Measuring Young s modulus of 20LP10L20-LLA40 Microspheres and Gelatin-Methacrylamide (GelMA) Hydrogel using nanoindentation

Transcription

1 Thesis Measuring Young s modulus of 20LP10L20-LLA40 Microspheres and Gelatin-Methacrylamide (GelMA) Hydrogel using nanoindentation Josip Rauker

2 Abstract Mechanical properties of different tissues are important for ensuring their proper functioning. Nanoindentation is a commonly used method for measuring mechanical properties of artificial materials, but also different biological materials. Indenters in nano or micro meter range are used to indent the surface of the material sample being tested and a force-displacement curve is recorded. Using the forcedisplacement curve and different analytical methods, the Young's modulus can be calculated. 20LP10L20-LLA40 microspheres (InnoCore Pharmaceuticals, Groningen, Netherlands) were developed as a drug delivery system. In order to insure proper functioning of this drug delivery system, microspheres need to have certain mechanical properties, namely Young s modulus. Young s modulus effects the way drug is being released, but also interaction between the microspheres and surrounding tissue. Three different analytical methods: Oliver-Pharr's, Hertz's and Sneddon's are compared in order to find the optimal method for calculating the Young's modulus. GelMA is a hydrogel intended as a scaffold for chondrocyte proliferation. It is cross-linked using UV light. Depending on the amount of UV irradiation, the surface properties of GelMA could change, it is assumed that it becomes stiffer with higher levels of UV irradiation. Two types of nanoindentation tests were performed: single loading-unloading cycles where force-displacement data is recorded and creep tests where the change of displacement with time is being measured. Key words: Nanoindentation, AFM, 20LP10L20-LLA40, Microspheres, GelMA, Oliver-Pharr, Hertz, Sneddon

3 Introduction Mechanical properties of different tissues are important for ensuring their proper functioning. Change in mechanical properties can be a symptom of disease and can interfere with normal functioning of the tissue. Materials which are used to replace damaged tissue need to have similar mechanical properties to this tissue. Human cartilage is one tissue that is often damaged and needs to be repaired or replaced. In order to develop materials for healing or replacing cartilage its mechanical properties need to be known. Nanoindentation is a commonly used method for measuring mechanical properties of artificial materials, but also different tissues. First goal of this paper is to present different types of nanoindentation tests and analytical methods which are used to calculate mechanical properties from data obtained by these tests. Data obtained using nanoindentation on polymeric microspheres will be used to calculate their Young s modulus and to compare results from three different analytical methods. Second goal is to calculate Young s modulus of a hydrogel and see if the modulus changes with different levels of UV irradiation used during crosslinking. Two different types of nanoindentation tests will be performed: single loading-unloading cycle and creep test. Osteoarthritis is the most common disease that affects joints. Radiographic results show that 80% of people aged 75 years and older are affected with osteoarthritis. It is also one of the leading causes of work disability in United States 1. In osteoarthritis articular cartilage that covers the surface of joints enabling smooth relative movement of the bones in the joint, starts to deteriorate and loose its function. Since cartilage is avascular it cannot repair itself in the same way other tissues can (like skin or bone), so the damage becomes permanent. Affected joints become very painful and have limited movement. Despite all the research done on osteoarthritis, there is still no consensus on the cause of this disease. Currently there is no cure for osteoarthritis. Severe cases are treated by replacing affected joints with artificial ones, but success rates are different for different joints. Currently, osteoarthritis can be treated using non-steroidal anti-inflammatory (NSAID) drugs 2. These drugs are only used to relieve the pain, they do not slow down or reverse the progress of the disease. The main problem is the way this drug is being delivered to joints affected with osteoarthritis. Currently there are two ways of delivering this drug, topical and oral. Topical drug delivery causes some local side effects such as rash, itching or burning and is less effective than oral drug delivery. The problem with oral drug delivery is that it can cause gastrointestinal problems 3. Drugs can also be injected directly into the joint. The problem with this method of delivery is that the concentration of the drug will rapidly drop below needed concentration requiring frequent injections. There is also the problem of infections that comes with frequent use of injections 4. 20LP10L20-LLA40 microspheres (InnoCore Pharmaceuticals, Groningen, Netherlands) were developed as a drug delivery system that would be more efficient and have less side effects than the afore mentioned delivery systems. Drugs would be attached to these microspheres and would be injected into the joint. Microspheres should release the drug continuously over a longer period of time. In this way an optimal concentration of the drug would be always present in the diseased joint. In order to insure proper functioning of this drug delivery system, microspheres need to have certain mechanical properties, namely Young s modulus. Young s modulus effects the way drug is being released, but also interaction between the microspheres and surrounding tissue. If the Young s modulus of microspheres would be too high, they

4 might damage the cartilage. Since microspheres are very small (5-30 μm in diameter), nanoindentation using Atomic Force Microscope (AFM) needs to be employed for the task of recording forcedisplacement curves. Three different analytical methods for calculating the Young s modulus were used to calculate the modulus from the obtained force-displacement curves in order to compare their results. Second way of treating osteoarthritis is by using tissue engineering. Different hydrogels are used as scaffolds in which chondrocytes, cells native to cartilage, are being proliferated. The idea is to grow new cartilage tissue in places where it has been damaged 5. In order to perform its role as replacement cartilage tissue, hydrogels need to have similar mechanical properties as cartilage. This is a big challenge since cartilage is a highly heterogeneous tissue with different mechanical properties in different directions. GelMA is a hydrogel intended as a scaffold for chondrocyte proliferation. It is cross-linked using UV light. Depending on the amount of UV irradiation, the surface properties of GelMA could change, it is assumed that it becomes stiffer with higher levels of UV irradiation. The change in Young s modulus caused by different levels of UV irradiation were measured using two types of nanoindentation tests: single loading-unloading cycles where force-displacement data is recorded and creep tests where the change of displacement with time is being measured. There are two main types of machines used for nanoindentation measurements: nanoindenters and Atomic Force Microscopes (AFM) (Figure 1). The main difference between these two machines is in the way force is applied to the material sample. Nanoindenters are usually load controlled machines and they apply force directly on to the sample. Displacement is then measured using capacitance displacement gage. The probe is fixed to the transducer which produces force using electromagnets. Nanoindenters apply forces in μn range and probes usually have radiuses in μm range. AFM has a probe mounted on a cantilever. AFMs are usually displacement controlled machines and force is applied to the sample by deflecting the cantilever, which acts as a spring. Deflection is measured using a laser. Based on the deflection of the cantilever, both force and displacement are calculated. AFMs apply forces in nn range and tips have radiuses in nm range. Figure 1 Nanoindenter (left) and Atomic Force Microscope (right)

5 Materials and methods 20LP10L20-LLA40 Microspheres A newly developed tri-block copolymer called 20LP10L20-LLA40 (InnoCore Pharmaceuticals, Groningen, Netherlands) comes in spherical form (microspheres) with three different diameters: 5, 15 and 30 μm. A thin film of epoxy based glue (Bizon, Netherlands) was applied on substrate (microscope slide) in order to firmly attach the microspheres. Microspheres were tested both in air and in fluid. PBS was used as fluid to simulate conditions inside the human body. For testing in fluid, microspheres were held in deionized water for three days prior to testing in order to insure their proper swelling. Force-displacement curves were recorded using AFM (Atomic Force Microscope) (Veeco, Dimension V, Japan). For each size of microspheres around 500 loading and unloading curves were recorded both in air and in PBS. Each curve has 1024 data points. For fluid testing a special holder for tips called a fluid cell was used. Fluid cell insures that the fluid forms a meniscus around the sample and the tip, so they are completely submerged in fluid. Conospherical contact mode AFM tips were used (Bruker, Camarillo, USA) with tip radius of 2nm, 22.5 cone half-angle and nominal spring constant of 0.35 N/m. Before each series of measurements, thermal fluctuations technique 6 was used to calculate the real spring constant of each tip based on its resonant frequency. This was done because the difference between the nominal and real spring constant can be up to 100%. Since microspheres are made out of polymers, it is reasonable to assume that they are viscoelastic materials that exhibit creep and stress relaxation phenomena. There are methods for calculating viscoelastic material properties from creep and stress relaxation curves, but they need to be measured using nanoindeters. AFM machines are not suitable for these kinds of tests because they apply force to the sample using spring loading (cantilever deflection) 7. The problem with measuring microspheres with nanoindenter is that the radius of the probe is around the same size as the microspheres, so it is extremely hard to place the probe on top of the microsphere specimen and insure contact between them. Also the camera resolution and light intensity on the available nanoindenter machine were not sufficient to be able to distinguish individual microspheres, especially in fluid. For this reason only AFM was used to record force-displacement data. AFM is displacement controlled machine, so displacement (movement in Z direction) was set to 500 nm for all types of microspheres to make sure that there is no influence of the substrate on the results. It was noticed that Young s modulus becomes extremely high for lower displacements, so only results with displacement larger than 50 nm were used for calculating mean values. Matlab subroutine containing all three analytical methods was written in order to calculate Young s moduli from force-displacement data. AFM data was converted into text files containing Deflection and Z data using Matlab subroutine provided by Bruker. Loading and unloading data was saved in separate files. Once the data has been recorded it needs to be prepared for calculation. AFM machines do not produce force-displacement curves directly; they measure movement of the indenter in Z direction produced by the piezo motor and the deflection of the cantilever. Displacement is then calculated as: h = Z Def (1) where Z is the movement of the indenter in the Z direction and Def is the deflection of the cantilever. Since the cantilever works as a leaf spring, the force applied on the material sample is calculated as: F = Def Sc (2) where Def is the deflection and Sc is the spring constant of the cantilever.

6 Figure 2 shows one loading-unloading Z-Deflection curve, where the blue curve is loading and red is unloading. A typical Z-Deflection curve consists of two parts: approaching part, where the indenter is not in contact with the material sample, and loading/unloading part. Approaching starts at point A and ends up in point C, which is the point of contact between the indenter and the sample. When the indenter approaches the sample, the adhesion forces will pull it into contact, so the deflection (and force) will become negative. By finding the minimum value of deflection (or force), the point of contact will be identified. Loading stops when the given displacement is reached, in point D. At the end of unloading, again because of adhesion forces, the indenter gets stuck inside the material, so the deflection becomes negative again (point B). Adhesion during unloading is often stronger than in loading, so with unloading curves the point of contact is further away from point D, than with loading curves. This will make Young's modulus calculated using unloading curves lower than the modulus calculated using loading curves. Because the displacement is zero at the point of contact, the total displacement is equal to the difference in depth between points D and B or D and C, depending if we use unloading or loading data respectively. Figure 2 Typical Z-Deflection curve There are different analytical techniques that relate Young s modulus to force-displacement data. The most commonly used is the Oliver-Pharr method. This method has become a standard in calculating Young s modulus of linearly elastic materials from force-displacement data. Unlike other methods, Oliver-Pharr method uses the slope of the unloading curve to calculate the Young s modulus. Unloading curve is used because unloading is always completely elastic, while loading might be elasto-plastic, which is hard to determine on the force-displacement curves. Since AFM force-displacement curves are usually linear, their path is very similar and strains are relatively low, it was assumed that there is no plastic deformation occurring during loading, so it was decided to use both loading and unloading curves to calculate the Young s modulus using Oliver-Pharr method. Figure 2 shows a typical Deflection Z curve recorded by the AFM machine. This curve needs to be transformed into force-displacement curve using equations (1) and (2), before any analytical method for calculating Young s modulus can be applied. Oliver and Pharr s analytical expression for calculating Young s modulus from force displacement data 8 : E = π S 2 A (3) where S is the slope of the unloading curve, E * is the combined Young s modulus of the indenter and material sample and A is the contact area. In order to calculate the modulus of the material from the combined Young s modulus, the following expression needs to be used 8 :

7 1 = (1 ν m 2 ) E E m + (1 ν 2 i ) (4) E i where E m and ν m are the Young s modulus and Poisson s ratio of the material sample and E i and ν i are the Young s modulus and Poisson s ratio of the indenter. The indenter for AFM is made out of silicon nitride, a very hard material with Young s modulus of 290 GPa and Poisson s ratio of Poisson s ratio of microspheres was assumed to be 0.5. Area function shows how the contact area between the indenter and material sample changes with displacement. It depends on the shape of indenter, so for conical indenters the following expression is used 10 : r = D tanα (5) A = r 2 π = D 2 tan 2 α π (6) where r is the radius of circle of contact, D is displacement and α is the cone half angle (Figure 3). Figure 3 Important dimensions for conical indenters 10 Second method used for calculating the Young's modulus of microspheres is Hertz's theory of elastic contact. Hertz derived analytical expressions based on the geometry of two bodies in elastic contact. Since the radius of microspheres is more than a 1000 times bigger than the radius of the tip of the indenter, the surface of microsphere can be considered as flat. In this case the analytical expression for elastic contact between a cone and elastic half-space is used 11 : E = 2 F tanα r 2 π (7) where E * is the combined Young's modulus, F is the applied force, α is the cone half-angle and r is the radius of the circle of contact. Third analytical expression was derived by Sneddon 1965, Shimizu et al. 1999, Sakai and Shimizu It also relates force and displacement to Young's modulus: E = F (8) C Dn

8 where E is the Young's modulus of the material, F is the force, C and n are factors that depend on the indenter shape. For conical indenter n = 2 and C is equal to: g tanβ C = 2 (1 ν 2 m ) γ 2 (9) where β is the angle between the surface of the material sample and the side of the cone (Figure 3), ν m is the Poisson's ratio of the material sample, g and γ for conical indenters are equal to: g = π cot 2 β (10) γ = π 2 (11) Gelatin methacrylamide (GelMA) GelMA is a hydrogel which is cross-linked using UV light. Depending on the time of cross-linking and the power of the light used, surface properties of the hydrogel may vary. Four different samples were tested depending on the time and UV light power (full power is 150 mw/cm 2 ): 20 minutes at full power (20FP), 40 minutes at half and full power (40HP and 40FP) and 80 minutes at half power (80HP). All the samples were tested only in fluid, PBS was used as fluid. Samples were kept in a freezer at -26 C prior to testing. The samples were glued on the substrate (polystyrene) using cyano-acrylate based glue (Bizon, Netherlands). AFM was used to record 300 force-displacement curves on each sample. A conospherical indenter with tip radius of 15nm, 35 cone half-angle and nominal spring constant of 0.06 N/m (BudgetSensors, Bulgaria) was used. The data was analyzed using only Oliver-Pharr method described in previous chapter, equations 3,4,5 and 6. Only results where the displacement was larger than 50 nm where used, because the modulus becomes extremely high at lower displacements. Since GelMA samples are much larger than microspheres, they could also be tested using nanoindenter machine. Dimension 3100 (Veeco, Japan) AFM machine was converted into nanoindenter using a different transducer (Hysitron,MN, USA). A diamond conospherical probe with tip radius of μm was used for indentation tests. The Young s modulus of diamond is 1220 GPa and Poisson s ratio is 0.2. Eight creep tests were performed on each sample, two series of four tests with 50μm space between each indentation. The force was set to 900 μn, but in reality it wasn t larger than 400μN. The reason for this is unknown, but the displacement was sufficient, around 4,5 μm, which is almost the maximal possible displacement that the machine can produce (maximum is 5μm). Since the thickness of GelMA samples was around 4 mm, displacement was much below the 10% of thickness, which is set as the limit beyond which the substrate can have influence on the results 13. Data containing force, displacement and time is automatically saved in text format. Both loading and unloading data is saved into one file. Different Matlab subroutine was written for analyzing nanoindenter data since the procedure for locating the starting and ending points for loading and unloading is different than for data recorded by the AFM where loading and unloading data is saved into separate files. Since nanoindenter is a load controlled machine, it is appropriate for performing creep tests. When viscoelastic or poroelastic materials are loaded with a constant force, the displacement will change with time. This is called creep. A method developed by Oyen 7 uses Prony series to fit a curve to creep data in order to calculate the long term shear modulus of the material sample. It was assumed that the Poisson s

9 ratio of GelMA is 0.5, so the Young s modulus could be calculated from shear modulus using the following equation: E = G 2 (1 + ν) (12) For ν = 0.5 E = 3 G (13) As it was mentioned before, first step is to fit a Prony series to displacement, D(t), data: D 3 2(t) = A 0 A k exp ( t ) (14) τ k Levenberg-Marquardt algorithm in Matlab was used to fit the data to a Prony series In the next step Prony series coefficients C 0,C 1,C 2 and C 3 are calculated from A 0,A 1 and A 3 using following expressions: C 0 = 8 A 0 R 3 F max (15) C k = 8 A k R RCF k 3 F max (16) where R is the radius of the spherical indenter, F max is the maximal applied force and RCF k is the ramp correction factor which takes into account that the load isn't applied instantaneously, but it takes a certain amount of time to reach the maximum load. RCF k = τ k t R (exp ( τ k t R ) 1) (17) After the Prony series coefficients C 0,C 1,C 2 and C 3 have been obtained, instantaneous shear modulus can be calculated: G = 1 2 (C 0 C k) (18)

10 Results Microspheres As it was mentioned before, microspheres were tested both on air and in fluid. The difference in Young's modulus between the two is significant. Table 1 shows all the mean results and standard deviations for every analytical method used. 5 micron dry [MPa] 5 micron fuid [kpa] 15 micron dry [MPa] 15 micron fuid [kpa] 30 micron dry [MPa] 30 micron fuid [kpa] Load Unload Load Unload Load Unload Load Unload Load Unload Load Unload Oliver-Pharr Standard deviation OP Hertz Standard Deviation Hertz Sneddon Standard Deviation Sneddon Table 1 Histograms show the distribution of calculated values of Young s modulus for different microsphere sizes, testing condition and analytical techniques used.

11 5 μm microspheres tested in air Loading Unloading Figure 4 Histograms showing Young's modulus of 5 μm microspheres tested in air distribution for (from top to bottom): Oliver-Pharr, Hertz and Sneddon's analytical methods

12 It can be seen for 5μm microspheres tested in air (Figure 4) that the mean Young s modulus is almost the same for both loading and unloading curves. The differences are quite small, below 1 MPa. Histograms show that there is a difference in data distribution between each analytical method, but also between loading and unloading data. Histograms for Oliver-Pharr s and Hertz s solutions are more similar than the histogram for Sneddon s solutions. Both Hertz s and Oliver-Pharr s methods show the highest peaks at around 20 MPa for loading and around 10 MPa for unloading. Sneddon s method has the highest peak at 25 MPa for loading and 20 MPa for unloading. Sneddon s method has the biggest range of data, and more peaks, especially for unloading data, than the other two methods, which results in higher standard deviation. It is interesting to notice that all histograms for 5μm microspheres tested in air have a peak at around 5 MPa which is the same size for every method and for both loading and unloading curves. Only for Oliver-Pharr s method this peak is not distinguishable as for other two methods. The results for one way ANOVA for unloading data of 5μm microspheres tested in air show that the mean results for Oliver-Pharr s and Hertz s method are significantly different than the mean result for Sneddon s method, p = When Oliver-Pharr s and Hertz s mean results are compared, the results also show significant difference, p = The results for one way ANOVA for loading data of 5μm microspheres tested in air show that all three methods have significantly different results with p = When Oliver-Pharr s results for loading and unloading are compared, there is no significant difference between the mean values, p = Loading and unloading data for Hertz s method also show no significant difference between mean values with p = Sneddon s results for loading and unloading show no significant difference in mean values, p =

13 15 μm microspheres tested in air Loading Unloading Figure 5 Histograms showing Young's modulus of 15 μm microspheres tested in air distribution for (from top to bottom): Oliver-Pharr, Hertz and Sneddon's analytical methods

14 15 μm microspheres tested in air (Figure 5) also have similar loading and unloading mean results, difference between the two is less than 1 MPa within each method. Histograms on Figure 5 show that loading results for Oliver-Pharr s method have the highest peak at 25 MPa, Hertz s at 30 MPa and Sneddon s at 50 MPa. Mean results also show that for both loading and unloading curves Sneddon s method will results with the highest Young s modulus and Oliver-Pharr s method with the lowest. Histograms for unloading data show that data distribution is very similar for all methods. All three methods have the highest peak at 10 MPa, with Oliver-Pharr s method having one higher peak at 5 MPa. Both Oliver-Pharr s and Hertz s method have a second peak for unloading data at 45 MPa and 50 MPa respectively. When loading and unloading histograms are compared, it can be seen that for Sneddon s method there is a big difference in data distribution. While loading data has one peak at around 5 MPa and another one at 50 MPa, with no peaks between the two points, unloading data has one big peak at 10 MPa and another smaller one at 40 MPa. The results for one way ANOVA for unloading data of 15 μm microspheres tested in air show that the mean results are significantly different for all three methods, p = Mean loading results are also significantly different for all three methods, p = When loading and unloading mean results calculated using Oliver-Pharr s method, it can be seen that there is no significant difference between the two mean results, with p = Mean loading and unloading results calculated using Hertz s method are even more similar, with p = Sneddon s method also results in no significant difference between loading and unloading mean results, p = 0.96.

15 30 μm microspheres tested in air Loading Unloading Figure 6 Histograms showing Young's modulus of 30 μm microspheres tested in air distribution for (from top to bottom): Oliver-Pharr, Hertz and Sneddon's analytical methods

16 Histograms showing data distribution for 30 μm microspheres tested in air (Figure 6) show significant difference in loading and unloading data distribution. The main difference is the big peak at around 55 MPa for Oliver-Pharr loading data, 75 MPa for Herz loading data and 130 MPa for Sneddon s loading data. Unloading data histograms have no peaks at these points. The biggest peak on unloading data histograms is around 30 MPa for Oliver-Pharr, 35 MPa for Hertz and 60 MPa for Sneddon s method. Again, both loading and unloading data show a peak for Young s moduli smaller than 5 MPa, but this peak is more pronounced in unloading than loading histograms. Main difference between loading and unloading data is that loading data shows a gap between 40 and 110 MPa depending on the analytical method used. Most of unloading results are grouped in the range from 0 to 70 MPa, with several smaller peaks at higher Young s moduli. Although the differences between loading and unloading histograms are substantial, mean results are pretty similar, although a little bit higher than in case of 5 and 15 μm microspheres. The results for one way ANOVA for unloading data of 30 μm microspheres tested in air shows that the mean results calculated using all three methods are significantly different with p = Again, mean results calculated using Oliver-Pharr s and Hertz s methods are more similar then the results calculated using Sneddon s method. One way ANOVA results are the same when loading results are compared, but the p value is a bit larger, p = When both loading and unloading mean results calculated using Oliver-Pharr s method are compared, there is no significant difference between the two, p = There is no significant difference between mean loading and unloading results for Hertz s method as well, p = 0.5. When loading and unloading results are compared for Sneddon s method, there it can be seen that there is also no significant difference between the two data sets, with p = 0.5.

17 Loading 5 μm microspheres tested in fluid Unloading Figure 7 Histograms showing Young's modulus of 5 μm microspheres tested in fluid distribution for (from top to bottom): Oliver-Pharr, Hertz and Sneddon's analytical methods

18 Histograms for 5 μm microspheres tested in PBS (Figure 7) are very similar for both loading and unloading data, they show almost the same distribution of results. All histograms show one significantly higher peak between 100 and 200 kpa depending on the method. Only Oliver-Pharr s method for unloading data has two peaks for values between 90 and 100 kpa. Again, Sneddon s method will result in highest Young s modulus and Oliver-Pharr with the lowest. Mean Young s modulus obtained using Sneddon s method is more than twice as high as mean modulus obtained using Oliver-Pharr s method. This difference between the two methods is much higher than in case of dry microspheres. Loading and unloading data distribution is very similar for all methods. The difference in mean results between different analytical methods is much greater than the difference between loading and unloading mean results within each of those methods. The results for one way ANOVA for unloading data of 5μm microspheres tested in PBS show that the mean results for all three methods have significantly different mean results, p = 0. Again, as with dry 5μm microspheres, Sneddon s mean results are more different than Oliver-Pharr s and Hertz s mean results. When Oliver-Pharr s mean results are compared to Hertz s mean results using one way ANOVA, it can be seen that they are significantly different since p = Mean loading results are also significantly different for all three methods with p = 0. When loading and unloading mean results for Oliver-Pharr smethod are compared it can be seen that they are significantly different, p = 8.6*10-8. Loading and unloading mean results for Hertz s method are also significantly different, p = 3.3*10-9, as are the mean results calculated using Sneddon s method, p = 9.4*10-7.

19 15 μm microspheres tested in fluid Loading Unloading Figure 8 Histograms showing Young's modulus of 15 μm microspheres tested in fluid distribution for (from top to bottom): Oliver-Pharr, Hertz and Sneddon's analytical methods

20 15 μm microspheres tested in PBS (Figure 8) also have loading results higher than unloading, but this difference is much smaller than for 5 μm microspheres tested in PBS. Again, the highest results are the ones obtained by Sneddon s method and the lowest are the ones obtained by Oliver-Pharr s method. Histograms showing loading data distribution for Hertz s and Oliver-Pharr s methods are quite similar, with one peak higher than all the others at 150 MPa for Oliver-Pharr s method and 190 MPa for Hertz s method. Histogram showing the distribution of loading results for Sneddon s method has no distinguishable peaks like Oliver-Pharr s or Hertz s methods. The highest peak is at 290 MPa, but this peak is not pronounced as the peaks in loading histograms for Oliver-Pharr s and Herrz s methods. Histograms for unloading data tell a similar story. Unloading data distribution for Oliver-Pharr s and Hertz s method is quite similar. Both have three distinguishable peaks, with two of them being higher than the third one. Histograms for Oliver-Pharr s data have peaks at 100, 150 and 200 MPa, while histograms for Hertz s data shows peaks at 130, 180 and 210 MPa. Histogram showing the distrinution of unloading data for Sneddon s method is quite different from Sneddon s loading histogram. It has more pronounced peaks at 220, 310 and 400 MPa. The mean results for one way ANOVA for unloading data of 15 μm microspheres tested in PBS are significantly different for all three methods, p = Mean loading results also show significant difference between the three methods, p = Mean loading and unloading results calculated using Oliver-Pharr s method show no significant difference, p = Hertz s method also shows no significant difference between mean loading and unloading results, p = Mean results obtained using Sneddon s method show no significant difference between loading and unloading data, p = 0.91.

21 30 μm microspheres tested in fluid Loading Unloading Figure 9 Histograms showing Young's modulus of 30 μm microspheres tested in fluid distribution for (from top to bottom): Oliver-Pharr, Hertz and Sneddon's analytical methods

22 Mean results for 30 μm microspheres tested in PBS (Figure 9) are higher for loading results than for unloading results for all three methods. This difference is between 9 and 12 kpa. Sneddon s results are highest and Oliver-Pharr s are the lowest, as it is the case with all other microsphere samples. Histograms show a similar data distribution for loading and unloading data within each method, but the peaks are higher in unloading histograms, at least for Hertz s and Oliver-Pharr s methods. Histogram showing data distribution for Oliver-Pharr s loading data has 4 distinguishable peaks at 70, 150, 200 and 230 MPa, while unloading histograms show peaks at 70, 150 and 190 MPa. The 150 MPa peak is much higher for unloading than loading. Hertz s loading histogram has two peaks at 90 and 200 Mpa. Unloading histogram has more peaks, at 70, 190 and 210 MPa. Again the 190 MPa peak in unloading histogram is higher than 200 MPa peak in loading histogram. Both loading and unloading histograms for Sneddon s method are quite similar. They show similar data distribution and the peaks are at similar locations, with unloading peaks being higher than unloading ones. First peak is at 120 MPa for loading and 110 MPa for unloading data. Loading histogram has three more peaks at 300, 350 and 430 MPa, the highest one being the one at 350 Mpa. Unloading histogram has peaks at 290, 320 and 400 MPa, the highest one is at 320 MPa. The mean results for one way ANOVA for unloading data of 30 μm microspheres tested in PBS show that they are significantly different for all three methods used, p = Loading results show the same thing, with p = For both loading and unloading mean results, Oliver-Pharr s and Hertz s methods have more similar results than Sneddon s method. When loading and unloading results for Oliver-Pharr s method are compared, it can be see that they are significantly different, p = Mean loading and unloading results obtained using Hertz s method are also significantly different with p = Sneddon s method has the lowest p value of all three methods when loading and unloading results are compared, p = 0.18, meaning that the results are significantly different. GelMA Force-displacement tests The following table shows mean loading and unloading values for Young s modulus of 4 different GelMA samples. The samples differ according to the level of UV irradiation used for crosslinking. All the results were calculated using Oliver-Pharr s method. 20FP 40FP 40HP 80HP Load All Unload All Load All Unload All Load All Unload All Load All Unload All Young's modulus [kpa] Standard Deviation OP [kpa] Table 2 Mean Young s modulus calculated using Oliver-Pharr method for GelMA samples tested with AFM Mean results show that the highest Young s modulus belongs to the 80HP sample, which was expected because this sample got the highest level of UV irradiation. The surprising thing is the low modulus of the 40FP sample, which got the same level of UV irradiation as the 80 HP sample. There is around 50% difference between 20FP and 40HP samples although they got the same level of UV irradiation.

23 20FP sample Loading Unloading Figure 10 Histograms showing Young's modulus of 20FP GelMA sample tested in fluid The mean results for both loading and unloading data are very similar, the difference is 5 kpa. Histograms show that the distribution of data is very similar. Loading histogram has one peak at around 5 kpa which is absent on the unloading histogram. Both histograms have the highest peak at around 50 kpa and a few smaller ones between 100 and 200 kpa. There are a few smaller peaks between 250 and 350 kpa for loading data and between 200 and 300 kpa for unloading data. ANOVA statistical analysis shows that there is no significant difference between loading and unloading data, p = FP sample Loading Unloading Figure 11 Histograms showing Young's modulus of 40FP GelMA sample tested in fluid

24 Histograms on Figure 11 show that the data distribution is very similar for loading and unloading data measured on 40FP sample. Both samples have the highest peak at 20 kpa. The following three peaks have a bit higher values for unloading data, between 60 and 70 kpa. For loading data these peaks are between 50 and 65 kpa. This results in a higher unloading modulus. Althogh the difference between loading and unloading mean results is 5 kpa, ANOVA statistical analysis shows that the results are significantly different, with p = This is the result of relatively low standard deviation, which is 16 kpa for loading and 19 kpa for unloading data. 40HP sample Loading Unloading Figure 12 Histograms showing Young's modulus of 40HP GelMA sample tested in fluid Histograms on Figure 12 show that mean results for 40HP sample have a rather small deviation. There are no significant peaks in data distribution, like in histograms of previous samples. The mean Young s modulus for loading data is 149 kpa and 142 kpa for unloading data. Although the difference is only 7 kpa or 5%, ANOVA statistical analysis shows that the data is significantly different with p = This is the results of a relatively low standard deviation of around 20 kpa.

25 80HP sample Loading Unloading Figure 13 Histograms showing Young's modulus of 80HP GelMA sample tested in fluid It can be seen on histograms on Figure 13 that loading data has is spread out more than unloading data, it has a higher standard deviation. Unloading data has the highest peak at 1000 kpa, while loading data has the highest peak at 1300 kpa. Mean results show that Young s modulus is higher for loading data, 1369 kpa than unloading data, 936 kpa. This sample has the highest difference between loading and unloading results. ANOVA statistical analysis shows that there is a significant difference between loading and unloading mean results, p = GelMA Creep tests The following tables present all the results calculated using creep test data. For each material sample eight different creep tests were performed and eight different Young's moduli were calculated. In the end the mean value and standard deviation for each sample was calculated. E [MPa] C0 C1 C2 C3 tau1 tau2 tau E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table 3 Creep test results for 20 minutes crosslinking time at full UV lamp power (20FP sample) Mean Young's modulus and standard deviation for 20FP sample: 3.13 ± 0.45 MPa

26 E [MPa] C0 C1 C2 C3 tau1 tau2 tau E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table 4 Creep test results for 40 minutes crosslinking time at full UV lamp power (40FP sample) Mean Young's modulus and standard deviation for 40FP sample: 2.82 ± 0.53 MPa E [MPa] C0 C1 C2 C3 tau1 tau2 tau E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table 5 Creep test results for 40 minutes crosslinking time at half UV lamp power (40HP sample) Mean Young's modulus and standard deviation for 40HP sample: 2.49 ± 1.07 MPa E [MPa] C0 C1 C2 C3 tau1 tau2 tau E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Table 6 Creep test results for 80 minutes crosslinking time at half UV lamp power (80HP sample) Mean Young's modulus and standard deviation for 80HP sample: 3.24 ± 0.22 MPa

27 In Tables 3 to 6 the first column (E), represents the long term Young's modulus, columns 2 to 8 represent Prony series factors (C 0, C 1,C 2,C 3,tau 1,tau 2,tau 3 ). In order to fit a Prony series curve to creep data obtained from nanoindentation tests, starting values for Prony series factors need to be set in the curve fitting algorithm. For all C factors the starting value was 10-12, and this value changed during curve fitting process. The initial values for relaxation time factors (tau 1,tau 2,tau 3 ) remained unchanged. It was observed that a good fit can be obtained only by using certain values for relaxation time factors. In this case these values were 1, 10 and 20 respectively. Discussion 20LP10L20-LLA40 Microspheres 20LP10L20-LLA40 microspheres are a completely new material and their Young s modulus is unknown. To the best of my knowledge there is only one paper about Young s modulus of this material written by Moshtagh et al. 14 and the same force-displacement data is used in this thesis. Moshtagh et al. used Sneddon s analytical method with loading data to calculate the Young s modulus. Table 1 shows all the results of AFM test done on microspheres. It can be seen that the differences in Young s modulus can be substantial for different analytical methods, up to more than 100%. Different results will be obtained if loading or unloading curves are used. The biggest difference can be observed between microspheres tested in air and in fluid. Young s moduli of dry micropsheres are in MPa range, while swelled microspheres tested in fluid have moduli in few hundred kpa range. This is because the water molecules, because of their polarity, interact with the hydrophilic components of the polymer and reduce the brittleness of the copolymer matrix 15. In other words, swelling will make them more compliant. It can be noticed that Sneddon s method will regularly produce highest results, while Oliver-Pharr method will produce the lowest. The difference between the two methods is between 58% and 54%. Standard deviation is quite high for all microspheres tested in air regardless of the method used, ranging from 80% to almost 120%, and is consistent for all three analytical methods. Because AFM machines use small indenters (2 nm in radius), it is possible to measure the properties of single components of this copolymer, resulting in data with big standard deviation. Main difference between Oliver-Pharr s method and the other two methods (Hertz and Sneddon) is that Oliver-Pharr s method uses the ratio of slope of the load displacement curve and contact area multiplied by some constant for calculating Young s modulus. The other two methods use the ratio of force and displacement multiplied by some constant. When the force-displacement curve has a lot of noise, using the slope of the curve can be beneficial since it will iron out the noise of the curve resulting in smaller fluctuations of the modulus along a single force-displacement curve. When equation 6 is inserted in equation 3 (Oliver-Pharr's method), the relationship between force, displacement and Young's modulus is revealed: E = S D tanα (19) The same thing can be done with equation 7 (Hertz's method) when equation 5 is inserted:

28 E = 2F π D 2 tanα (20) When equations 9,10 and 11 are inserted into equation 8, complete relationship between force, displacement and Young's modulus for Sneddon's analytical expression is obtained: E = F π (1 ν m 2 ) 3 2 cotβ D2 (21) The first difference between the methods is that Oliver-Pharr's and Hertz's methods show the relationship between force, displacement and combined Young's modulus. That is why equation 4 needs to be used in order to calculate the Young's modulus of the material sample. On the other hand, equation 21 shows that by using Sneddon's analytical method, the Young's modulus of the material sample is obtained directly. If equation 21 is examined closer, it can be seen that there is no Poisson's ratio and Young's modulus of the indenter in this equation, only the Poisson's ratio of the material sample. Equation 4 uses both the Young's modulus and the Poisson's ratio of the indenter in order to calculate the Young's modulus of the material sample. This is one of the reasons why Sneddon's method has higher results than the other two methods. When equations are examined, it can be seen that the numerator and denominator in those equations are quite different. First difference is in the exponent on the displacement (D), which is 1 for Oliver-Pharr (eq.19), 2 for Hertz (eq.20) and 3/2 for Sneddon (eq.21). Because of this, the denominator in Hert's solution will rise faster with depth. Both Hertz's and Oliver-Pharr's expressions have tangens of the cone half angle in denominator, but Hertz's expression also has π in denominator. This would make the denominator in Hertz's expression higher than the denominator in Oliver-Pharr's expression. Sneddon's expression has cotangens of the angle β (Figure 3) in denominator. It can be seen on Figure 3 that β = π/2- α, meaning that cotangens β is equal to tangens α. The analysis of denominators shows that Oliver-Pharr's expression should have the smallest denominator and Hertz's expression should have the biggest denominator. In the case that all three expressions would have the same numerator, Hertz's method would have the lowest and Oliver-Pharr's method would have the highest solution, but this is not the case. Oliver-Pharr's method has the slope of the force-displacement curve in numerator, unlike Hertz's and Sneddon's expressions which have force in that place. Since both force and displacement are in nano range (10-9 ) and the slope is a number between 0 and 50, it can be seen that higher exponent for displacement will actually result in a smaller denominator (10-18 )in Hertz's expression. All this will result in higher results for Hertz's solutions compared with Oliver-Pharr's. The numerator in Sneddon's expression is higher than the numerator in Hertz's expression. For ν m =0.5, the numerator in equation 21 will be equal to 2.36*F, which is higher than the numerator in equation 20. Since the denominator in equation 21 is a bit lower than the denominator in equation 20, the overall result should be higher for Sneddon's method when compared with Hertz's. Swelled microspheres show a significant drop in Young s modulus compared with dry ones. Standard deviation is also much lower for swelled microspheres, ranging from 14% to 50%. This could mean that swelling makes the material more homogenous. For all three sizes of microspheres loading results are higher than unloading. This shows that the pull-out force, force needed to separate the indenter from the material surface at the end of unloading, is higher when microspheres swell.

29 ANOVA statistical analysis of dry microspheres shows that there is significant difference in results obtained using different analytical methods, p < 0.05 for all microsphere sizes. Results obtained from loading and unloading data with the same analytical method show no significant difference, p > μm and 30 μm microspheres tested in PBS have significantly different loading and unloading results, p < 0.05, when the same analytical method is used. The reason for this difference probably lies in the higher pull-out force during unloading. Longer unloading curve means that the displacement will be larger for the same force in case of unloading, resulting in lower Young s modulus. It very hard to decide which analytical method is the best choice for calculating Young s modulus from force-displacement data. Oliver-Pharr method is most commonly used method in nanoindentation tests 13. Since Oliver-Pharr method uses the ratio of the slope of the force-displacement curve divided by the area of contact, it shows smaller fluctuations of Young s modulus along a single force displacement curve. If the force-displacement curve has a lot of noise, the impact will be greater on Hertz s and Sneddon s analytical methods because they use the ratio of the force and radius of contact in every point of a single force-displacement curve. This can be seen on Figure 14 where the pink curve belonging to Oliver-Pharr method has less noise than the curves belonging to other two methods. Figure 14 Change of Young s modulus with depth of indentation GelMA There are four different factors that influence the mechanical properties of GelMA and they are related to the production process of this hydrogel: 1. Degree of methacrylation which shows the number of side groups attached to the main chain. 2. Concentration of GelMA in PBS 3. Concentration of crosslinker 4. UV light exposure Samples used in our experiments had all the same properties, except for the UV light exposure. Because all the aforementioned factors influence the mechanical properties of GelMA, it is very hard to compare results from different papers, since there might be differences in the production process.