Breaking Nano-Spaghetti: Bending and Fracture Tests of Nanofibers

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Breaking Nano-Spaghetti – Bending and Fracture Tests of Nanofibers Tomas P. Corrales, Kathrin Friedemann, Regina Fuchs, Clément Roy, Daniel Crespy, and Michael Kappl Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b04176 • Publication Date (Web): 11 Jan 2016 Downloaded from http://pubs.acs.org on January 16, 2016

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Breaking Nano-Spaghetti – Bending and Fracture Tests of Nanofibers Tomas P. Corrales1, 2, Kathrin Friedemann1, Regina Fuchs1, Clément Roy1,3, Daniel Crespy1, Michael Kappl1* 1

Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany

2

Instituto de Alta Investigacioon, Universidad de Tarapaca, Casilla 7-D Arica, Chile

3

University of Nantes, Graduate School of Engineering, 2, rue de la Houssinière,

FR 44322 Nantes Cedex 3

Keywords: Electrospinning, nanofibers, atomic-force microscopy, mechanical properties, fracture. Nanofibers composed of silica nanoparticles, used as structural building blocks, and polystyrene nanoparticles introduced as sacrificial material are fabricated by bi-colloidal electrospinning. During fiber calcination, sacrificial particles are combusted leaving voids with controlled average sizes. The mechanical properties of the sintered silica fibers with voids are investigated by suspending the nanofiber over a gap and performing three-point bending experiments with atomic force microscopy. We investigate three different cases: fibers without voids, with 60 nm and 260 nm voids. For each case we study how the introduction of the voids can be used to

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control the mechanical stiffness and fracture properties of the fibers. Fibers with no voids break in their majority at a single fracture point (70% of cases), segmenting the fiber in two pieces, while the remaining cases (30%) fracture at multiple points, leaving a gap in the suspended fiber. On the other hand, fibers with 60 nm voids fracture in only 25% of the cases at a single point, breaking predominantly at multiple points (75%). Finally, fibers with 260 nm voids fracture roughly in equal proportions leaving two and multiple pieces (46% vs. 54% respectively). The present study is a pre-requisite for processes involving the controlled sectioning of nanofibers to yield anisometric particles. Introduction The shape of nanoparticles is known to play an important role in nanoparticles-cell interactions.1 Properties such as adhesion to living cells or cell uptake depend critically on particle geometry. Although several synthetic approaches have been developed to control the shape of nanoparticles,2–5 their large-scale production remains challenging. Recently, we developed a facile method for large scale synthesis of anisotropic particles based on electrospinning.6 Electrospinning is a technique that was first developed to obtain micro- and nanofibers.7–11 In recent years, interesting variants of the technique have emerged, such as the production of composite fibers by electrospinning organic or inorganic colloidal particles dispersed in a polymer solution.12,13 In the case of a high solid content of the dispersion, it is even possible to remove the polymer matrix either thermally14–16 or by solvent extraction while still preserving the fiber shape. On the other hand, thermal decomposition of polymer colloids opens the possibility of producing micro- and nano-sized pores within the fiber. 17 In our previous work, silica and sacrificial polystyrene (PS) colloidal particles were introduced within the polymer matrix of the electrospun fibers. During heat treatment, i.e. fiber calcination, silica particles were


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sintered to form silica nanofibers while the organic polymer matrix and the sacrificial compartments were removed, leaving voids within the fibers. Void size and average spacing were controlled by the PS particle size and the relative particle concentration, respectively. By sonicating such fibers with a defined density of voids, fragmentation of the fibers into smaller sized rods occurred and resulted in highly anisometric nanoparticles. Although intuitively the voids are expected to act as predetermined breaking points, precise information about the mechanism and forces involved in the fragmentation process of such fibers and the role of the voids themselves remain unclear. Such information would, however, be highly suitable for a better control of the process. Atomic Force Microscopy (AFM) is a key technique in nanotechnology due to its imaging and manipulation capabilities.18,19 Over the last decade the technique has gained new importance in biology, chemistry, and material science due to the possibility of obtaining quantitative mechanical information of the sample using force spectroscopy.20 In this study we use AFM to characterize the mechanical properties of nanofibers with tunable-sized voids using a nanomechanical three point bending experiment.21 From such experiments, the effective Young’s modulus and fracture strength of individual nanofibers can be obtained.22–26 Experimental Section Preparation of nanofibers. Before calcination, the fibers were composed of 20 nm diameter silica particles embedded in a PVA polymer matrix. In addition, sacrificial PS particles of defined sizes could be mixed in the electrospinning feed. Three types of fibers were prepared: without adding PS particles, with 60 nm PS particles, and 260 nm PS particles. The mass concentration of PVA and silica particles in the electrospinning feed was kept constant (70 g/L). PS particles were added to the electrospinning dispersion with the same mass concentration (24


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g/L). The fibers were spun directly onto commercial HS-500 MG silicon calibration grids (Budget Sensors, Sofia, Bulgaria) with square holes of 2.5 µm or 5 µm width and 0.5 µm in depth. This fabrication procedure led to fibers, with some fiber segments suspended above the gaps, forming a stable freestanding nano-bridge. This configuration facilitates the mechanical characterization in a three point bending test.26 A subsequent calcination step of the fiber material at 600 °C yielded sintered silica fibers without or with voids left by the removal of the sacrificial PS particles. The final fiber morphology was visualized by scanning electron microscopy (SEM) at low accelerations voltages of 1-2 kV (LEO 1530 Gemini, Zeiss). Characterization of Mechanical Properties with AFM. Imaging and mechanical bending experiments were performed using a Dimension 3100 AFM (Veeco, Sta. Barbara, CA) with an XY closed loop piezo translation system. The XY closed loop system is important in order to achieve precise placement of the tip on top of the fiber. We recorded force curves over 20-30 equidistant positions along the suspended segment of fiber. At each position we recorded 50 force versus piezo-position curves with a defined maximum load controlled by the trigger mode of the AFM. For fibers without voids, typical loads of 600 nN were applied to achieve more than 5 nm of deformation along the whole fiber using stiff AFM cantilevers (Olympus OMCLAC 160 TN-W2) with a nominal spring constant of k = 42 N/m and 300 kHz resonance frequency. At such high loads, tip wear is expected and we indeed observed in some cases drop in imaging resolution due to tip rounding, especially for the fracture experiments. However, force curves taken for determining the Young’s modulus always showed a linear response without hysteresis betweenapproach and retract, which excludes significant plastic deformation. For fibers with 60 nm and 260 nm voids, smaller loads were required to produce more than 5 nm of fiber bending (30 nN and 100 nN respectively). In these two cases we used softer cantilevers (Olympus


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OMCLAC 240 TS) with a nominal spring constant of k = 2 N/m and 70 kHz resonance frequency. Actual spring constants of all cantilevers were determined using the thermal tune method.27 To verify that force distance curves were taken on well-defined positions along the top of the fiber, suspended fiber segments were imaged by tapping mode AFM. Upon switching from imaging to force spectroscopy mode, the oscillation amplitude of the cantilever was set to zero. The acquired raw data, i.e. the detector voltage versus piezo position curves, were converted offline to force versus distance curves using a self-written LabView program. For the conversion, the spring constant of the respective cantilever and the deflection sensitivity, i.e. the conversion factor between detector voltage and cantilever deflection in nanometers, need to be previously known. Deflection sensitivity was derived from reference force curves recorded on the surface of the silicon substrate onto which the fibers were spun. Fracture experiments were carried out using the same arrangement with the difference that increasing forces were applied at the center of the suspended segment of the fiber until rupture occurred. After rupture, the fiber was imaged again in tapping mode to examine how fragmentation occurred. Fiber manipulation under an optical microscope (Zeiss Axiotech) to verify their attachment to the substrate was done using a three axis hydraulic micromanipulator (MMO-3, Narishige, Japan). Fracture test of real spaghetti. In order to understand the fracture processes occurring in sintered nanofibers, we investigated a macroscopic model system. The model system consists of a piece of dry spaghetti (Barilla no.1 with a radius of r = 0.57 mm) that is clamped at both ends over a gap of 3.5 cm using two steel nuts on a screw thread. The spaghetti piece was loaded in


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the middle by a metal syringe displaced uniformly and spaghetti fracture was imaged by a high speed camera at 1000 frames per second. Results and Discussion The silica nanofibers were prepared by colloid electrospinning followed by a calcination step of the obtained nanofibers as described previously.6 After calcination, we obtained fibers with diameters ranging between 200 nm to 500 nm (Table 1). Fibers without voids were generally thicker (Figure 1a-d) whereas fibers with 60 nm voids were clearly thinner (Figure 1b) and less uniform (Figure 1e) than fibers without voids. In particular, superficial holes distributed along the fibers were observed. The fact that fibers with 60 nm voids were thinner is explained by a higher stretching of the polymer jet experienced during electrospinning due to the higher solution conductivity.6 Fibers with 260 nm voids (Figure 1c-f) had diameters comparable to the fibers without voids (Figure 1a-d), but the embedded voids generated bulges along the main axis (Figure 1f). Fibers containing sacrificial compartments were produced using the same weight concentration of PS particles within the electrospinning dispersion (24 mg/ml). Therefore, the volume ratio of PS to silica for both 60 nm and 260 nm PS particles spinning solutions is 42%. After calcination, the total void volume to sintered silica volume ratio is expected to be of similar order. However, a slightly different degree of shrinkage for voids and silica nanoparticles cannot be ruled out. Assuming that about 40% of a fiber segment is composed of voids originated from the sacrificial PS particles, about 4 voids of 260 nm among 16000 sintered silica particles are expected on average in a 5 µm segment. In fact, at least one localized bulge corresponding to a PS generated void was always found over a 5 µm gap. On the other hand, for the fibers with 60 nm voids, roughly 50 voids within 3300 silica particles exist along a 2.5 µm gap. Therefore, the


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nanofibers are expected to display different mechanical properties due to very different void density and size. After preparing and annealing the fibers on the microstructured silicon substrates, three point bending experiments were performed with AFM (Figure 2a). The bending experiments were carried out on microstructures with a 5 µm gap width for fibers without voids and with 260 nm voids. For fibers with 60 nm voids, we used structures with a 2.5 m and 5 m gaps. In all cases the length of the suspended fiber segment was at least ten times the fiber diameter. Force versus distance curves were obtained from bending experiments (Figure 2b), for which negative distances correspond to fiber deformation ( ). Our results showed a linear relation between applied force and fiber deformation. This is a strong indication that the whole fiber is bent rather than deformed locally or indented. Indeed, an local deformation of the fiber would lead to force /

curves with a non-linear, Hertzian load dependence ( ∝ ). Furthermore, no significant hysteresis was observed between the approaching and retracting parts of the curve, which implies that neither plastic indenting nor sliding of the fibers occurred. From the linear slopes of force versus deformation curves for all given positions (), we obtain a stiffness profile ( = ⁄ of the suspended fiber. As expected from beam bending theory, the fiber stiffness decreased as we moved from the supported edge to the center of the suspended part of a fiber. This is another strong indication that our measured deformation was due to the bending of the entire suspended segment. Stiffness profiles along the fiber ( ) were fitted using beam bending models to extract the fiber’s effective Young’s modulus. It should be pointed out that this is an effective Young’s modulus of the whole fiber structure including voids, which is expected to be lower than true Young’s modulus of single silica nanoparticles. In principle, the Young’s modulus of a fiber could already be obtained from force curves in a single position.


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However, recording of full stiffness profiles ( ) has several advantages. Fitting the full stiffness profile leads to more reliable determination of the Young’s modulus, gives valuable insight on the boundary condition for the suspended fiber, and allows insights on the effect of localized voids. The classical models used in mechanical three point bending experiments are the simply supported beam model (SSBM) and the double clamped beam model (DCBM), where the fibers are either free to slide over the edges (SSBM) or are fixed to the supporting substrate (DCBM), respectively.28 The DCBM was found to better fit our stiffness profile results (Figure 2c). To further verify that our calcinated fibers are indeed clamped to the edges, shear forces were applied to supported fiber segments using a stiff AFM cantilever mounted on a micromanipulator while recording optical images of the fiber. The calcinated fibers were ruptured instead of being moved or bent (Figure 2d). This indicates that the silica nanofibers were cemented to the silica substrate during the sintering process. Therefore, the DCBM was used to relate the stiffness profile ( ) to the Young’s modulus () by:

=

(1)

Where L is the length of the suspended fiber segment and I is the second moment of inertia of the fiber. Assuming that the fiber has a cylindrical shape with radius R, then the moment is given by I = ⁄4 . The suspended length ! and fiber radius () are obtained from AFM images. The fiber radius is used to calculate the second moment of inertia ("). Both the fiber length and second moment of inertia enter as fixed fitting parameters in equation (1).The clamping positions, # , is a fitting parameter that accounts for uncertainties in determining the exact clamping position of the fiber ends.


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We observed some differences in the shape of the curves for the different types of voids. For each type of void, several fiber segments were measured using different cantilevers. By normalizing the fiber segment stiffness by its minimum value at the center ( ⁄ $%& ), and normalizing the position by the segment length (⁄!), the measurements taken on different fibers using different cantilevers were combined onto a single plot (Figure 3) For fibers without voids (Figure 3a), the curves collapsed on a single plot with small variations between the curves when plotting normalized stiffness vs. normalized position. An average effective Young’s Modulus of 5.4 ± 2.6 GPa was obtained by averaging 5 DCBM fitted stiffness curves (figure 3a) and additionally taking 4 extra stiffness measurements on a single point (/! = 0.5). This value is a tenfold increase compared to the earlier determined value for the fibers before calcination of 0.55 GPa6, indicating the formation of stable sinter necks between the particles. However, this value of the Young’s modulus is still significantly lower than that of bulk silica (~70 GPa)29 which reflects the incomplete sintering of the silica nanoparticles at 600 °C, which are still clearly visible as individual entities (Fig. 1d). It is also lower than the value of ~40 GPa reported for silica microcapsules formed from nanoparticles and calcinated at 600 °C.30 The higher value for these silica shells results from formation of silica bridges from silanol groups between the nanoparticles that occurs already during synthesis before calcination via a Stöber process. For fibers with 60 nm voids, the normalized curves maintained a U-type shape centered at ⁄! = 0.5 (Figure 3b), but the data points were more scattered compared to the case of fibers without voids. For fibers with 60 nm voids, an average effective Young’s modulus of 2.0 ± 1.6 GPa was obtained by fitting 4 different stiffness curves (figure 3b) and additionally taking 7


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single point stiffness measurements at the middle of the fiber (/! = 0.5). Thus, the introduction of 60 nm voids yielded a lower effective Young’s modulus of the suspended fiber. Because of the large concentration of 60 nm voids, the defects are more or less evenly distributed along the fiber, leading to a symmetric stiffness profile that follows the shape of Equation 1. Finally, for fibers with 260 nm voids, an average effective Young’s modulus of 3.0 ± 2.3 GPa was obtained by fitting 3 stiffness profiles and additionally taking 8 extra single point stiffness measurements. Although the size of the voids (260 nm) were comparable to the fiber diameter, the effective Young’s modulus of these fibers is higher than for samples with 60 nm voids. The 260 nm voids were not evenly distributed along the fiber, thus acting as single localized defects. As a consequence, the shape of the stiffness profiles varied from fiber to fiber, i.e. the position of the stiffness minimum became off-centered depending on the exact position of the localized defect. The 260 nm voids obviously reduced the fiber stiffness but not as pronounced as for the 60 nm voids. Due to the bulges around the voids (Fig 1f), the moment of inertia for the fibers at the void locations may in fact be comparable to the one of the void-free regions, alleviating the weakening of the fiber by the voids. In addition to measuring the effective Young’s modulus of the fibers, their fragmentation behavior was investigated by applying increasing loads with the AFM tip at the middle of suspended fibers segments (/! = 0.5) and detecting the force at which the fiber breaks. Figure 4a shows a series of force curves with increasing applied load. For loads below 400 nN, a linear response of the fiber is observed (1). At a force of about 405 nN, a first sudden drop in force is observed (2), indicating the onset of material failure. Consecutive force curves show full rupture of the fiber (3) and then a much softer response of the remaining part of the fiber (4). The maximum stress within the fiber was estimated from the fracture force and considered to be


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equal to the surface stress at the clamping point with coordinates (0,R). According to beam mechanics, the stress within a rigid beam - is proportional to the radius of curvature of the beam. The radius of curvature can be in turn approximated by the second derivative of the deformation profile ( .):

- ., 0 = 0

1 2 34

(2)

15 2

where . is the position along the fiber and 0 is the distance from the central axis of the fiber. The deformation profile ( .) when a load is applied at the center of the suspended segment (/! = 0.5) is:

. =

5 2 6

3! − 4.

(3)

By taking the second derivative of equation (3) and combining with equation (2) the maximum stress, located at the ends of the clamped fiber, i.e. y=0, is:

- 0, =

8 6

(4)

It is well known that slender rods - with spaghetti as a prominent example - can randomly break in two, three, or even more pieces when subjected to bending.31,32 In our fracture experiments, we also observed breakup in either two or multiple fragments depended on the type of void present in the fiber. The maximum stress before fracture for a fiber that ruptures at a single or multiple points, i.e. leaving a gap behind, is not differentiable for each fiber case as seen in histograms (supporting information S1). This is why we only report the average stress before fracture taken for both single and multiple point fracture cases.


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In the case of the pure silica fibers without voids, both fracture scenarios were observed, being the single point fracture the predominant case. From a total of 10 cases, 70% of the fibers with no voids fractured at a single point, leaving behind two fiber segments, while 30% broke at two or multiple points, i.e. leaving a gap in the fiber. The stress before fracture calculated using equation 4 and averaged over both fracture scenarios was 139 ± 126 MPa. This value has to be considered as an upper limit of the actual failure stress, since breakage may occur at a point different from the clamping or loading point, where the stress was smaller but the fiber was weaker due to a void acting as a defect. On the other hand, fibers with 60 nm voids predominantly fractured leaving a gap, i.e. two or more fracture points (Figure 4d). From a total of 14 cases measured, 25% broke at a single point, i.e. two segments (supporting information S2), while 75% broke at two or multiple points leaving a gap behind. This represents a reversal from the fracture behavior of fibers with no voids. The maximum stress averaged for both cases was estimated to be 97 ± 88 MPa. Finally, fibers with 260 nm voids exhibit a more balanced proportion of fracture scenarios. From 13 measured events, 46% of the cases broke at a single point leaving two fiber segments, while 54% of cases fractured at two or more points leaving a gap in the suspended fiber. The average stress before fracture taking into account both cases (Figure 4e-f) was 295 ± 257 MPa. The fracture in such fibers usually occurs near the voids, emphasizing the role of voids as singular defects. For a direct comparison with macroscopic experiments, analogous three point bending experiments were performed with spaghetti that were clamped at both ends and subjected to a load in the center (Figure 5) while imaging with a high speed camera. Unmodified spaghetti


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always broke at a single point, either the clamping point (Figure 5b) or at the loading position (Figure 5a), where the stress maxima are expected. In the presence of drilled holes in the spaghetti, breakage occurred at two points: at the central loading point and at one of the holes (Figure 5c). It may appear surprising that breakage occurred first at the central loading point even in presence of the two defects. However, the stresses are minimum half way between the center and the clamping points. Therefore, not only the size but also the exact position of a defect determines if it acts as breaking point in a three point bending experiment. Since there is a much higher density of voids in the case of the 60 nm voids, the probability that defects are present within zones of high mechanical stress is high, which explains the highest probability for multiple fractures for these fibers. Finally, we compare the stress before fracture (100-300 MPa) measured by AFM experiments with the pressures involved in fiber fragmentation by sonication, which is used to section the fibers to form anisotropic particles in previous works.6 In these experiments, sintered fibers were dispersed in water and sonicated to produce fragmented rod-like particles. The sonicator consisted of a cylindrical resonator with a radius of 0.3 cm and was immersed approximately 2.5 cm within the solution. Given this geometry and the sonication power for distilled water (100 W), an intensity of I = 20 W/cm2 was estimated. This intensity is related to the maximum acoustic pressure Pm within the solution by33

"=

2 #

(5)

where ? is the density of water and @ is the velocity of ultrasound waves in water. The calculated maximum acoustic pressure calculated from Eq. 5 would be 0.8 MPa, which should not be large enough to induce the fracture of the fibers, even in the presence of voids. However,


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it is known that at the employed frequencies (20 kHz) and intensities (20 W/cm2), transient cavitation bubbles are produced within the liquid.34 Pressures within cavitation bubbles have been long studied,35 and are known for their destructive power when interacting with solid surfaces,36–39 which could even be employed for the fabrication of nanostructures.40,41 The imploding bubbles are known to generate pressures over 100 MPa upon collapse and have sizes ranging from 0.1 µm to 100 µm.42,43 Such pressure bursts should therefore be intense enough to fracture the fibers, whereas the maximum ultrasound pressure itself will clearly not be sufficient. It has been demonstrated, that a convex surface curvature can even dramatically enhance the pressures developing during cavitation44. This could in principle lead to a fracture of nanofibers at any position, if their fracture strength would much lower than the peak pressures. The mechanical properties of our silica nanofibers therefore match quite will the requirements to control the average fragment size during sonication by the average density of voids along the fiber. Conclusions The mechanical properties of sintered silica fibers containing voids created by the removal of sacrificial polymer particles were investigated by AFM. The effective Young’s modulus of the fibers appears to be controlled by the size of the voids. Void size and distribution also appears to control the fracture behavior of the fibers. Comparing the stresses necessary to break the fibers with typical ultrasound pressures used in sonication to section the fibers leads to the conclusion that breakage of the fibers occurred due to cavitation. Bending of nanofibers yielded failure at single or multiple places within the fiber, as observed for the failure of brittle macroscopic fibers or spaghetti.


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a)

b)

c)

d)

e)

f)

Figure 1. SEM micrographs of nanofibers electrospun and sintered on a micro-structured silicon substrate (a) without (b) with 60 nm, and (c) with 260 nm voids. Images with higher magnification are also shown for each type of fiber: (d) without, (e) with 60 nm and (f) 260 nm voids.


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b)

a)

Silica Fiber x L Microgrid

Force(nN)

AFM

30 25 20 15 10 5 0 -5 -10 -15 -15

x=0 x = L/4 x = L/2 substrate

-10

-5

0

5

10

15

Distance(nm)

d)

c) 100

kF(N/m)

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10

1 0.0

0.2

0.4

0.6

0.8

1.0

x/L Figure 2. (a) Schematics of the three point bending experiment. (b) Calibrated force curves for different positions along the fiber and reference force curve taken on the micro-grid substrate, (c) Stiffness profiles for a 600 °C calcinated fiber without voids. Comparison between the DCBM (red curve, fit = 0.95) and the simply supported beam model SSBM (black curve, fit = 0.84). d) optical microcopy image after scratching through a fiber without voids. The inset image shows the AFM cantilever at lower magnification as it passes through the fiber (black scale bar is 50 µm).


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a)

b)

100

100

〈〉 = 2.0 ± 1.6 FGH

kF /kFmin

〈〉 = 5.4 ± 2.6 GPA

kF/kFmin

10

1

10

1

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

x/L c)

0.4

0.6

0.8

1.0

x/L

100

〈〉 = 3.0 ± 2.3 FGH

kF /kmin

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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10

1 0.0

0.2

0.4

0.6

0.8

1.0

x/L Figure 3. Normalized stiffness versus loading position curves for fibers (a) without voids, (b) with 60 nm voids, and (c) with 260 nm voids. Different colors indicate independent experiments on different fibers using different cantilevers.


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Figure 4. (a) Successive AFM force curves with increasing load. For loads below 400 nN, a linear response is observed. An initial failure at a force of about 405 nN is seen in curve 2. For subsequent force curves, further fiber fracture (3) and softer fiber response of the remaining part of the broken fiber is measured (4). (b)-(c) Fragmentation scenarios observed for fibers without voids and fibers with (d) 60 nm voids, and (e)-(f) 260 nm voids. The scale bar in the insets represents 200 nm for (c) and 500 nm for (f), respectively. The right-side color bar on each figure represents the topographical height of the image as measured by AFM.


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b)

a)

c)

Figure 5. Fracture test for real spaghetti. Each image contains a series of five overlaid snapshots from a high speed camera. The white arrow indicates advancing time, and therefore, increasing applied force F. For a piece of spaghetti without holes (homogenous cylinder), rupture occurs either: a) at the middle or b) at the clamped edges (green arrows indicate rupture positions). This observation is comprehensible, given that surface stresses are maximal at these positions. In a third case c), 2 holes of 0.5 mm diameter were drilled in the spaghetti (left half of the clamped piece). Such holes considerably change the way the spaghetti breaks, now rupturing at two points simultaneously: at the middle and at the leftmost hole. By further pressing what is left of the spaghetti, a third rupture is produced at the right clamping point. In this process two spaghetti fragments are generated, in contrast to the other cases, where at most, a single fragment is produced.


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Table 1. Hydrodynamic diameter DPS of the PS particles and fiber diameter Df after calcination.

DPS a

Df b

[nm]

[nm]

1

−

371 ± 44

2

61 ± 16

239 ± 64

3

256 ± 10

374 ± 49

Entry

(a)

Measured by DLS; (b) Measured by SEM.

AUTHOR INFORMATION Corresponding Author *[email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


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ACKNOWLEDGMENTS We thank Maren Müller for SEM imaging and Daniela Fell for assistance in high speed imaging. T.P.C. acknowledges funding from Fondecyt PAI 7912010015 and was supported by a joint Deutscher Akademischer Austauschdienst (DAAD) − Becas Chile scholarship. Support by the German Science Foundation with the priority program 1486 “PiKo” is acknowledged as well. Supporting Information Available: Histograms for the effective Young’s modulus and stress before fracture for the different types of fiber investigated. This information is available free of charge via the Internet at http://pubs.acs.org/.

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Breaking Nano-Spaghetti: Bending and Fracture Tests of Nanofibers

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