomaterials, in particular, are ideal candidates for tools within mechanobiology, given their ability to both detect and apply small forces on a length scale that is compatible with cellular dimensions. The choice of piezoelectric material is crucial to ensure compatibility with cells under investigation, both in terms of stiffness and biocompatibility. Here, we show that poly-l-lactic acid nanotubes, grown using a melt-press template wetting technique, can provide a “soft” piezoelectric interface onto which human dermal fibroblasts readily attach. Interestingly, by controlling the crystallinity of the nanotubes, the level of attachment can be regulated. In this work, we provide detailed nanoscale characterization of these nanotubes to show how differences in stiffness, surface potential, and piezoelectric activity of these nanotubes result in differences in cellular behavior.


S-2
where G is the shear modulus of the material, A is the surface area over which the force acts and l is the thickness of the material. Defining the effective stiffness of the bulk material kbulk as the ratio of force to displacement gives where r is the diameter of the nanostructures, assumed to be cylindrical. From this expression, the nanostructured bending stiffness follows = 3 4

3
The area in this case is = 2 and the aspect ratio is defined by = ⁄ . Substituting these relationships into the above equation gives

S2. Importance of polymer chain alignment in piezoelectric polymers
For PLLA, the '3' direction of the base vectors that describe the dij piezoelectric tensor is aligned along the length of the polymer chains. It is therefore important to consider how the polymer chains are oriented inside the nanotube, as this will dictate if the applied strains couple to the piezoelectric modes. In nanostructures grown by template wetting, there are two cases of chain orientation to consider: axial and radial alignment. Figure S2 shows simulated nanotubes with each type of chain orientation. Here it is clear that only the axial chain orientation leads to any significant piezoelectric potential. This axial chain orientation is observed in PLLA nanotubes grown by melt-press template wetting, as demonstrated previously by our group 2 .

Figure S2
-Simulated piezoelectric potential of a PLLA nanotube as a function of polymer chain orientation. (a) Schematic representation of two possible polymer chain orientations. Surface plot of simulated piezoelectric potential in PLLA nanotube having chain orientations corresponding to (b) 〈001〉 (chains parallel to length of the tube), and (c) 〈010〉 (chains radially aligned in the nanaotube). It can be seen that only the axial 〈001〉 case leads to any significant piezoelectric potential. This axial chain alignment is observed in nanotubes produced by the melt-press template wetting method. S-4

S3. Parametric sweep of tube geometry
The length, radius and wall thickness of the simulated PLLA nanotube (with axial chain alignment) were varied systematically to demonstrate the effect of geometry on the piezoelectric potential. In all cases, the force applied was 1 nN. The potential values were calculated as a surface average over one half of the nanotube surface. Figure S3(a) shows the influence of nanotube length and radius, with a constant radius-to-wallthickness ratio of 3. It is evident that the potential is roughly independent of the nanotube length, consistent with beam theory which states that the shear stress along a rigidly fixed endloaded cantilever is constant along its length. The potential increases with decreasing tube radius. Figure S3(b) shows the influence of radius and wall thickness on a nanotube 3 μm long. At a given radius, a thicker walled tube will result in a greater surface potential. Likewise, for a given wall thickness a smaller radius will give a higher potential. Inspecting the surface plot suggests that a radius-to-wall-thickness ratio might be the governing factor on the magnitude of the developed potential. However, Figure S3(c) demonstrates that this is not the case. The contours in part (b) are not actually parallel, and fitting the contours with linear regression gives a different gradient for each potential value, hence the radius-to-wall-thickness ratio is not the only important parameter, the absolute values of radius and wall thickness are also important.

Figure S3
-The average surface potential of a PLLA nanotube, deformed as an end-loaded cantilever by a 1 nN load, as a function of outside radius, length and wall thickness. (a) and (b) are surface plots representing the parameter space for each variable. (c) shows how the surface potential varies as the radius is increased, with a proportional increase in wall thickness governed by the ratios show. As the radius is increased, the potential decreases, even though the wall thickness is increased proportionally. This indicates that the radius-to-wall-thickness ratio is not the sole governing factor in the piezoelectric performance of the nanotube.
S-6 S4. Convergence of FEA modelling Figure S4 -A convergence test on the PLLA nanotube mesh, observing how (a) the averaged surface potential from the outer face of one side of a PLLA nanotube and (b) the average total displacement of the top face vary as the mesh is refined. The 'mesh element length' is the length of mesh nodes along the axis of the tube. The 'mesh ratio' is the ratio of the maximum element size to the tube wall thickness. Decreasing values represent a finer mesh. The values for each parameter used in all simulations in this work are marked with vertical dashed lines. It can be seen that refining the mesh beyond these points leads to no significant change in the results. Parameter values used for subsequent simulation: element length = 50 nm, mesh ratio = 0.5.
S-7 The geometric patterning seen in part (b) is a feature of the nanotube surface and is not created by the cells. It is believed that the formation of these clumps is related to capillary forces when drying the samples. Parts (e) and (f) demonstrate that nanotubes part of the same group are pulled in opposite directions by two different cells.

S5. Additional SEM images of cell/nanotube interaction
S-8

S6. Upper and lower bounds of bending stiffness and effective shear modulus
The maximum displacement x of an end loaded cantilever is given by where F is the force, Y is the Young's modulus, I is the second moment of area of the cantilever and l is the cantilever length. For a hollow cylindrical beam, the second moment of area is given by where r is the inner diameter and R is the outer diameter. The bending stiffness can therefore be written as The experimentally observed values, together with a literature value of Young's modulus, can be used to calculate a bending stiffness. For the lower bound, the dimensions of a single nanotube were used. For an upper bound, a cluster of nanotubes was assumed to behave as a single, much larger nanotube. Observations of the SEM images in Figure S5 indicate that each cluster contains between 10 and 30 nanotubes. A close-packed array of 19 tubes was therefore used in this estimation, and approximated to a single nanotube as shown in Figure S6. Outer and inner radii were taken to be five times that observed for a single tube. It is clear that this is a gross overestimate of the actual bending stiffness and that the true value is likely to be much closer to the lower bound.

S-9
To calculate an effective shear modulus, the displacement due to shear deformation a bulk material shear = ′ and the displacement due to beam bending beam = 3 3 are set equal, where G' is the effective shear modulus and A is the area over which force F is acting, taken to be the cross-sectional area of the tube (c.f. Figure S1). The effective modulus can then be expressed as  .

S8. FEA modelling of nanotube side wall deflection
Quantitative Nanomechanical Mapping is so called because in principal, values can be assigned to material properties. In practice, however, determining accurate values is challenging.
Accurate material properties require various aspects of the tip and cantilever to be accurately known. Routines exist to estimate the cantilever spring constant and tip apex radius, but these are both subject to large errors. The uncertainty in the tip calibration propagates into the values of mechanical properties, meaning that absolute values should be treated with caution. It is therefore far more trustworthy to perform comparative measurements, looking for trends rather S-13 than absolute values. In this instance, even if the tip calibration is inaccurate, the results are still reliable.
The system is complicated further when considering the behaviour of nanoscaled materials.
Leaving aside any potential changes in intrinsic material properties that can occur in nano- In nanomaterials, the curvature of the sample is of a similar order of magnitude to that of the tip apex. The sample cannot, therefore, be approximated to a flat plane. If the DMT model is used to determine modulus values of nanoscaled materials, the values will not be accurate even if the tip calibration is perfect.
Indentation of nanotubes, as in the present case, adds more uncertainty to the system. This is highlighted in Figure S6. Parts (a) and (b) show the distribution in deformation of a nanotube and film, each with identical material parameters and each subjected to a 10 nm indent from the tip. In the film, the majority of the deformation is localised to the region immediately beneath the tip. The relatively unclamped nature of the nanotube, however, allows for the same tip displacement to be accommodated by deformation distributed throughout the nanotube structure. An indentation of a film therefore mostly probes material deformation, whereas in a nanotube the deformation can be considered as structural. The difference in behaviour is further shown by the force-distance curves in Figure S6(c). For a given force, the tube structure deforms to a greater extent than the nanotube, even though the material in each has the same properties. This effect is amplified as the wall thickness is reduced.

S-14
Since the estimated modulus values from QNM are not valid, a different metric must be used to assess the mechanical properties. The deformation data is a more appropriate channel to use for this comparison. The deformation is the amount the sample deforms as a result of the `peak force' applied by the tip. This data is extracted directly from the raw force-distance curves -i.e.
no assumptions are made about the loading geometry, and no models are fitted to the data -and is therefore more appropriate for analysis of QNM data from PLLA nanotubes. Figure S6(d) shows that provided the wall thickness to radius ratio is constant, the deformation characteristics are the same. The constant r/t ratio is known to be a feature of melt-grown polymer nanotubes 5 . Figure S6 S-19

S13. Extended PFM data
The variation in intensity of the crystalline PFM signal shown in Figure S11(b) was observed in several separate nanotubes. Its origin is not currently understood, but could be a result of the underlying crystal structure. PFM Scans were also performed in the absence of an oscillating potential (0V line in Figure S11(c)) to ensure that the signals were of electromechanical origin. These scans mostly consist of noise, however some slight activity can be seen as the tip approaches the edges of the nanotube, which could be attributed to electrostatic interaction between the tip side-wall and the nanotube S-20

S14. PeakForce QNM of PLLA nanotubes to observed surface morphology
The PeakForce error signal in PF-QNM displays the difference between the peak force set point and the recorded peak force at each pixel. It is especially useful at highlighting changes in height, rather than absolute values of height. The peak force error signal was therefore used to visualize the surface morphology on the nanotubes. Peak force error signals of amorphous and crystalline nanotubes are shown in Figure S14. There are no discerning features of either group are no significant differences between the two groups. The surface roughness of each nanotube is likely dictated by the inner surface of the AAO template used for growth. Experimental details of how these images were obtained can be found in reference 6 . S-22

S15. Attachment of HDFs to polypropylene nanotubes
Wide-angle X-ray diffraction (WAXD) was performed with a Bruker D8 diffractometer in Bragg-Brentano geometry with Cu Kα radiation.
PP has been used here as a control against the influence of piezoelectricity. Comparing crystalline PP NTs to crystalline PLLA NTs is of little benefit, given that there are several other differences between these polymers besides the absence or presence of piezoelectric behaviour.
Surface chemistry will be different between PP and PLLA, as will the exact geometry of each Significance assessed with two sample t-test (N = 4 for each condition, ns = not significant; * = p < 0.05; ** = p < 0.01).
S-23 type of nanotube given the different processing conditions used in their growth. Comparing amorphous PP to crystalline PP, and then amorphous PLLA to crystalline PLLA, removes these inconsistencies. The outcome of each of these comparisons can then be directly contrasted.
Using this differential method, the PP NTs act as a control against the effects of piezoelectricity. S-24

S16. Material parameters for FEA modelling
The following material parameters were used for the finite element model: