Metallo-supramolecular cross-linking of PMMA films A study into the mechanical properties

L.I.J.C.Bergers 0500797 Report number: Internal trainee Coach: Supervisors: Technical UnivDepartment of Chemical EnginMechanics of MChemistry and

MT 04.16

ship 04-2004/07-2004

Ir. D.Wouters

Prof. Dr. Ir. M.G.D.Geers Prof.Dr. U.S.Schubert

ersity Eindhoven Mechanical Engineering/Department of eering and Chemistry aterials/Laboratory of Macromolecular

Nano Science

Summary The effect of metallo-supramolecular cross-linking on the mechanical properties of thin terpyridine containing PMMA films was evaluated through nanoindentation. The studied material consisted of thin 20 um thick films of PMMA containing pendent terpyridine groups which was exposed to a solution of iron(II)chloride in methanol resulting in inter and intra chain complex formation between two terpyridine moieties and a single metal ion. The goal was to investigate the influence of the amount of cross-linking on the E-modulus, hardness and resulting deformations of the thin films. This was investigated through nanoindentation with a dedicated nanoindenter. AFM was used to investigate any possible surface abnormalities. The possibility of using AFM for indentation experiments by means of recording force distance curves was evaluated by comparing results to the dedicated indenter. Indentation theory developed by Oliver and Pharr was employed for the analysis of the nanoindentation. The cross-linking resulted in two types of surface structures: opaque and transparent. The opaque part turned out to have a rough coral like structure. The transparent part remained smooth. The formation of the coral structure was most likely an effect of swelling due to the solvent for Fe2+. Effects in the transparent part were only seen at 100% cross-linking of the terpyridines, most probably due to the relatively small amount of terpyridines in the system. An increase in E-modulus from 3.75 GPa to 6.32 Gpa was observed. The hardness didn’t show any significant change. The plastic indentation depth doubled whilst the maximum indentation depth decreased by about 15%. The opaque part showed effect already at 50% cross-linking. A decrease of 50% in E-modulus, 30% in hardness and a great increase in plastic and maximum indentation depth were observed. Obtaining absolute values from the indentation experiments with AFM proved to be unsuccessful due to the difficulty of determining the tip shape and thereby a correct contact area. The research showed that this new method of cross-linking can have a positive influence on mechanical properties, perhaps yielding more significant effects in softer polymers.

Index 1 Introduction and goals................................................................................................. 1 2 The chemistry.............................................................................................................. 2

2.1 PMMA-terpyridine ............................................................................................. 2 2.2 UV-vis spectroscopy........................................................................................... 3

3 Indentation Theory...................................................................................................... 3 3.1 Hertzian Mechanics ............................................................................................ 4 3.2 Modern contact models....................................................................................... 6

3.2.1 Quasi-static analysis.................................................................................... 6 3.2.2 Dynamic Mechanical Analysis ................................................................... 8 3.2.3 The tip area function ................................................................................... 9 3.2.4 The correction factor β.............................................................................. 10

4 AFM.......................................................................................................................... 12 4.1 Principle of AFM .............................................................................................. 12 4.2 Contact mode .................................................................................................... 13 4.3 Non-contact mode............................................................................................. 14 4.4 Force spectroscopy............................................................................................ 14

4.4.1 Force-distance curves................................................................................ 14 4.4.2 Tip-sample interactions during contact..................................................... 15 4.4.3 Converting raw data to force-displacement curves................................... 16 4.4.4 Cantilever stiffness measurement ............................................................. 18

5 Experimental ............................................................................................................. 19 5.1 Sample preparation ........................................................................................... 19 5.2 Sample indentation............................................................................................ 19 5.3 Sample scanning ............................................................................................... 21

6 Results....................................................................................................................... 22 6.1 Sample preparation results ................................................................................ 22 6.2 UV-vis spectra .................................................................................................. 23 6.3 Hysitron indentation.......................................................................................... 24

6.3.1 E-modulus ................................................................................................. 24 6.3.2 Hardness.................................................................................................... 27 6.3.3 Resulting deformations ............................................................................. 29

6.4 AFM indentation............................................................................................... 33 6.5 AFM imaging.................................................................................................... 35

6.5.1 Sample 1.................................................................................................... 35 6.5.2 Sample 2.................................................................................................... 35 6.5.3 Sample 3.................................................................................................... 36 6.5.4 Sample 4.................................................................................................... 37 6.5.5 Sample 5.................................................................................................... 37 6.5.6 Topographic results................................................................................... 38

7 Conclusions and recommendations........................................................................... 39 Appendices........................................................................................................................ 42

Appendix A................................................................................................................... 42 Appendix B ................................................................................................................... 42

1 Introduction and goals Cross-linking is a well-known method for strengthening polymers. A common example is vulcanisation of rubber: addition of sulphur bonds results in cross-linking of the system. Typically polymers are cross-linked by adding reactive components that will form covalent chemical bonds between the polymers. These bonds are permanent. Making these bonds reversible would be interesting and might perhaps lead to new smart materials. Therefore a new type of PMMA with terpyridine groups was synthesized. These groups are ligands: they can bind to other ligands via addition of metal ions. The metal ions can be removed thus reversing the bond. This would be a new mechanism for cross-linking polymers with the advantage of reversibility. Possible applications could be found in coating and thin film industries. This study investigated the influence of this type of cross-linking on the Young’s modulus, the hardness and resulting deformations. The Young’s modulus was of interest, because many other material parameters can be derived from it, such as the shear modulus. The hardness and plasticity were of interest, because they indicate the wear and load resistance of the material. Thin films with thicknesses of about 20 µm were investigated with AFM and nanoindentation. The AFM was used to investigate the material morphology and for nanoindentation, whilst a dedicated nanoindenter was used too. This was done to compare the possibilities of indentation with AFM and a dedicated nanoindenter.

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2 The chemistry

2.1 PMMA-terpyridine A system that can be reversibly cross-linked was desirable. To synthesize such a system supramolecular and macromolecular chemistry had been used by Hofmeier [1]. Supramolecular chemistry utilises non-covalent binding mechanisms to build from simple molecules more complex structures. The non-covalent bonds are e.g. hydrogen, Van der Waals, ionic or coordinative interaction bonds. Non-covalent bonds are not as strong as covalent bonds, but this is their advantage: they can be reversed easier and more controllable. Hofmeier functionalised PMMA with terpyridine ligands. In Figure 2.1 the chemical structure is shown. It acts as a receptor for ions. This is achieved by the three nitrogen atoms having an extra pair of valence electrons available due to the composition and structure of the terpyridine. The extra valence electrons are thus able to attract ions, without forming a permanent covalent bond. This enabled the reversible crosslink function and at the same time still yielded a strong bond. The reversibility can be achieved by razing the temperature, by introducing competing ligands, or by redox chemistry. The PMMA-terpyridine system is a random copolymer of terpyridine functionalised MMA molecules polymerised with commercial MMA. Figure 2.1 shows the synthesis of the PMMA-terpyridine copolymer system. It starts with the reaction of 4’-chloro-terpyridine (1) with 1,3-propanediol. Afterwards an ester coupling is performed with methacrylic acid to yield terpyridine-functionalised methacrylate (3). Finally through free radical polymerisation initiated by AIBN the MMA-co-MMA-terpyridine polymer (4) is formed.

Figure 2.1: Synthesis of PMMA-terpyridine complex. [1]

Figure 2.2 shows the cross-linking process. The PMMA (long chain) with terpyridine side groups (brackets) is in an uncomplexed state. The terpyridines are free to bind to metal ions (dots). When these are introduced they can bind to two terpyridines, forming a crosslink if the terpyridines are from different chains. However, for short chains it is possible that two terpyridines from the same chain are bond together. So the amount of ions introduced plays a role in the amount of cross-linking. Another

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crucial point in this process is the mobility of the chains. Two terpyridines have to be near to each other in order to form the bond. Thus the mobility of the chains is also of influence on the cross-linking process. If the cross-linking is performed in solution the chain is highly mobile and can rearrange easily to form the bonds. However, in a solid state, such as a thin film, this is not the case. The solid state prohibits metal ions from penetrating the film and it prohibits high chain mobility. A solvent needs to be used to increase the chain and ion mobility. The surface will swell with the solvent thus allowing for the metal ions to travel easier and the chains to rotate and translate into different positions. For this purpose the solvent needs time to swell the surface, so time also plays a factor in the cross-linking.

Figure 2.2: The cross-linking of PMMA-tpy through addition of metal ions. [1]

2.2 UV-vis spectroscopy The cross-linking can be measured by UV-VIS spectroscopy [2], because the terpyridine-Fe2+ complex absorbs light at a specific wavelength. UV-VIS spectroscopy measures the amount of absorption a material displays at different wavelengths. The spectrum of wavelengths starts at around 700 nm (visible red light) and goes down to 200 nm (UV light). The absorption is due to electrons being excited into higher energy states. These states are superimposed on rotational and vibrational energy states of atoms and groups of atoms. Thus certain molecules or groups in molecules can absorb at different wavelengths. This way it is possible to assign certain wavelengths to certain groups. For the terpyridine group complexed with an iron ion this wavelength is 561 nm. Beer’s law correlates the amount of absorption A to the concentration c of the absorbing group, the molar absorbtivity ε of the group and the path length b through witch the radiation beam travels as follows: A bcε= Equation 2.1 After calibrating the spectrometer by measuring a spectrum from a known material, it is possible to measure the concentration from other materials. Thus the amount of terpyridine-Fe2+ complexes can be measured and the amount of cross-linking can be determined.

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3 Indentation Theory To investigate Young’s or E-modulus and hardness H of thin films nanoindentation experiments can be performed. Hardness and resulting plastic deformations are an indication as to how easily surface damage might occur. This is of much interest to the coating industry, as they want to deliver products that are scratch resistant and will therefore look good even after intensive usage. The E-modulus is of much interest because it is a basic material parameter from which other material parameters can be deduced, so that stress and strain can be related. Macroscopically it can be determined by performing a tensile test on a specimen. The elastic deformation of a tensile test is described by Hook’s law: Eσ ε= . It relates the stress σ to the strain ε through the E-modulus. The tensile test requires a relatively large amount of material to make a suitable test sample. The nanoindenter needs only enough to produce a thin film. This is an advantage, because less material needs to be produced. The past decades research has been done into developing models to describe the indentation process in terms of force, displacement, E modulus and hardness. The basic procedure is indenting a tip with a certain shape into the material, which is under investigation. The indentation is described by contact mechanics. One of the first people to look into this was Hertz in the late 19th century. He observed elliptical fringes when bringing two lenses into contact. He produced a model describing this contact. Later Boussinesq, Tabor and Sneddon [3] elaborated the model to different contact geometries. These results have been brought together by Johnson in Contact Mechanics [3]. In the past decade Oliver and Pharr [4],[5] as well as Hay et al.[6] have analysed and adjusted these results for more accurate descriptions of modern day indentation experiments. In the following paragraphs these models will be explained.

3.1 Hertzian Mechanics Herz developed a model to describe the stresses and deformations occurring during contact of spherical bodies [3]. Figure 3.1 depicts two spheres in contact. The dimensions are:

• Surface displacements δ1 and δ2, adding together to the total displacement δ • The contact area radius a • The relative radius of curvature R, derived from • 1/R=1/R1+1/R 2, with R1 and R2 being the significant radii of curvature of

respectively sphere 1 and 2 • Lateral and depth being characterized by length l,

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Figure 3.1: Contact of two spheres. [3]

The model however is only applicable to elastic contact. The model imposes the following constraints:

1. The surfaces are smooth, continuous and non-conforming: a<<R 2. Strains are small: a<<R 3. Each solid is an elastic half space: a<<R1,2 and a<<l 4. The surfaces are frictionless, so tangential loads are not transferred, only

normal loads. These constraints apply to most contact models, with the exception of a few when using special indenter shapes. Hertz observed that the deformation during contact of two bodies resembles two springs in series. He defined a reduced modules Ered as:

( ) ( )2

22

1

21 111

EEEred

νν −+

−= . Equation 3.1

Here νi and Ei are respectively the Poisson’s ratio and E-modulus of the respective bodies. For the case of solids of revolution e.i. spherical and parabolical indenters, the Hertz solution for describing the load is as follows [3]:

2/3

34 δREP red= Equation 3.2

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with P the applied load. For non-smooth and discontinuous shapes i.e. square or conical indenters Hertz’s model is not valid. Sneddon however solved the problem for these differences in geometries. For the conical shape he obtained the following result [3]:

( ) 2tan2 δϕπ redEP = Equation 3.3

with φ the half included angle of the cone. To calculate the hardness the following definition is used:

cAP

H max= Equation 3.4

Pmax is the load at maximum indentation depth and Ac is the projected area of the hardness impression. In the above cases the contact areas will be circular. Therefore Equation 3.5 2aAc π= The radius of contact a is determined for the spherical/parabolical case as follows [3]:

1/32 2

2

916 red

a PR RE

δ

= =

Equation 3.6

a Rδ= Equation 3.7 For the conical case a follows simply from the geometry as: ( )δϕtan=a Equation 3.8

3.2 Modern contact models Various people have investigated the above models. Oliver and Pharr[4] were some of the people to analyse the predictive capabilities of the models mentioned in 3.1. These models were only applicable to quasi-static loads: a full load-unload cycle was necessary to determine the quantities of interest. They also introduced a dynamic method, allowing for continuous measurement of the quantities. This method is called Dynamic Mechanical Analysis and is the same as the analysis performed on bulk materials. Paragraph 3.2.1 deals with the quasi-static analysis, whilst 3.2.2 will explain the DMA.

3.2.1 Quasi-static analysis A common quasi-static load-displacement curve for an indentation experiment is shown in Figure 3.2. The plot introduces the following quantities: initial unloading stiffness S, indentation displacement h and the final indentation depth after unloading hf. Figure 3.3 shows a cross section of an indentation.

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Figure 3.2: Common load displacement Figure 3.3: Cross section of an indent .[4]

curve showing main parameters of interest .[4] Here hs, the vertical displacement of the free surface, and hc, the contact depth or the vertical distance along which contact is made, are introduced. Thus hc is the depth at which the contact radius and area should be determined. Oliver and Pharr gave the following relation for hc:

maxmaxc

Ph hS

ε= − Equation 3.9

Here ε is empirically determined and dependent on the indenter geometry. It is 0.72 for conical indenters and 0.75 for paraboloids of revolution. For spheres Equation 3.9 simplifies to

( )max

2f

c

h hh

−= Equation 3.10

Because the unloading of a material is always elastic, the unloading part of the curve is of interest. Oliver and Pharr concluded that the results for the load-displacement relations given by Herz, Sneddon and others could be generalized and applied to many indenter shapes by using the following power law: Equation 3.11 m

fhhP )( −= α Here α and m are constants. It can be seen that m is related to the indenter shape; for m=3/2 the power law takes on the form of Equation 3.2 and for m=2 Equation 3.3. Furthermore in their paper from 1992 [4] they noted the following relation for S:

cred AEdhdPS

π2

== Equation 3.12

However in one of their most recent publications[5] they proposed the following relation:

cred AESπ

β 2= Equation 3.13

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They introduced the factor β, because finite element and other numerical research for various materials indenter shapes had shown that Equation 3.12 was only applicable to small deformations of elastic materials by a rigid axisymmetric indenter. The factor β is used to correct for non-circular, non-symmetric indenters, larger strains, elastic-plastic and work-hardening behavior. Many researchers have investigated and are investigating the many parameters that influence this factor. The indenters used in this study will be conical or spherical and therefore results pertaining to these geometries will be given in paragraph 3.2.3. Usually S is measured from the first portion of the unloading curve (see Figure 3.2). It can also be calculated from

dhdPS = . Equation 3.14

Now if Ac is known Ered can be calculated. The hardness H can also be calculated at this point by using Equation 3.4. To determine Ac Oliver and Pharr proposed a method to be explained in paragraph 3.2.4. Further when applying their method to indentation of thin films the following constraints need to be taken into account:

1. The film thickness has to be much larger than the indentation displacement. This is to avoid substrate effects. Deep indents can ‘feel’ the substrate and thus measure a combination of sample and substrate stiffness. A rule of thumb is that the indentation displacement h does not exceed 10% of the film thickness.

2. The width and length of the film is much larger than the dimensions of the contact area. This is derived from the elastic half-space constraint.

3. The substrate has to be much stiffer than the sample. This allows for neglecting substrate deformations.

4. The surface must be smooth. Every surface however has a roughness Ra. If h is smaller than the roughness the contact area can vary. Thus only depths deeper than the contact area will give reliable results.

3.2.2 Dynamic Mechanical Analysis (DMA) The DMA is based on basic dynamics. By applying an oscillating load, Pos with frequency ω the complete system of sample support, sample and load frame will show a dynamic response. This can be modelled with the dynamic model shown in Figure 3.4.

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Figure 3.4: Schematic representation of the dynamical model of the indenter. [4]

The constants in the model are: Cf = load-frame compliance Kf = load-frame stiffness, the inverse of the compliance S = contact stiffness Ks = column support stiffness D = damping of the system m = mass of indenter The mathematical representation of the response given in an amplitude and phase response are given by the following equations:

( )11 2 2(

Pos S C K m Df shω ω

ω

− −= + + − +

2 2) Equation 3.15

( ) 211)tan(

ω

ωθmKCS

D

sf −++= −−

Equation 3.16

with h the magnitude of the resulting oscillation and θ the phase angle between the force and displacement signals. Amplitude and phase of the displacement signal h as a result of Pos can be measured by a lock-in amplifier. All the constants except for S are known at forehand thus leaving S as the unknown in Equations 3.15 and 3.16. These other constants can be measured from free excitation: the system is excited in non-contact through a range of frequencies. The free excitation gives S=0. The machine compliance Cf can be measured from a static test with a known material and indenter geometry. The mass of the tip is also known. Thus only Ks and D are unknown, but can be solved from Equations 3.15, 3.16.

3.2.3 The tip area function To determine the elasticity and hardness one needs to know the contact area Ac. In paragraph 3.1 this was determined by assuming a circular contact area with contact

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radius a due to an axisymmetric indenter. This means one needs to know the exact shape of the indenter at forehand. This can be quite difficult and tedious to determine, because one has to investigate each indenter through e.i. SEM. Therefore Oliver and Pharr proposed a different method. They assumed Ac could be described by a polynomial of the following form: Equation 3.17 2 1/ 2 1/ 4

0 1 2 3 8....c c c c c cA C h C h C h C h C h= + + + + + 1/128

To determine the coefficients C0 to C8 they proposed the following calibration method. The indenter is to be indented into a material with known E-modulus and constant hardness over the depth range under examination. Measuring S, Pmax, hmax and filling these into Equation 3.12 gives Ac for certain values of hc. The polynomial for Ac, 3.17 can now be fitted to these, resulting in an area function suitable for the calibrated depth. This procedure also makes it easier to imply non-symmetric indenters such as cube-corners or Berkovich, (pyramidal) indenters.

3.2.4 The correction factor β The correction factor β was introduced to correct for non-circular, non-symmetric indenters, large strains and elastic-plastic or work hardening behaviour. The correction has been found necessary, because finite element simulations and careful analytical analysis have shown that applying Equation 3.12 can lead to errors. Only for the case of a rigid axisymmetric indenter with smooth profile and small deformations will β be 1 and is Equation 3.12 applicable. For other situations values of β=1.0055 to β=1.085 have been found [5],[6]. A number of reasons have been found for the errors. One major reason is the deviation from the smooth axisymmetric indenter profile. This leads to large strains at the non-smooth borders of the profile. Another factor that plays a role is the elastic-plastic and work-hardening behaviour. Hay et al.[6] investigated the deviation of β when a conical tip was used. In Sneddon’s result the radial displacement of the surface of the material in the contact area is not accounted for. This displacement is given by

( )( ) ( )

( )( )

−−−

−+−−

= 2

2

2 //11

/11

/lntan14

21ar

ar

ar

arruϕν

ν Equation 3.18

For φ=90º, a flat indenter, or ν=0.5, an incompressible material, u will be 0. This means the surface will not displace radially and thus conform to the indenter shape. For other shapes and materials u will be negative and the actual shape of the area will take the form depicted in Figure 3.5 (b).

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Figure 3.5: (a) Geometry used by Sneddon to describe indentation of an elastic half-space by a right circular cone. (b) Schematic representation of the actual shape of the deformed surface

predicted by Sneddon’s analysis when the radial displacements are taken into account. [6]

Hay et al. found through FEM analysis that the half included cone angle φ and the poisson’s ratio ν have quite an influence on β. For different angles they found different dependencies of β on ν. They showed that for small angles the following equation gives the best correction:

( )( )

1 21

4 1 tanν

βν ϕ−

= +−

Equation 3.18

This not only corrects Equation 3.12 but also corrects the contact radius leading to effectivea aβ= . Equation 3.19

The calibration of the contact area function is also influenced because rewriting Equation 3.12 and isolating Ac gives

( ) 22

2

112c

SA

Eνπ

β

−=

Equation 3.20

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4 AFM AFM is a versatile microscopic instrument due to its high resolution and the ability to be operated in different modes resulting in different contrast mechanisms. Therefore this chapter will explain AFM and it’s two major operating modes. These are contact mode and non-contact mode.

4.1 Principle of AFM AFM stands for Atomic Force Microscopy. It consists of a cantilever with a sharp tip at the end, piezo’s for positioning the tip and a feedback control loop. A schematic setup of the device is given in Figure 4.1.

Figure 4.1: Schematic setup of an AFM. In the Figure the piezo positions the cantilever, but it can

also be attached to the sample and position the sample. [7]

The resolution in lateral direction is determined by the tip radius easily reaching 10 nm, whilst the resolution in z-direction is limited by the accuracy of the piezo actuation in z-direction. So high resolution is feasible. Furthermore it is easy in use: no ultra high vacuum, no special sample preparations. These give it certain advantages over SEM, TEM and optical microscopy. In principle the tip is brought into close contact with a surface. Forces such as Van Der Waals forces cause the cantilever to deflect upon approaching the surface. This deflection can be used as a feedback signal during scanning of the surface. From this a 3-D topography can be constructed. Measuring the cantilever deflection also results in a measured force. Hence one not only has information on the surface topography, but also on the surface forces.

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Figure 4.2: Laser beam being deflected off a cantilever onto a four-quadrant photodiode to

measure the deflection. [8]

The deflection is usually measured by reflecting a laser off the cantilever and onto a four-quadrant photodiode, displayed in Figure 4.2. By adding and subtracting the signals of the quadrants one has information on the beam position. This diode has the ability not only to measure vertical deflections, but also lateral deflections. This is necessary, because the cantilever beam can display torsion, which results in lateral deflection of the laser beam. AFM can be operated in different modes and used for different purposes. It can measure topographies, but also surface stiffness, adhesion. One can also use tips with special coatings. Measurement of magnetic forces can be enabled this way. One can even apply voltages and currents over tip and sample, which can be used for electrochemistry.

4.2 Contact mode There are two modes of operating the AFM: contact and non-contact or tapping mode. In contact mode the tip is in direct contact with the surface under investigation. The tip is moved over the surface and either the deflection is measured to give a height image or the deflection is kept constant through a feedback loop with the z-piezo as actuator. At the same time one can measure the torsion of the beam. Torsion will occur because of lateral forces acting on the tip, constituting of friction and height differences. Because determining the torsion stiffness of the tip and beam is not easy, the lateral information is mostly interpreted qualitatively. A disadvantage is that the tip is in direct contact with the surface and thus exerting a force on it. For soft materials this can be a problem, because the force can be big enough to deform the surface plastically. An advantage however is that the scan speed is higher than that of the non-contact mode.

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4.3 Non-contact mode The non-contact mode is operated as follows. The beam is put into resonance by exciting it at its eigenfrequency. The amplitude of the resonance is the parameter that is controlled by feedback. One sets the free resonance amplitude to a certain value and assigns a smaller value as a setpoint for the resonance when the tip is near the surface. Now the tip is brought to the surface till the amplitude setpoint is reached. The tip is now tapping on the surface. The difference between the free resonance amplitude and the setpoint can lead to hard or soft tapping: the bigger the difference, the harder the tapping. Soft tapping will only skim the surface, while hard tapping might even penetrate it a bit. Measuring the z-piezo travel needed to keep the amplitude constant produces a height image. This is not the only information one can use in this mode. The dynamic response can be used as well. Different materials can give different responses. This results in different amplitudes and phases of the feedback signal. In general a dynamic response is affected by an imposed displacement or force. Therefore differences can occur due to height differences, but also properties that result in force differences, such as surface adhesion, stiffness or damping. The amount of tapping can influence the contrast of the amplitude and phase measurement. It also can result in measuring different effects because of the different force and penetration depth. The advantage of non-contact mode AFM is that samples are not loaded heavily and will not be damaged. This is necessary for polymers and biological samples. However, the scan speed is limited because of the feedback system: high speeds will need strong feedback, which can result in overshoot or instability.

4.4 Force spectroscopy Force spectroscopy can be used to determine surface forces. The force as a function of z-piezo travel is measured at a certain point. This is called a force-distance curve. Measuring force-distance curves in all the image pixels gives a force-volume image. A typical curve for bringing a tip into contact and retracting it is given in Figure 4.3. The attractive forces are negative and repulsive forces are positive.

4.4.1 Force-distance curves At large distance there is no force acting on the tip. This part is the zero-line, see Figure 4.3 (1). When it approaches the surface it starts to feel surface forces, such as Van Der Waals, capillary forces due to liquids (water), and electro-static and magnetic forces. These attract the tip to the surface at long range. At a certain point a maximum will be reached for these forces, which is called the pull-on force, Figure 4.3 (2). The tip is brought further into contact, which is called the contact-line, Figure 4.3 (3). The intersection between the contact-line and the prolongation of the zero-line is taken as the contact point. Here forces are zero and deflections of beam and deformation of sample surface are taken to be zero. Going past this point means indenting the tip into the surface. Contact can be elastic, elastic-plastic or fully plastic. After indenting the tip is retracted from the surface. Depending on the type of contact the tip retraction curve will follow the attraction curve (elastic) or lie below it ((elastic-)plastic). Another maximum will occur for the attractive forces when passing through the attractive region. This is called the pull-off force, Figure 4.3 (4). Due to 14

hysteresis it can be lager than the pull-on force. This is due to the stiffness of the cantilever.

Figure 4.3: AFM force distance curve: (1) tip approach; (2) jump to contact; (3) contact between the tip and the sample surface (repulsive forces); (4) adhesive forces and jump off contact; (5) tip

withdrawing. [7]

The stiffness determines the potential of the beam. This contributes to the Van Der Waals interaction resulting in the Lennard-Jones potential. The distance to the surface determines the equilibrium position of the tip. It is in the minimum of the Lennard-Jones potential. For small distances this minimum is determined by the Van Der Waals part of the total potential and for larger distances it is determined by the potential from the cantilever stiffness. For low stiffness there will be a jump from one equilibrium to another and there will be greater difference from the position at where this happens between retracting and attracting the tip to the surface. In other words there will be more hysteresis. Larger stiffness reduces these effects and can eliminate them. However this does reduce the force resolution of the cantilever, because it is harder to measure the smaller deflections resulting from the forces.

4.4.2 Tip-sample interactions during contact There are various models to describe the tip-sample interactions during contact. For no surface energy and relatively large applied forces the Hertzian/Sneddon analysis is applicable. In this study it is assumed no surface forces except for the indentation force interact between the tip and surface, therefore allowing for the Hertzian/Sneddon analysis modified by Oliver and Pharr described in chapter 3 to be applied. However if surface forces are to be taken into account one of the following four models is to be applied [9],[10]. For contact between two rigid spheres with a Lennard-Jones potential describing the forces between them the Bradley analysis is to be applied. Then there is the Derjaguin-Müller-Toporov (DMT) theory, which extends the Hertzian/Sneddon analysis by taking the surface forces around the contact area into account. This makes it applicable to systems with low adhesion and small tip radii. Further there is the Johnson-Kendall-Roberts (JKR) theory. This neglects long range surface forces outside the contact area and only short range forces within it. It is

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applied to highly adhesive systems with low stiffness and large tip radii. The final theory is the Maugis theory. It uses a dimensionless parameter to take into account all of the material and geometry parameters, making it applicable to all situations. Figure 4.4 gives an idea of what the interactions are for the different models.

Figure 4.4: Schematic representation of interaction regimes for the different models. [11]

4.4.3 Converting raw data to force-displacement curves To be able to calculate hardness and stiffness a number of things have to been done, because the raw data is actually an output of photodiode current I as a function of z-piezo travel z. The current has to be converted into a deflection and then into a force. First the point of contact is determined as defined in 4.4.1. The data before point of contact is left out. See Figures 4.5 and 4.6. Then the conversion from current to deflection is done which is fairly straightforward, see Figure 4.7. A surface with a stiffness much greater than the cantilever stiffness is used. The assumption is that this surface will not deform, when the tip is brought into contact. Any extra travel of the z-piezo towards the surface will cause the cantilever to deflect. This is what the photodiode measures. Thus a conversion factor dz dI=K is obtained, with z being the z-piezo travel and I the photodiode current. The maximum deflection that can be measured is limited by the photodiode, because it saturates at a certain level. The next step is to convert deflection to force, see Figure 4.8. This is done by implying Hook’s law: F kc cδ= . Here kc is the cantilever stiffness and δc is the cantilever deflection. Thus kc needs to be known. Cantilever manufacturers give a specification, but the spread of the specification is large. Therefore this needs to be measured as well. This will be described in 4.4.4. Here another limit is imposed, because the relation is based on elastic deformation, therefore limiting the deflection of the beam and thus the measured force. This can be checked by plotting the force against the measured cantilever deflection and checking if the curve shows the linearity described by Hook’s law. The point where the curve starts to deviate should be taken as maximum deflection. Crossing this point should be avoided, because the cantilever will be damaged above it. The final step is plotting the force as a function of the displacement of the surface h, which is illustrated in Figure 4.9. For a rigid cantilever h would equal z and for a rigid surface δc will equal z. Therefore the relation simply is:

ch z δ= − Equation 4.1

Thus a plot of force as function of surface displacement is obtained and the analysis of Oliver and Pharr can be applied.

16

Figure 4.5: Raw Current vs. z-piezo

displacement curve. Figure 4.6: Zero point determined in curve.

Figure 4.7: Current converted to cantilever

deflection. Figure 4.8: Cantilever deflection converted

to force.

Figure 4.9: Force plotted as function of sample displacement.

17

4.4.4 Cantilever stiffness measurement There are various methods to measure the stiffness of a cantilever. One can simply determine the exact dimensions of the beam and it’s material properties and use the beam formulas from elastic deformation theory to calculate it. This would require a good imaging technique as well as knowledge of the material the beam is made of. Imaging can be time consuming and one cantilever can contain multiple materials making it difficult to determine the material properties. Another method is the thermal vibration method, where the tip is vibrated in almost 0 K environment. The vibration energy is confined according to the equipartion theorem, and leaves the stiffness as the only unknown. This requires a specific environment, making it also not an easy method. Therefore another method has been used. This method was developed by Sader et.al.[12,13]. It is based on the free resonance of the cantilever in a medium. In Sader et.al.[12] the following formula for the stiffness was determined: ( )20.1906c f f ik b LQ f fρ ω ω= Γ Equation 4.2

Here ρf is the density of the medium, b is the width of the cantilever, L the length, Qf is the quality factor of the resonance, ωf the free resonance frequency and Γi the imaginary part of a hydrodynamic function depending on ωf. Qf and ωf can be determined from a resonance spectrum of the tip, which is easily obtained within the AFM software. The width and length can easily be measured with an optical microscope. The hydrodynamic function Γ is given by Sader et.al.[13] : i

( )

( )1

0

4 Re1

Re Rec

iK i i

i K i i

−Γ = +

− Equation 4.4

real iiΩ = Ω + Ω Equation 4.5 2

3 4

6 2

3 4

6

(0.91324-0.48274 +0.46842

-0.12886 +0.044055 -0.0035117 +0.00069085 )/(1-0.56964 +0.48690 -0.13444 +0.045155 -0.0035862 +0.00069085 )

real τ τ

τ τ 5

5

τ

τ τ

τ τ

τ

Ω =

τ

τ

Equation 4.6

2

3 4

5 2

3 4 5

6

(-0.024134-0.029256 +0.016294

-0.00010961 +0.000064577 -0.000044510 )/(1-0.59702 +0.55182 -0.18357 +0.079156 -0.014369 +0.0028361 )

i τ τ

τ τ

τ τ

τ τ τ

τ

Ω =

τ Equation 4.7

In these equations 10log Reτ = , with 2

4f f bρ ω

Reη

= and η is the medium viscosity.

The modified Bessel functions of the third kind K0 and K1 were used which are a function of Rei i− . Results from Sader et.al had been compared in the same publication to other methods and showed an error of less than 5%. This method yielded a quick and good measurement of the cantilever stiffness.

18

5 Experimental

5.1 Sample preparation The PMMA-terpyridine used in this study had a Mn of 6600 g/mol, a PDI 2.06 and a terpyridine content of 10 Mol% of the PMMA. It is assumed that there are enough terpyridine groups to form crosslinks. From this a solution of 68 mg/ml was made in chloroform. Six samples were drop cast on quartz surfaces. The films were left to slowly evaporate by placing them in a container saturated with chloroform vapour. This resulted in 20 µm thick films. The thickness was measured with a Fogale Zoomsurf 3D microscope, which works with Michelson interferometry. The next step was to crosslink the films. This was done by dipping the films in a 0.045 M solution of FeCl2 in methanol and then subsequently rinsing with distilled water. Different degrees of cross-linking were achieved by varying the dipping time. The times are noted in Table 5.1. The rinsing was done to wash any left over iron off the surface. It was assumed here that the cross-linking was only dependant on the availability of Fe2+-ions and not on the freedom of mobility of the chains, which could be influenced by the time the surface was in contact with the solvent.

Sample 1 2 3 4 5 6 Time Uncrosslinked 1 s 3 s 10 s 30 s 90 s

Table 5.1: Cross-linking times for the samples. Measuring the amount of cross-linking was done with a Lambda 45 UV-VIS spectrometer from Perkin Elmer Instruments. Sample 6 was used to obtain all measurements of the amount of cross-linking. This was done by dipping it and then directly measuring the amount of cross-linking. This process was repeated until the measured spectrum showed no more increase in absorption for the specific group, indicating all terpyridine groups had crosslinked. The amount of cross-linking was then given as a percentage of the maximum amount. After this the samples were marked on the bottom with black waterproof marker and glued to steel disks for placement in the AFM and nanoindenter.

5.2 Sample indentation Indentation was firstly done with the Hysitron triboindenter equipped with a nanoDMA unit for dynamic mechanical analysis and continuous stiffness measurement. It was however only operated in quasi-static mode. The analysis by Oliver and Pharr is incorporated in the software of the triboindenter. So the hardness was obtained by applying Equation 3.4, the E-modulus through the combination of Equations 3.1 and 3.11 and the plastic indentation depth from Equation 3.10. The correction factor β is not taken into account by the software. The Poisson’s ratio ν of the PMMA was assumed to be constant at 0.35 for all experiments.The tip used by the triboindenter was a conical tip with 5 µm radius. Indentation with the triboindenter was load controlled. However the control was not very accurate. There was on average an 8% error, but for very small loads this could even be 20%. On every sample 5 measurements were done. One measurement consisted of 10 indents starting from 2 till 20 µN with steps of 2 µN and 20 indents starting at 25 µN up till 1000 µN

19

with steps of 51 µN. The indents were made in a grid with 25 µm spacing between the indents. The loading and unloading rates were set at P/4 µN/s assuming that at these rates no time dependent effects would take place. A schematic representation of the experimental apparatus is shown in Figure 5.1.

Figure 5.1: The experimental setup of a dedicated nanoindenter. A is the sample, B the indenter,

C the load application coil, D indentation column guide springs and E the capacitive displacement sensor.

Secondly, the AFM was operated in force-spectroscopy mode and used to perform indents. The AFM used was an NT-MDT Solver Pro Basic. Commercial silicon cantilevers with high eigenfrequency were used. Because of wear several cantilevers were used. The specifications by the manufacturer for the tip radius, height and half included cone angle were used. The stiffness of these cantilevers was determined via the method given in 4.4.4. The cantilever properties are summed in Table 5.2.

Cantilever Eigenfrequency ωf [kHz]

Stiffness kc [N/m]

Tip angle [˚]

Tip radius [nm]

NSC05 A 290.42 25.74 20 10 NSC05 B 296.10 27.18 20 10

Table 5.2 Characteristics of used AFM cantilevers. Because the indents had to be done manually in force spectroscopy mode, only three sets of measurements were performed. The only input in force-spectroscopy mode was the z-piezo travel. This can be inaccurate due to drift. Therefore the sample displacement was not consistent every time. The indents were performed in the following order: 0.1 to 1 nm with steps of 0.1 nm, 1.5 nm to 6 nm with steps of 0.5 nm, 8 nm to 26 nm with steps of 2 nm and 36 nm to 136 nm with steps of 10 nm. The small tip radius allowed for smaller spacing between indents: 500 nm. The raw data was converted by following the procedure in 4.4.3. After this the method of Oliver and Pharr was used with the exception of the tip area function calibration. Models for conical and spherical tips were fitted to obtained unloading curves and the best fit was used for the calculations. From this fit it was also determined which analytical solution was to be used for the contact area. Determining the contact area from the contact area calibration function would probably result in altering the tip thus rendering it useless. Thus Equations 3.5, 3.7 and 3.8 were used. The correction factor β was also employed.

20

5.3 Sample scanning Sample scanning was done with the same AFM as for indenting. Environment conditions were ambient. The scans were made after indenting with the Hysitron machine and before and after the indents were made with the AFM. Scans were performed in non-contact mode to avoid damage to the surface. The resolution was always set to 512 by 512 pixels. The topography obtained from these scans was used to explain results from the indentation experiments. Large scans were made of which the size would depend on how well it represented the overall surface. This was determined after visual inspection of which the results will be given in section 6.1. In some cases close ups were made of 500 nm by 500 nm to be able to inspect potential molecular effects.

21

6 Results

6.1 Sample preparation results Figure 6.1 shows how the samples looked like after preparation. One can see the effect of the Fe2+-terpyridine complex formation: it turned purple. It was observed that sample 2 turned purple but remained transparent. Note that 2 was scratched afterwards to have a marking during indentation. This is the clear cross scratch in the middle and they are not an effect of the cross-linking. In the next step, 3, the film turned opaque from the centre outwards and the transparent part turned to a deeper color. 4 shows that the next step turned the film completely opaque and induced delamination in the centre after the sample was removed from the Fe2+-solution. Further cross-linking induced further delamination in 5. However in this sample not all of it turned opaque and as a result did not delaminate. This can be seen around the top left corner, where the centre of it has turned opaque. 6 finally shows the same result as 5. The dark flakes on the substrate are loose pieces of delaminated film. These delaminated parts appeared very brittle. Because 3 and 5 had transparent and opaque parts, indentations were performed on both these types of area. The transparent parts were labelled 3T and 5T, respectively and the opaque parts 3P and 5P. 6 was not used for indentation measurements, because the visual inspection along with the UV-VIS results in the next paragraph determined it to be equal to 5 in the amount of cross-linking. It was also determined that areas of 50 µm by 50 µm would be representative of the different surface types. This was taken as the size of the large AFM scans.

Figure 6.1: Picture of the result of cross-linking the samples. The samples were glued to steel disks for placing in the nanoindenter and in the AFM after being marked on the bottom with

black marker.

22

6.2 UV-vis spectra Directly after removing the sample from the Fe2+-solution the UV-VIS spectrum was recorded. The complete delamination seen in 5 and 6 only occurred long after the measurement was done. Thus the UV-VIS spectra of the last cross-linking times were still obtainable. Figure 6.2 shows the spectra obtained form the UV-vis spectrometer for the different cross-linked samples. A clear increase in absorption for increasing cross-linking time could be seen at the 561 nm wavelength where the terpyridine-Fe2+ complex absorbs, see Figure 6.3. 5 showed a maximum absorption, after which 6 showed a slight decrease in absorption, which may be a result of delamination. This indicates that already all terpyridines had complexed with Fe2+. It was assumed that this meant that all accessible groups had formed cross-links to other chains. Therefore 5 was taken as 100% cross-linked. The assumption was verified by a small experiment. 3 was dipped in pure methanol till the same amount of time had been reached as 5 had been dipped. The hypothesis was that 3 had enough iron to form the cross-links but not enough time in the solvent for the chains to rearrange. However the extra time in the methanol only showed a minor increase in cross-linking. The delamination however did increase a lot. Thus it was concluded from this experiment that the cross-linking is mostly dependant on the amount of available ions. It also showed that the solvent helps the cross-linking process, but is not the main factor.

Figure 6.2: UV-vis spectra for the six samples.

23

Figure 6.3: Amount of cross-linking as function of time. Left in arbitrary units, right in

percentages of the maximimum.

6.3 Hysitron indentation The results from the Hysitron indentations have been split up in three paragraphs. One for the E-modulus, one for the hardness and one for the plastic indentation depth.

6.3.1 E-modulus Figure 6.4 to 6.6 show the E-modulus as a function of maximum indentation depth. In 6.4 the standard deviation is plotted along to give an impression of the spread. Figure 6.5 is plotted without the standard deviations and is a close up whilst Figure 6.6 is the same as Figure 6.5 without the standard deviation.

Figure 6.4: Plot of E-modulus vs. maximum indentation depth with standard deviations.

24

Figure 6.5: Close up of the plot of E-modulus vs. maximum indentation depth.

Figure 6.6: Close-up of the plot of E-modulus vs. maximum indentation depth

without standard deviation.

25

First the large spread below about 20 nm was observed in Figure 6.5. This might have been a result of the surface roughness and of the indenter roughness. Therefore results from below this depth have not been taken along in any averages. Further it seemed the E-modulus is independent of the depth, except for the transparent part of sample 5. This showed a jump around 150 nm. An average was determined for every measurement. This was plotted in Figure 6.7 as function of the percentage of cross-linking. See appendix A for numerical results. The uncross-linked sample, 1, had an average E of 3.78 GPa, which matches the average literature value of 4 GPa for PMMA. At about 35% cross-linking the E-modulus had dropped slightly, but not significantly, see 2. At 55%, 3T still revealed no deviation from the uncross-linked sample, but 3P showed a decrease to 2.5 GPa. This decrease was also seen in 4 at 80% and in 5P at 100%. However 5T showed almost a twofold increase of E at transparent parts. Figure 6.6 showed that at depths below approximately 150 nm E was about 5 GPa and between 150 and 250 nm E is 7.5 GPa.

Figure 6.7: Average E-modulus plotted with standard deviation as function of the percentage of cross-linking. The dots are the results from measurements on the transparent parts, pentagrams

are for the opaque parts. In short there seemed to be a dependency on the amount of cross-linking and whether the surface turned opaque or remained transparent. For the parts that remained transparent virtually no change could be seen until 100% cross-linking was reached. Then the E-modulus was almost doubled. This could be explained by the fact that polymers get their stiffness from the amount of entanglements and bonds within the network. By cross-linking extra physical entanglements are introduced, thus increasing the stiffness. Why only an effect was seen at 100% was probably due to the absolute amount of crosslinks formed. The terpyridine content was only 10% in the PMMA. The parts that turned opaque showed a decrease in E-modulus. An explanation for this might be sought in a change of surface topography. This will be clarified at the end of paragraph 6.5, where topographical results will be presented. Furthermore, it seemed the transparent part would be favorable as it yielded an increase in stiffness.

26

6.3.2 Hardness The hardness was set out as a function of maximum indentation depths in Figures 6.8, till 6.10. Figure 6.8 shows the full extent of the results. Figure 6.9 is a close up of 6.8 to show the spread better. Figure 6.10 is a plot of the results without the spread to provide a better view. Again it was noticed from Figure 6.8 the large amount of spread below 20 nm. Also the opaque surface lead to a decrease in hardness. This could be seen for 3P, 4 and 5P. The transparent surfaces, 2, 3T and 5T did not show an increase. This was clearer from Figure 6.11, where the average hardness as function of percentage of cross-linking is given. Appendix B has the numerical results. From this it could be concluded that for the transparent parts the hardness did not change and remained at about 170 MPa. The opaque surfaces again showed a decrease; the hardness was almost reduced to a third of the uncross-linked value. Again this gave reason to prefer transparent films.

Figure 6.8: Hardness as a function of maximum indentation depth. The standard deviation is

plotted along to give an impression of the spread.

27

Figure 6.9: Close up of the hardness as function of the maximum indentation depth plotted with

the standard deviation.

Figure 6.10: Hardness as function of maximum indentation depth plotted without standard

deviation.

28

Figure 6.11: Average hardness set out against the percentage of cross-linking. The dots are the

results of measurements on transparent parts, the pentagrams are from the opaque parts.

6.3.3 Resulting deformations The resulting deformations can be described by the plastic indentation depth as function of the maximum indentation depth, the plastic indentation depth as function of applied load and the maximum indentation depth as function of the applied load. The plastic indentation depth was given as a function of the maximum indentation depth in Figure 6.12 and 6.13. In Figure 6.12 the standard deviation was plotted along to show the spread, whilst in Figure 6.13 a close up was given for a better overview. The first observation was that the plastic indentation depth was almost zero up till 100 nm maximum indentation depth. For deeper maximum depths 2 and 3T did not differ from 1. For 5T however, the plastic indentation depth did increase for the same maximum indentation depth compared to the uncross-linked sample. The opaque surfaces showed a tremendous increase in plastic indentation depth as well as maximum indentation depth. The path of the increase followed the same trend as the increase for 5T. These results lead to the observation that cross-linking increased the plastic indentation depth, with the most effect seen in the opaque parts. This means that the permanent deformation after unloading becomes larger for increasing cross-linking.

29

Figure 6.12: Plastic indentation depth hf as function of the maximum indentation depth plotted

with the standard deviation.

Figure 6.13: Close up of the plastic indentation depth hf as function of the maximum indentation

depth displayed with standard deviation.

30

Figure 6.14 and 6.15 show plots of the plastic indentation depth as function of the applied load for respectively all samples and for the transparent parts. Figure 6.14 also shows that the plastic indentation depth changed only slightly for the amount of cross-linking on the transparent surfaces. The increase was almost a factor 2 at the same applied load between 1 and 5T. The opaque surfaces showed a far greater increase, almost tenfold on average, but the opaque samples also showed a lot of spread.

Figure 6.14: Plastic indentation depth as function of applied load.

Figure 6.15: The plastic indentation depth hf as function of the maximum indentation depth for

the transparent samples.

31

The maximum indentation depth as function of applied load is plot in Figure 6.16. Figure 6.17 shows a normalized plot of the maximum indentation depth as function of the applied load for the transparent parts. The maximum indentation depth was normalized to the results from the uncross-linked sample. The opaque parts were left out for a better overview. It is clear that the maximum indentation depth increases a lot with increased cross-linking for the opaque surfaces. From the normalized plot in Figure 6.17 it was concluded that the increase in maximum indentation depth was more or less constant with respect to the applied load. Again only at 100% cross-linking, 5T, an effect could be seen. Again a jump was observed at about 140 nm. On average the decrease was about 15% of the maximum indentation depth. This effect is in accordance with the increased E-modulus.

0 100 200 300 400 500 600 700 800 900 10000

200

400

600

800

1000

1200

1400

1600

1800

2000Maximum indentation depth vs. applied load

Pmax [muN]

hmax

[nm

]

Sample 2 Sample 3 (transparent) Sample 5 (transparent) Sample 1 (uncrosslinked)

Sample 2 Sample 3 (transparent) Sample 3 (opaque) Sample 4 Sample 5 (transparent) Sample 5 (opaque) Sample 1 (uncrosslinked)

Figure 6.16: Maximum indentation depth as function of the applied load.

32

0 100 200 300 400 500 600 700 800 900 10000.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8Maximum indentation depth vs. applied load

Pmax [muN]

hmax

/hm

ax(s

ampl

e 1)

[-]

Sample 2 Sample 3 (transparent) Sample 5 (transparent) Sample 1 (uncrosslinked)

Figure 6.17: Normalized maximum indentation depth as function of applied load for the

transparent surfaces.

6.4 AFM indentation One set of indents on 1 was analysed. Figure 6.18 showed the result for the E-modulus and Figure 6.19 the result for the hardness. These results were compared to the results obtained from the Hysitron indents. They clearly did not match. The E-modulus found in the Hysitron experiments was constant over depth and was 3.78 GPa for 1. The E-modulus from the AFM indents was not constant, nor did it have the same value as the Hysitron value. However it did seem to come near the Hysitron results for larger depths. Further both graphs showed that the results had a lot of spread especially below the 30 nm. Like in the Hysitron results this might have been an effect of the surface roughness and will be addressed in paragraph 6.5. The main problem here lied in the determination of the contact area. The analytical way didn’t seem to be adequate. This was evident from the deviation from the Hysitron results. Errors in determining the contact area could have lied in the tip radius and tip angle. These were taken from the factory specifications, without accompanying tolerances. The result also depended on how well the data was fit and how correct the model applied to the indenter shape. Another impracticality was the poor control capability of load and displacement during indentation. The z-piezo displacement was the only way of control. Piezo drift also played a hampering role. Furthermore the photo diode saturation resulted in the upper limit of maximum indentation depth to be so low. For these above mentioned reasons AFM indentation was found not suitable for studying the sought material parameters. To be able to perform nanoindentation with an AFM the most crucial part would be to determine the area function. Imaging the tip at forehand seems to be the only way to

33

determine the shape and thus an area function. This could be done with an (E)SEM for plain silicon tips. However, cantilevers with diamond tips are available. This would enable the use of contact area calibration method, because the tip would not wear during calibration. The control problems should be overcome by using different and better controllers and piezo’s. The photodiode saturation can be overcome by using a stiffer cantilever: more force will be needed to obtain the same deflection as a less stiff one before the same photodiode intensity is reached.

Figure 6.18: E-modulus as function of maximum indentation depth for 1.

Figure 6.19: Hardness H as function of maximum indentation depth for 1.

34

6.5 AFM imaging From each surface a topography was investigated to give an idea of the roughness. In some cases the phase image was also recorded to see if any non-topographic abnormalities could be seen.

6.5.1 Sample 1

Figure 6.20: Topography of sample 1, 50 by 50 µm, 512 by 512 pixels. Encircled are four indents

made by the Hysitron.

Figure 6.21: 500 by 500 nm scan at 512 by 512 pixels of sample 1. Left topography, right phase

image. The large scan revealed the topography depicted in Figure 6.20. This also revealed four indents made by the Hysitron: two large indents 25 µm apart and two smaller indents 25 µm lower. The small white dots with approximately 1 µm diameter were dust particles. The surface roughness Ra measured here was 1.4 nm. This can clearly be seen in the close up depicted in Figure 6.21 left. The phase image on the right shows no abnormalities. Therefore it was concluded that the uncross-linked film was smooth and completely amorphous.

6.5.2 Sample 2 Because the results from paragraph 6.1 gave the impression that the cross-linking started in the centre and spread out to the rim of the sample, images were made of the centre and at the rim. These are displayed in respectively Figures 6.22 and 6.23. The centre clearly showed a difference from the rim. The rim appeared still smooth whilst the centre started forming a coral like surface. The Ra of the centre surface was about 28 nm and the Ra at the rim about 1.5 nm. This again indicated that the cross-linking started at the centre and spread out to the rim. A close up of the rim can be seen in

35

Figure 6.24. Again not more than the surface roughness could be seen. No close up of the centre could be obtained.

Figure 6.22: 50µm by 50 µm topography with 512 by 512 pixel resolution of the centre of sample 2.

Figure 6.23: 50µm by 50 µm topography with 512 by 512 pixel resolution of the rim

of sample 2.

Figure 6.24 500 by 500 nm scan at 512 by 512 pixels of the rim of sample 2. Left topography,

right phase image.

6.5.3 Sample 3 Figure 6.25 and 6.26 show respectively the topography of the centre, opaque part, 3P and of the transparent rim 3T. Again the effect of the cross-linking was stronger at the centre than at the rim. Another observation was that the material started grouping much more together forming broader structures compared to 2. The Ra at the centre was about 630 nm and at the rim it was 85 nm. The roughness was too big to be able to obtain suitable close up scans.

Figure 6.25: 50µm by 50 µm topography

with 512 by 512 pixel resolution of the opaque centre of sample 3.

Figure 6.26: 50µm by 50 µm topography with 512 by 512 pixel resolution of the

transparent rim of sample 3.

36

6.5.4 Sample 4 The topography of sample 4 in Figure 6.27 showed another increase in broadening of the coral structure. The roughness increased further to about 1.1 µm, also prohibiting a close-up investigation.

Figure 6.27: 50µm by 50 µm topography with 512 by 512 pixel resolution of sample 4.

6.5.5 Sample 5 The topography of the opaque part 5P can be seen in Figure 6.28, whilst Figure 6.29 shows the topography of the transparent part 5T. Again the broadening of the coral structure was continued in 5P. The Ra measured there was about 1.5 µm. 5T however did not show much difference from the rim of sample 2. The Ra here was only about 1.4 nm again. The encircled holes in Figure 6.29 are the Hysitron indents. Figure 6.30 shows a close up 5T. No morphological differences from 1 were seen.

Figure 6.28 50µm by 50 µm topography with 512 by 512 pixel resolution of 5P.

Figure 6.29 50µm by 50 µm topography with 512 by 512 pixel resolution of 5T. The

Hysitron indents are encircled.

Figure 6.30 500 by 500 nm scan at 512 by 512 pixels of the transparent part of sample 5. Left

topography, right phase image. The curvature at the bottom is due to piezo creep.

37

6.5.6 Topographic results In short from the previous paragraphs the following observations could be summarised. The first was that the cross-linking induced from the centre outwards more and more surface roughness. This lead to the surface turning opaque. The structure of the opaque surface was like a coral, of which the branches kept growing thicker as the cross-linking increased. This ‘coral’ idea would explain the great increase in plastic and maximum indentation depth and loss of hardness and stiffness. The coral structure might have cavities in it, which offer little resistance to any object penetrating the surface. Also the contact area would be incorrect because the indenter and surface would not be in full contact due to the empty areas underneath the tip. The measured surface roughness for the opaque parts was so big that most of the indents lied within the surface roughness and were therefore not reliable. For the transparent parts the surface roughness was 1 to 2 nm. The spread in the graphs of E vs. hmax and H vs. hmax however showed large spread to about 20 nm, indicating a roughness of this order. Since the surface had only 1 to 2 nm roughness, this might have indicated that the indenter had some roughness. This could have been due to the fabrication of the indenter itself, but it could also have been due to bits of polymer sticking to the indenter after indentation. The reason for the coral formation is not clear. The increase of thickness of the branches might be due to clotting of chains due to the cross-linking. Most likely the solvent creates the ‘coral’ structure. It first swells the film by forming droplets within. When evaporating it leaves holes behind.

38

39

7 Conclusions and recommendations From the visual inspection it was clear that two types of surfaces were formed during the cross-linking, an opaque part and a transparent part. The AFM topographies revealed that the surface roughness of the opaque parts increased with increasing amount of cross-linking, whilst the roughness of the transparent part did not increase. They remained around 1 to 2 nm. The roughness in the opaque parts was due to the formation of a coral like structure of which the branches grew thicker with increasing amount of cross-linking. The surface roughness of the opaque parts was actually bigger than the maximum indentation depths, thus making the results for the opaque parts not very reliable. The difference between opaque and transparent also had its effect on the mechanical properties. The E-modulus for the uncross-linked material was 3.78 GPa 0.29 GPa and the hardness H was 176.3 MPa

±± 5.5 MPa.

For increased cross-linking the opaque parts showed a reduction in E-modulus of about 50% after 50% cross-linking was reached. After this it did not change for increased cross-linking. The hardness reduced to about 30% of the uncross-linked value at about 50% cross-linking, where after it also did not change. The opaque parts showed a great increase in plastic indentation depth. This was clear from Figure 6.14, where the plastic indentation depth was plotted as function of the applied load. The increase was on average about tenfold. The maximum indentation depth also increased in the same way as the plastic indentation depth. The transparent parts did show interesting results, but only at 100% cross-linking. Why this was only observed at 100% might have been due to the amount of terpyridine groups in the polymer. This was only 10%. Therefore this might not have been enough at lower cross-link amounts to have a significant effect. The increase in E-modulus was from 3.78 GPa to 6.32 GPa ± 1.0 GPa. A jump was observed to higher stiffness and smaller maximum indentation depth at about 140 nm. Why this happened could not be explained. Furthermore, the hardness did not show any significant increase or decrease in the transparent parts as function of the amount of cross-linking. The plastic indentation depth only showed a slight increase. Figure 6.14 showed that this was not more than twice the amount of the uncross-linked sample at 100% cross-linking. The maximum indentation depth showed a decrease of about 15% at 100% cross-linking, which is expectable if the E-modulus increases. What the exact reason was for the difference between coral formation and transparency was not clear. Since it did not form all over the surface it was probably not entirely due to the cross-linking. The transparent parts were clearly preferable. Perhaps experiments with different solvents or post annealing could find a solution to this ‘coral’ formation. During the measurement of the amount of cross-linking, the chain mobility due to the solvent was not taken into account. It was also assumed that every Fe2+-ion formed a bond with two terpyridines from different chains. The influence of the solvent on the chain mobility could be investigated by seeing if any difference occurs if a film is dipped only in a Fe2+-solution or partially in a Fe2+-solution and afterwards in a pure solvent. The implementation of indentation with AFM was not a success. This was mainly because the contact area was not well definable. The best method is applying the contact area calibration function described in paragraph 3.1.3. This would only be feasible for diamond tips, because at this scale silicon tips would be damaged already

during calibration. If silicon tips would be implied, imaging them with (E)SEM would be advisable. Furthermore the control setup of the AFM has to be very accurate. For further research it would be also of interest to investigate what influence the percentage of terpyiridine groups would have on the mechanical properties. It would also be interesting to do the DMA analysis to learn about time dependant behaviour. In short, it has been shown that when the structure of the film doesn’t change an increase in E-modulus of PMMA can be obtained through cross-linking with the use of terpyridines and iron ions. The increase was not very large. Perhaps applying this system to softer polymers might yield a more significant increase.

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References

[1] Hofmeier, H., Metallo-supramolecular architectures based on terpyridine metal complexes, Ph.D. Thesis, Technical University of Eindhoven, Eindhoven, 2004

[2] http://www.shu.ac.uk/schools/sci/chem/tutorials/molspec/uvvisab1.htm [3] Johnson, K.L., Contact Mechanics, (Cambridge University Press, London,

1987 [4] Oliver, W.C., Pharr, G.M., J. Mater. Res. 1992, 7, 1564-1583 [5] Oliver, W.C., Pharr, G.M., J. Mater. Res. 2004, 19, 3-20 [6] Hay, J.C., Bolshakov, A., Pharr, G.M., J. Mater. Res. 1999, 14, 2296-2305 [7] Tromas, C., Garcia, R., Topics in Current Chemistry 2002, 218, 115-132 [8] Vellinga, W.P., Lecture notes for course Microscopic Measurement

Techniques, 2004 [9] Capella, B., Dielter, G., Surf.Sci.Reports 1999, 34, 1-104 [10] Burnham, N.A., Colton, R.J., Pollock, H.M., Nanotechnology 1993, 4, 64-

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Appendices

Appendix A Sample 1 2 3T 3P 4 5T 5P Emean [GPa]

3.7803 3.4452 3.6593 2.5205 2.1052 6.3294 2.1112

σE [GPa]

0.2953 0.1467 0.1833 0.7630 0.3361 1.0954 0.7517

σE [%] 7.8 4.3 5.0 30.3 16.0 17.3 35.6 Table A. 1: Statistical values, average E per sample, standard deviation in [GPa] and [%].

Appendix B Sample 1 2 3T 3P 4 5T 5P Hmean [GPa]

0.1763 0.1651 0.1576 0.0930 0.0686 0.1764 0.0615

σH [GPa]

0.0055 0.0142 0.0147 0.0464 0.0158 0.0140 0.0261

σH [%] 3.1 8.6 9.3 49.9 23 8.0 42.4 Table A.2: Statistical values, average H per sample, standard deviation in [GPa] and [%].

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