Detecting the Biopolymer Behavior of Graphene Nanoribbons in Aqueous Solution

Graphene nanoribbons (GNR), can be prepared in bulk quantities for large-area applications by reducing the product from the lengthwise oxidative unzipping of multiwalled carbon nanotubes (MWNT). Recently, the biomaterials application of GNR has been explored, for example, in the pore to be used for DNA sequencing. Therefore, understanding the polymer behavior of GNR in solution is essential in predicting GNR interaction with biomaterials. Here, we report experimental studies of the solution-based mechanical properties of GNR and their parent products, graphene oxide nanoribbons (GONR). We used atomic force microscopy (AFM) to study their mechanical properties in solution and showed that GNR and GONR have similar force-extension behavior as in biopolymers such as proteins and DNA. The rigidity increases with reducing chemical functionalities. The similarities in rigidity and tunability between nanoribbons and biomolecules might enable the design and fabrication of GNR-biomimetic interfaces.

consistent features with a single detachment peak were considered for further analysis. Some of the force curves have a single force peak while others have multiple force drops and peaks, similar to those observed in forced unfolding of proteins or unzipping of nucleic acids. We separated force-extension curves into two groups: i) ones with single detachment peaks and ii) ones with multiple force peaks. A typical AFM image (Fig. 4) of GNR shows the morphology of these nanoribbons, which resembles the filamentous biopolymers such as proteins and DNAs. One hypothesis of the multiple force peaks is that these are from pulling a GNR polymer with wrinkles and loops. Because the non-linear behavior in the force-extension curves appears to be similar to that of biological molecules [9][10][11] , and our GNR/GONR are nearly one-dimensional, we first attempt to fit the force curves to the extensible wormlike chain (eWLC) model 12,13 to obtain an estimate of the scale of bending and stretching energies, c p where x is the extension, F is the force, K is the elastic stretch modulus, β = 1/k B T where k B is the Boltzmann constant, T is the temperature, L c is the contour length and L p is the persistence length. Figure 5 shows the histogram distributions of the measured values of L p and K. For GONR with only one force peak, the most probable values, resulting from Gaussian fits to histograms, are L p = 15 nm and K = 3 nN (Fig. 5A,B). For GONR with multiple force peaks, the value of the peak force F = 170 pN (Fig. 5C). For GNR with only one force peak, the L p = 35 nm and K = 1 nN (Fig. 5D,E). For GNR with multiple force peaks, the value of the peak force F = 120 pN (Fig. 5F). The measured L p values agree well with reported values of 10-100 nm for GNR 14,15 . The L c of 100-1500 nm for GNR are also consistent with reported values 2 .

Discussion
The persistence length (L p ) of GNR, obtained by fitting to the eWLC model, is comparable to that in other carbon materials, such as carbyne (one-dimensional chain of carbon atoms) or pristine GNR (Table 1). However, the stretch modulus (K) of GNR is 2-3 orders of magnitude smaller than the simulation results of carbyne and pristine GNR.  Our experiments were carried out in aqueous solution, which may have an effect on their flexibility. In solution, GNR act more like a biopolymer, and thus the mechanical properties of GNR might depend on its environment. This has been demonstrated in cellulose paper, where a wet sheet had a lower strength and stiffness than a dry sheet 16 .  Loops and wrinkles in GNR are common [17][18][19] , and their mechanical properties can be probed by AFM force measurements. The existence of spirals, helicoids, wrinkles, and loops in GNR may explain the multiple kinks and force drops in our AFM experiments 15 . Force-drops have been observed in molecular simulations of GNR, as well as in functionalized GNR upon the application of a tensile force 20 .
The K = 1 nN and L p = 35 nm of GNR are consistent with the values seen in double-stranded DNA (dsDNA). This may indicate that GNR and dsDNA are biocompatible mechanically and that GNR may form a structure or conformation similar to that of dsDNA (like a double helix) 20 . Both dsDNA and proteins can exist in different conformations, and GNR may contain different deformations and transform among those conformations when subject to external mechanical forces.
Because of the finite width of the graphene nanoribbons, GNR and GONR differ from the true one-dimensional biopolymers such as proteins and DNA, which can only form structures such as folds and loops. There have been a number of theoretical studies and models on the mechanical properties of ribbons, which can form a variety of structures such as helicoids, wrinkles, and spirals in additional to folds and loops. The ground state of nanoribbons can be helix or helicoid, depending on the width to thickness ratio of the material 21,22 . The chiral ribbon can form different structures such as helicoid and spiral, depending on a critical value, Föppl-von Kármán

Biopolymers
Single-stranded DNA 27 1-4 2 Native titin (folded) 28  (FvK) number, which is determined by the competition between the bending and stretching energy 23 . When subjected to tension, the elastic macroscopic ribbons can undergo transitions between these morphologies 24 , which may be the origin of the kinks observed in the force curves. Furthermore, thermal fluctuations may have a nontrivial effect on the mechanics and give rise to anomalous elasticity, and its effect has been calculated to result in an enhanced bending rigidity and a suppressed stretching rigidity 25 . The increased bending stiffness with size in a two-dimensional graphene has been observed experimentally 26 and the decrease in stretching stiffness may explain the lower than expected values of the stiffness K observed in our experiments of this nearly one-dimensional system. The simple eWLC model used in the current work does not take into account of these deformations, which may underlie the kinks and force drops in the observed force-extension curves that resemble biopolymer force curves. More theoretical and experimental studies are necessary to answer the questions about what effects the finite width of a nanoribbon, which constitutes the basic difference between the elasticity of filamentous and ribbon-like materials, have on the mechanics of nanoribbons. The mechanical properties reported here provide an insight into the behavior of GNR in solution. Forceextension curves of GNR in aqueous solution possess similar features compared to those from biopolymers, such as proteins and DNA. GNR can have different phases that result in force drops when stretched with external forces. With these different morphologies, diverse biomimetic designed structures may be achieved by using GNR, which have potential applications in biomimetics with tunable properties.

Methods
GONR were made by oxidative unzipping of MWNT through permanganate oxidation 2 . The widths of the nanoribbons range from 10 nm to greater than 100 nm and lengths range from 1 to 5 μ m after the reaction. These oxide samples were then reduced with hydrazine monohydrate to produce GNR (Fig. 1).
Sample substrates for AFM experiments were prepared by allowing 10 μ l of 0.1 mg/ml of the nanoribbon samples to absorb on to a fresh gold substrate for 10 minutes at room temperature. The substrate was then spincoated for one minute at 3,000 rpm to evenly distribute the nanoribbons on the surface. An AFM (Bruker, Inc.) was used to perform force-pulling measurements on the sample as illustrated in Fig. 2. Silicon nitride cantilevers with a spring constant of 0.04 N/m were used (MLCT, Bruker, Inc.). The nanoribbon samples were pulled in phosphate buffered saline (PBS, pH 7.4) at a pulling velocity of 1 μ m/s. The force-extension curves obtained in each experiment were analyzed with a program written in MATLAB (MathWorks, Inc.). The data were binned into histograms and fit to a Gaussian curve. The error in the measurements is half of the bin width of the histograms.
To prepare the substrate for imaging, mica discs were glued to steel discs using epoxy and allowed to dry overnight. The dried mica disks were cleaved with scotch tape to reveal a fresh surface. For nanoribbon samples (0.1 mg/ml) of approximately, 10 μ L were spincoated for one minute at 3,000 rpm, washed with Millipore water and then immediately dried with nitrogen gas and imaged in air. The ScanAsyst mode in air, using ScanAsyst air tips with a nominal spring constant of 0.4 N/m, was used for imaging.