# Mechanical Properties of Electrospun, Blended Fibrinogen: PCL Nanofibers

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Preparation of 50:50 Fibrinogen:PCL Solution

#### 2.2. Preparation of Striated Substrate

^{®}184, Sigma-Aldrich, St. Louis, MO, USA) onto an SU-8-silicon master grid in a large plastic Petri dish. A 1 cm × 1 cm stamp can then be excised with a scalpel. Excised stamps were stored in a 2% sodium dodecyl sulfate (SDS) solution to keep them clean; the stamps can be stored for at least several months and used repeatedly. To create the striated substrate, a drop of Norland Optical Adhesive-81 (NOA-81, Norland Products, Cranbury, NJ, USA) was placed on a 60 mm × 24 mm, #1.5 microscope cover slide (Thermo Fisher Scientific, Waltham, MA, USA). The PDMS stamp was pressed into the NOA-81 drop on the slide and cured with 365 nm UV light (Benchtop 3UV transilluminator, UVP, Upland, CA, USA) for several minutes. The substrate had ridges of width 7.3 μm and height 6 μm. The gaps between the ridges were 6 μm across.

#### 2.3. Electrospinning of 50:50 Fibrinogen:PCL Fibers

#### 2.4. Anchoring of Fibers to Ridges

#### 2.5. Combined AFM/Optical Microscopy

_{0}= 300 kHz and spring constant, k = 26 N/m). The cantilever thickness, t, which was determined from calculations as outlined in detail below, was on average 4 μm.

#### 2.6. AFM Force Measurements

^{11}Pa; G = 0.5·10

^{11}Pa).

_{n}= V

_{top}− V

_{bottom}, and a lateral force measurement results in a change in the lateral photodiode voltage signal, ΔV

_{l}= V

_{left}− V

_{right}.

_{n}or ΔV

_{l}. To convert voltage data and the data of the tip’s position into force–distance or stress–strain curves, the following procedure is performed.

_{n}, is proportional to the deflection, Δd

_{n}, of the cantilever; thus, Hooke’s law in the normal direction, F

_{n}= k

_{n}·Δd

_{n}, becomes

_{n}, to the normal voltage signal, ΔV

_{n}. This quantity is determined before each experiment by taking a force curve on a hard surface, deflecting the tip by a known amount Δd

_{n}and recording the corresponding voltage signal ΔV

_{n}. Alternatively, it may be determined via an Asylum software routine from the cantilever resonance frequency.

_{n}.

_{l}= k

_{l}Δd

_{l}, becomes

_{l}, to the lateral voltage signal ΔV

_{l}. This quantity is derived from the normal sensitivity as follows.

_{n}, is given by ${\theta}_{n}=\frac{3}{2}\times \frac{\mathsf{\Delta}{d}_{n}}{L}$. The photodiode output signal of the AFM in the normal direction, ΔV

_{n}, is proportional to the bend of the cantilever

_{l}, (which can be approximated by the arc length, Figure 3), the lateral deflection angle, ${\theta}_{l}$, is ${\theta}_{l}=\frac{\mathsf{\Delta}{d}_{l}}{\left(h+\frac{t}{2}\right)}$. Here, it is assumed that the cantilever tip is stiff (i.e., does not bend). The photodiode output signal of the AFM in the lateral direction, $\mathsf{\Delta}{V}_{l}$, is proportional to the bend angle of the cantilever,

_{n}, is termed InVols, and is recorded in m/V. In this AFM, the InVols (normal sensitivity) can be determined by two methods: calibration of the AFM tip, which provides an InVols value; and single touch. In the single-touch method, the tip is pressed on a hard surface (e.g., blank glass slide) and the sensitivity is recorded. The latter method is more direct and accurate, and was used here. However, the sensitivity values determined via the two methods were consistently within 10% of each other.

_{n}is determined as described above. The shear modulus of silicon, G, has a value of 0.5 × 10

^{11}Pa and the dimensions of the cantilever are provided by the cantilever manufacturer (and were verified using optical microscopy). However, the manufacturer-provided cantilever thickness, which enters the equation in the third power, has a large uncertainty. Thus, it was determined using Equation (1) for the normal spring constant, ${k}_{n}=\frac{E\xb7w\xb7{t}^{3}}{4\xb7{L}^{3}}$. The value for ${k}_{n}$ is determined from the equipartition theorem using built-in microscope software (calibration mentioned above): L, w, and E of the cantilever are known to high precision, so the thickness, t, can be extracted from this equation. This value is then used in Equation (10). The tip height, h, is also provided by the manufacturer and is 14 μm.

#### 2.7. Fiber Stress–Strain Curves

_{i}, which can be represented by the equation

_{f}, the final length of the fiber, can be found using the Pythagorean Theorem (Figure 3b), ${L}_{f}=\sqrt{{L}_{i}{}^{2}+{s}^{2}}$. Since the gaps between ridges were of a fixed size, L

_{i}had a constant value of 3 μm (half of 6 μm, the gap between ridges). L

_{f}is the length of half of the extended fiber (assuming the fiber was pulled in the middle).

_{fiber}is the force exerted on the fiber along the length of the fiber by the tip. For these experiments, the diameter of the fiber was assumed to be constant (the initial value before stretching), as the fiber was stretched. In other words, we are ignoring the thinning of the fiber as it is stretched out (Poisson’s ratio μ = ∞). According to Newton’s third law, for every action force, there is an equal and opposite reaction force; therefore, F

_{tip}is equal and opposite to sum of the x-components of the force applied to the whole fiber, −F

_{tip}. Considering Figure 3c, and assuming the fiber is pulled in the middle, the force on one arm (one half) of the fiber is given by:

_{l}, the force on the fiber can be calculated. Dividing it by the cross-sectional area of the fiber gives the stress on the fiber, Equation (12).

#### 2.8. Incremental Stress–Strain Curves

_{0}; (2) an elastic spring (modulus Y

_{1}) in series with a dashpot (viscosity η

_{1}); (3) an elastic spring (modulus Y

_{2}) in series with a dashpot (viscosity η

_{2}). All three elements are needed to fit the data. The first element is needed because the stress does not relax all the way to zero; there is a time-independent elastic component left as t→∞. The second and third elements are needed because the exponential decay shows two time regimes, a fast decay (τ

_{1}) and a slower decay (τ

_{2}). In Equation (15), σ

_{0}is the relaxed stress value of the fiber as t→∞. The coefficients σ

_{1}and σ

_{2}are values used to find the total modulus; Y

_{t}= Y

_{0}+ Y

_{1}+ Y

_{2}, where Y

_{i}= σ

_{i}/ε, with i = 0, 1, 2. The values of ${\tau}_{1}$ and ${\tau}_{2}$ represent the fast and slow relaxation times, respectively. The relaxation time, viscosity and modulus of the in series elements are related by τ

_{i}= η

_{i}/Y

_{i}, with i = 1, 2.

## 3. Results

#### 3.1. Simple Stress–Strain Curves

#### 3.2. Incremental Stress–Strain Curves

#### 3.3. Energy Loss and Elastic Limit

## 4. Discussion

^{2}, the values obtained for total and elastic moduli have large standard deviations, which is indicative of the large variability across fibers.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Schematic of the electrospinning setup. The electric potential difference between the needle and the collection site is set to 20,000 V. Figure adapted from [3]. (

**b**) Optical microscopy image of electrospun fibers on the striated substrate. Ridges (width, 7.3 μm; height, 6 μm) appear in darker gray; gaps (6 μm across) appear in lighter gray.

**Figure 2.**Geometry for normal and lateral atomic force microscopy (AFM) force measurements. (

**a**) Side view of cantilever. A normal force applied to an AFM cantilever results in a normal deflection of the cantilever (treated like a flexible beam) by a distance Δd

_{n}, and a bend angle θ

_{n}(measured tangentially at the end of the cantilever). (

**b**) Frontal view of cantilever. A lateral force applied to an AFM cantilever results in a lateral deflection of the cantilever by a distance Δd

_{l}, and a bend angle θ

_{l}. This is the situation when pulling on a fiber. (

**c**) Schematic diagram of an AFM probe showing the length (L), width (w) and thickness (t) of the cantilever and the height (h) of the AFM tip.

**Figure 3.**Schematic of fiber manipulation. (

**a**) Side view. The fiber is suspended over the grooves and pulled by the laterally moving AFM probe. The fiber is anchored to the ridges by epoxy (gray ellipses). The fiber can be viewed by the inverted microscope beneath the substrate. (

**b**) Top view. L

_{i}is half of the initial full length of the fiber while L

_{f}is half of the stretched length, assuming the fiber is pulled in the middle. The angle between L

_{i}and L

_{f}is β, and s is the distance travelled by the AFM tip. Figure adapted from [31]. (

**c**) Force diagram showing the force balance between the force applied by the tip on the fiber, F

_{tip}, and the force applied by the fiber on the tip, −F

_{tip}. These forces are equal and opposite according to Newton’s third law. F

_{tip}is the sum of the x-components of the two F

_{fiber}forces that are applied to the top and the bottom arm of the fiber. F

_{fiber}is applied along the length of the fiber. F

_{tip}is equal in magnitude to the lateral force measured by AFM, F

_{l}; F

_{fiber}is the force that stretches the upper and lower arm of the fiber (assuming symmetric pulling in the middle of the fiber).

**Figure 4.**Kelvin model consisting of an elastic spring in parallel with two elements consisting of a dashpot and an elastic spring in series. This model was used to fit the incremental stress–strain curves.

**Figure 5.**Electrospun 50:50 fibrinogen:PCL (poly-ε-caprolactone) fibers on striated substrate. (

**a**) Optical microscopy image of two single fibers on the substrate with the AFM taking an image of one of the fibers. AFM probe is the black, pointed shape). (

**b**) Optical microscopy image of an epoxy-anchored fiber. (

**c**) AFM image of a single electrospun fiber on a ridge. The inset shows the cross-section of the fiber; fiber height (diameter), 135 nm.

**Figure 6.**Stress–strain curve and modulus of an electrospun 50:50 fibrinogen:PCL fiber. (

**a**) Stress–strain curve of a single fiber. Fiber stress increases nonlinearly with strain, initially with a steep slope that decreases continually, and plateaus between 67% and 75%, reaching a maximum stress of 150 MPa. The fiber ruptures between 84% and 94% strain. (

**b**) A plot of the instantaneous slope (modulus) of the curve in (

**a**) shows the continual decrease in modulus with increasing strain. (

**c**) Histogram of maximum extensibility (maximum strain before rupture). The mean, around 110%, indicates the fiber is stretched to 2.1 times its initial length before breaking. (

**d**) Histogram of rupture stress, the maximum stress before the fiber breaks.

**Figure 7.**Incremental stress–strain curves and cyclical stress–strain curves of electrospun 50:50 fibrinogen:PCL fibers. (

**a**) Strain versus time curve showing sequential periods of increasing strain (20 s) followed by constant strain (30 s). (

**b**) Fiber stress versus time, fiber stress increases as the fiber is pulled; it decays during each constant strain period of the incremental stress-strain tests. (

**c**) Close up of Figure 7b, showing a single stress relaxation curve of an incremental stress-strain test. Plotting stress versus time permits curve-fitting to Equation (15) to extract the total and elastic modulus and stress relaxation times, see main text. There is a steep initial decrease with a fast relaxation time, τ

_{1}, followed by a slower relaxation with relaxation time, τ

_{2}. (

**d**) Cyclic stress–strain curve to determine energy loss and elastic limit. This graph represents one complete outward pull (black circles) and return (red squares); it highlights the large energy loss (inscribed area) experienced by the fibers. (

**e**) Plot of the total and elastic moduli grouped by strain, as extracted from the incremental stress–strain curves. The data points represent averages for the strain intervals expressed on the x-axis.

**Table 1.**Summary of the data collected in this paper. We followed the recommendation to use one decimal place more than the precision of our measurement [42]. We estimate the absolute error in our force measurement to be about 50% and in our extensibility measurement to be about 10%, given the error in the measured, experimental quantities. The high standard deviation of these values reflects the large variability across different fibers, not necessarily the error in measurements.

Value | Average +/− Std. Dev. | Data Points, N |
---|---|---|

Extensibility (Maximum Strain) | 110 ± 60% | 80 |

Maximum Stress | 410 ± 210 MPa | 86 |

Elastic Limit | 5 ± 5% | 51 |

Energy Loss | 75 ± 10% | 25 |

Fast Relaxation Time | 1.1 ± 0.4 s | 87 |

Slow Relaxation Time | 16 ± 6 s | 86 |

Initial Modulus, single pull (~10% strain) | 1700 ± 800 MPa | 9 |

Large strain Modulus, single pull (~100% strain) | 110 ± 90 MPa | 9 |

Total Modulus, incremental (0–25% strain) | 1400 ± 990 MPa | 90 |

Elastic Modulus, incremental (0–25% strain) | 980 ± 710 MPa | 90 |

Total Modulus, incremental (~100% strain) | 430 ± 420 MPa | 90 |

Elastic Modulus, incremental (~100% strain) | 310 ± 250 MPa | 90 |

Fiber Type | Extensibility (%) | Fast Relax (s) | Slow Relax (s) | Elastic Modulus (MPa) | Total Modulus (MPa) | Diameter (nm) |
---|---|---|---|---|---|---|

e-spun 50:50 Fibrinogen:PCL [this paper] | 110 ± 60 | 1.1 ± 0.4 | 16 ± 6 | 980 ± 710 (low strain values) | 1400 ± 990 (low strain values) | 230 ± 90 |

e-spun PCL Fibers (>30 days) [31] | 98 ± 30 | 0.98 ± 0.26 | 8.79 ± 3.08 | 52.9 ± 36.2 | 62.3 ± 25.6 | 440–1040 |

e-spun PCL Fibers (<30 days) [31] | 1.69 ± 0.44 | 21.22 ± 8.97 | 61.4 ± 51.1 | 99.2 ± 83.9 | 440–1040 | |

e-spun Fibrinogen (dry) [32] | 113 ± 22 | 1.2 ± 0.4 | 11 ± 5 | 4200 ± 3400 | 3700 ± 3100 | 30–200 |

Native Collagen [50] | 12 | 160–7500 | (tendon) | |||

Cross-linked Fibrin [51] | 147 | 2.1 | 49 | 8.0 | 4.0 | 124–800 |

Uncrosslinked Fibrin [51] | 226 | 2.9 | 54 | 3.9 | 1.9 | 94–700 |

Dry e-spun Collagen Fibers [33] | 33 ± 3 | 3 | 50 | 2800 ± 3100 | 200–800 | |

Spider Silk [52] | 270 | 3 | 1000–5000 |

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**MDPI and ACS Style**

Sharpe, J.M.; Lee, H.; Hall, A.R.; Bonin, K.; Guthold, M.
Mechanical Properties of Electrospun, Blended Fibrinogen: PCL Nanofibers. *Nanomaterials* **2020**, *10*, 1843.
https://doi.org/10.3390/nano10091843

**AMA Style**

Sharpe JM, Lee H, Hall AR, Bonin K, Guthold M.
Mechanical Properties of Electrospun, Blended Fibrinogen: PCL Nanofibers. *Nanomaterials*. 2020; 10(9):1843.
https://doi.org/10.3390/nano10091843

**Chicago/Turabian Style**

Sharpe, Jacquelyn M., Hyunsu Lee, Adam R. Hall, Keith Bonin, and Martin Guthold.
2020. "Mechanical Properties of Electrospun, Blended Fibrinogen: PCL Nanofibers" *Nanomaterials* 10, no. 9: 1843.
https://doi.org/10.3390/nano10091843