Inhomogeneity at the surface: multi-scale study of the optical properties of a smart polymer

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Department of Physics Master Degree in Physics

Universit`a degli Studi di Pisa, Academic Year 2018/2019

Inhomogeneity at the surface: multi-scale study

of the optical properties of a smart polymer

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“The relevant equation is: Knowledge = power = energy = matter = mass; a good bookshop is just a genteel Black Hole that knows how to read.”

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Introduction

The field of material science is an ever-expanding one, with fascinating and carefully engineered new materials being produced at an increasingly fast pace [1].

With such a budding field, more and more research is needed in order to gain a better under-standing of the properties of such materials, explore the untapped potential of already produced one, explore new applications, and aid in the invention of even more advanced ones in the future.

Within the field of material science, the so-called smart materials have risen to prominence, due to their incredibly vast range of applications and potentially ground-breaking characteristics [2], [3].

In 1990, Takagi defined intelligent materials1_{as “materials which respond to environmental} changes at the most optimum conditions and manifest their own functions according to the changes” [4]; our work revolves around the study of the optical properties of one of such materials, more specifically of a thermochromic host-guest system composed of a perylene bisimide derivative dye dispersed within a linear low-density polyethylene (LLDPE) matrix. The samples analysed were provided, in the form of thick films, by Prof. A. Pucci of the Department of Chemistry and Industrial Chemistry at the University of Pisa.

The experiment described in this thesis, together with our previous work on the same material

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[5], forms a larger picture, one in which we show that the nominal homogeneity of the studied material does not hold true at sufficiently small scales.

As previously mentioned, the studied material exhibits the interesting characteristic of thermochromism, which is the ability of a material illuminated by an external source to change colour upon thermal stimuli; when the change is reversible, as is the case for the studied samples, the material gets the smart function of a temperature sensor [6].

Our dye can be found in two aggregation forms: single molecules and supramolecular aggre-gates, which can be distinguished by their different wavelength of peak fluorescence. As per the model used in both our previous study and in this thesis work, we identify the fluorescence of the disaggregated form of the dye with the emission in the green spectral region and that of the aggregates with the emission in the red spectral region [7], [8].

In our previous study [5], we have shown how the local topography, along with other parameters, impacts the equilibrium between these two forms on a nanometric scale, by means of a Scanning Near-Field Optical Microscopy (SNOM) probe. As far as we know, this was the first experiment of this kind ever conducted on this type of materials.

In the present work, we expanded the scope of our research, first by performing spectroscopic measurements on the macroscopic scale, and then by acquiring fluorescence emission maps of the sample’s surface on the mesoscopic scale. In order to do so, the candidate personally designed and assembled a confocal microscope.

This change in experimental set-up allowed us to study the material at different temperatures in the extremely relevant physiological range and explore its potential as a sensor on the microscopic scale, a daunting task indeed when performed with a SNOM, due to the inherent difficulty in operating at different temperatures.

Whilst studying the material on the micro-scale, we identified different microscopic regions which showed quite remarkably different optical behaviours with respect to temperature. By comparing our data with the literature on the same system on the macroscopic scale, we formulated the hypothesis that this difference was due to different dye concentration in the

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various spatial domains.

In order to confirm this, we have developed a simple model, based on the isodesmic model for self-association phenomena, which has led us to very reasonable estimates of the local concentration of both the two aggregation forms and of the dye.

The main benefit of approaching the problem from such an angle is that it allows us to use various parameters for the equilibrium between single molecules and aggregates gathered by studying the dye in solution, which is a far less complicated system than a host-guest one. In light of these results, we were also able to formulate a very plausible explanation for the dependence of the equilibrium between the two aggregation forms of the dye on the local topography of the sample, observed in our previous study, in terms of local concentration. We are confident that the insight acquired during this work on the inhomogeneity in the equilibrium between aggregated and disaggregated dye molecules at the surface of a system like the one under study, which is at the core of its thermochromic properties, could very well prove useful in better understanding and exploiting this class of smart materials.

The thesis is organised as follows:

• Chapter 2: in this chapter, we briefly describe the thoretical background of our work. The main characteristics of the material under study are presented, as well as the theoretical derivation of the idosesmic model, which is the base for the development of our model in Sec. 6.2.3.

• Capter 3: in this chapter, we describe our previous study on the same material. The promising results from this experiment are what inspired us to continue analysing this host-guest system, thus making it the basis for the present work.

• Chapter 4: in this chapter, we describe in detail the experimental set-up of our experi-ment.

• Chapter 5: in this chapter, the different measurement procedures of the experiment are described, as well as the motivations behind them.

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and present our findings.

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Theoretical background

In this chapter, we examine the theoretical background of the topics covered in our work, in order to give a clear picture of the context in which our research is placed.

2.1 Chromogenic materials

Within the varied landscape of smart materials, a particularly interesting category is that of the chromogenic materials, which are substances whose optical properties change upon being exposed to external stimuli of various nature [6]. Depending on the particular type of stimulus prompting these changes, we can sort this kind of materials into different sub-categories, such as electrochromic [9], mechanochromic [10], photochromic [11], and thermochromic [12], with the name of each category being pretty self-explanatory.

It is worth noting, however, that the same substance can belong to more than one of these categories at the same time, a prime example being the system under study in our work, which shows both thermochromic [7], [8] and mechanochromic [7] properties; the same is also true for other similar materials, using slightly different perylene derivatives as dyes [13], [14]. Another distinction that can be made is if the changes are reversible or not, with our samples belonging to the former category [7], [8].

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As we can see, chromogeinc materials can vary quite a lot in nature and, consequently, in applications; in this work, however, we will focus on the reversible thermochromic properties shown by the samples under study.

2.1.1 Thermochromic materials

Thermochromism is the ability of a material to change its optical properties as a consequence of thermal stimuli.

Substances exhibiting such feature can be found both in liquid and solid form, and are generally categorised in organic, inorganic, and metal-organic thermochromic materials [6].

In this work, we will examine the first category, since it is the one to which our host-guest system belongs.

Depending on the mechanism which determines the change in optical response with regard to temperature, we can distinguish between intrinsic and indirect organic thermochromic materials [15].

In the first type, the thermochrmoic behaviour is caused by heat acting directly on the properties of the chromophores consisting of molecular dyes, without the need for any other agent: this usually involves the breaking of bonds (at high temperatures), interchange between different stereoisomers, or changes in macromolecular or supramolecular systems caused directly by heat.

In indirect thermochromic materials, on the other hand, the chromogenic features arise by physical changes in the environment surrounding the chromophores caused by heat: this is the case for our system, as already shown in other studies [7], [8].

2.2 Perylene derivative dyes

As already mentioned in the Introduction, the dye used in our experiment is the N,N’-bis-(R)-(1’-phenylethyl)-perylene-3,4,9,10- tetracarboxyldiimide (Fig. 2.1), which we will refer to as

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R-Pery for convenience. This molecule is part of the perylene bisimide derivatives, which have recently been the focus of various interesting studies [16], [17].

Figure 2.1:Chemical structure of the R-Pery molecule. Image adapted from [8]. .

Perylene derivatives represent a widely used class of organic dyes and are extremely ver-satile in their range of applications: from photovoltaic devices [18] to OLEDs [19], thin-film Field-Effect Transistors (FETs) [20], LCDs [21], fluorescence standards [22], temperature sensors [23], and chemical sensors [24], just to name a few.

Figure 2.2:Chemical structure of the perylene molecule. Image adapted from [23]. .

Perylene (chemical formula: C20H12) is an organic compound composed by two naphthalene molecules linked together in a planar structure (see Fig. 2.2); this arrangement results in the molecule being a conjugated system, i.e. one in which π orbitals are delocalised over the entire

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structure.

These π orbitals stem from the overlap of the pzorbitals of the carbon atoms constituting the

backbone of the dye [8] and are responsible for one of its most interesting features, namely the ability to form π-π stacked aggregates (Fig. 2.3).

The self-assembly process responsible for the creation of such structures is mainly caused by electrostatic and van der Waals interactions between conjugated molecules, which also determine the geometrical structure of the resulting aggregate [25].

The presence of these supramolecular aggregates and their equilibrium with the monomeric form of the dye is what determines the thermochromism in host-guest systems using perylene derivatives, as we will discuss in Sec. 2.3.

We would like to point out that the presence of large groups as substituents (represented by the R in Fig. 2.3) or side chains in the perylene derivative may prevent the formation of such aggregates due to steric hindrance, but this is not the case for the dye used in our experiments.

Figure 2.3: Representation of a generic perylene bisimide molecule and of its π-π stacking structure. The R in the chemical structure represents the substituent, which determines the specific derivative. Image adapted from [16].

.

Perylene’s optical properties are characterised by vibronic π-π* transitions: these involve the promotion of an electron from a bonding molecular orbital π to an antibonding molecular orbital π* and different vibronic levels, depending on the particular transition.

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In a molecule, each electronic state has several vibronic sub-levels, representing collective motions of the atoms composing the compound, and additional rotational sub-levels, with energy separations smaller than the corresponding vibrational ones.

Figure 2.4:Potential energy - bonding distance diagram showing absorptions and emissions between the ground (Ψ1) and first excited (Ψ2) electronic states of a molecule involving different vibronic levels (indicated by v and v’). Graph adapted from [26]

The energy separating two consecutive vibronic states, the so-called vibronic spacing, is of the order of 0.1 eV (∼1000 K); consequently, most bonds are found in the ground state from both an electronic and vibrational standpoint at room temperature [27].

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some vibronic sub-level of the first excited electronic state. This is generally followed by a very fast (time-scale of picoseconds) non-radiative relaxation to the lowest vibronic level of the same electronic state, from which the molecule, typically with a few nanoseconds lifetime, decays to the ground electronic level with the emission of a photon; if the final vibronic state is the lowest, the transition is called 0-0, if it is the first one it is called 0-1, and so on [27]. In Fig. 2.4, we show a schematic representation of this kind of processes. These transitions follow the Franck-Condon principle, which states that, since the absorption or emission of a photon happens on a much smaller time-scale than that of atomic re-arrangements, the inter-atomic spacing does not change significantly during the process, hence the arrows representing such transitions in the diagram being vertical [27].

In Fig. 2.5, we report the absorption and emission spectra of a 5×10−5_{M solution of} pery-lene in n-heptane: three absorption peaks can be clearly distinguished, corresponding to the 0-0 transition (at ∼430 nm), the 0-1 transition (at ∼410 nm), and the 0-2 transition (at ∼380 nm) [8].

As we can see from the figure, the emission spectrum appears to be a mirror image of the absorption one, obviously shifted in wavelength: this is merely a consequence of the vibronic spacing being very similar in the ground and excited states [27].

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Figure 2.5:UV-Vis absorption (black curve) and emission (blue curve, excitation wavelength: 300 nm) spectra of a 5×10−5 _{M solution of perylene in n-heptane. In the inset, picture of a} 5×10−4 _{M solution of the same components (left) and of neat perylene (right) illuminated by a} UV lamp. Image adapted from [28].

2.3 Dye-polymeric matrix systems

In a host-guest system composed of dye molecules dispersed within a polymeric matrix, the phenomenon of thermochromism is determined by the shifting equilibrium between different aggregation forms of the chromophores mediated by changes in the polymer’s structure under thermal stimuli.

R-Pery molecules can undergo π-π stacking aggregation, as previously mentioned. Depend-ing on their conformations and, consequently, the energy shift of their absorption bands with respect to the monomeric ones, we can distinguish between two types of aggregates: J and H. J-aggregates (from Jelley, one of the first scientists to study them) have their bands bathochromically-shifted, i.e. redbathochromically-shifted, while H-aggregates have theirs hypsochromically-shifted (hence the

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name), i.e. blueshifted [29].

Figure 2.6:Schematic representation of the relationship between molecular arrangement of an aggregate and its spectral shifts. Scheme adapted from [29].

These shifts in the absorption spectra of the aggregates can be explained by the exciton theory [30]: in this theoretical framework, a dye molecule is considered equivalent to a point dipole and the interaction between dipoles in different molecules determines a splitting of the excited level of the forming aggregate into two levels [29], [30].

In Fig. 2.6, we report a schematic and simplified representation of this phenomenon for two molecules with dipoles arranged either parallel to each other, or in a head-to-tail configuration. For an H-aggregate, the transition to the lowest excited level is forbidden, since the total transition dipole moment would be zero, which leads to the aforementioned blueshift; the opposite is true for a J-aggregate, for which the transition to the lowest excited level is allowed, hence the redshift [30].

When a dye molecule is excited by a photon, however, it can also interact with another one in the ground state, with the consequential formation of an excimer. The presence of this kind

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of aggregates gives rise to a structureless band in the emission spectra, since its lower state is dissociative, therefore it can be considered as a continuum [31] (see Fig. 2.7).

Figure 2.7:Energetic scheme of the formation of an excimer with respect to the intermolecular distance. Image adapted from [31].

The formation of both H- and J-aggregates, as well as that of excimers, is a diffusion-controlled process [8], [31], and this is where the presence of the polymeric matrix plays an essential role in determining the thermochromic properties of the host-guest system.

In order to form a supramolecular structure, in fact, two or more dye molecules need to be close to one another; this condition, of course, will be harder to achieve with a higher mobility of the guest molecules within the polymeric matrix, represented by a higher diffusion coefficient. The value of this coefficient rises with temperature for any viscous medium, with polymers above their glass transition temperature Tg (below -50 °C for LLDPE [7]) making no exception

[32]. Since the dye molecules are only present within the amorphous phase of the polymer [7], [8], [14], in fact, the matrix can be considered as an extremely viscous medium, with typical melt viscosities for LLDPE at 190 °C ranging from 30 to 30000 Pa·s, depending on the production process1_{. This, in turn, means that the formation of supramolecular structures is hindered by} larger average inter-molecular distances, thus moving the equilibrium between the aggregate

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and monomeric forms of dye molecules more towards the latter. This, as we have already stated, modifies the optical response of the material, giving rise to thermochromism.

2.4 Isodesmic model

In this thesis work, in order to better explain the results observed in our fluorescence confocal microscopy measurements (See Chapter 6), we have modified the isodesmic (or equal K) model. This model has already been successfully applied to other perylene derivatives in solution [16], [34], [35], [36], [37], liquid crystal phase [35], and solid phase [36], [38].

Using the isodesmic model is the simplest way to describe the equilibrium between extended aggregates and the monomeric form of the molecule A composing them: the aggregates are considered to be unidimensional and all equilibrium constants for the self-association processes are assumed to be equal [39], [40].

Following the study presented in [39], the indefinite self-association process of a certain species A in a solution can be described in terms of the molar concentrations and aggregation equilibrium constants for the monomers and various aggregates:

A + A A2, K2 = [A2] [A]2 A2+ A A3, K3 = [A3] [A2][A] = [A3] K2[A]3 A3+ A A4, K4 = [A4] [A3][A] = [A4] K2K3[A]4 ... Ai−1+ A Ai, Ki = [Ai] [Ai−1][A] = [Ai] K2K3...Ki−1[A]i

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A and the square brackets represent molar concentrations.

We would like to point out that, in order to keep the model as simple as possible, we are considering aggregation processes only adding one monomer at a time, and not the fusion of two or more aggregates.

The total concentration of the studied molecule is given by:

CT = [A] + 2[A2] + 3[A3] + 4[A4] + ... = (2.1) = [A](1 + 2K2[A] + 3K2K3[A]2+ 4K2K3K4[A]3+ ...)

The monomeric fraction α will then be:

α = [A] CT

= 1

1 + 2K2[A] + 3K2K3[A]2+ 4K2K3K4[A]3+ ... (2.2)

The molar fraction αi corresponding to the i-mer will be expressed by:

αi = i

[Ai] CT

(2.3)

We now introduce the assumption that all of the equilibrium constants are equal:

K2 = K3 = K4 = ... = KE (2.4)

By introducing the dimensionless quantities x = KE[A]and L = KECT and using Eq. 2.4, Eq.

2.1 becomes:

L = x(1 + 2x + 3x2+ 4x3+ ...) = x

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where we have made use of the convergence of the following series for x < 1: ∞

X

n=0

(n + 1)xn = (1 − x)−2 By solving Eq. 2.5 for x, we find:

x = 2L + 1 −

√

4L + 1

2L (2.6)

If we now substitute [A] = x/KE and CT = L/KE in Eq. 2.2, we get the final expression for

the monomeric fraction:

α = 2L + 1 −

√

4L + 1

2L2 (2.7)

This model will be used as the basis for the development of our own model in Sec. 6.2.3, which will allow us to link optical properties of the material observed on the mesoscopic scale to the local concentration of dye on its surface.

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Previous studies

The work presented in this thesis follows a previous study on the same material, on which the candidate based his Bachelor’s Thesis, titled Studio delle propriet`a ottiche di polimeri smart attraverso tecniche di microscopia a campo prossimo[5].

In the following chapter, we provide a brief summary of that work, in order to better contextu-alise the experiment analysed in this thesis and to highlight some of its scientific motivations.

The experiment made use of a Scanning Near-Field Optical Microscope (SNOM) in order to examine the local optical properties of R-Pery-LLDPE samples from the same batch as the one studied in the current work and provided by Prof. A. Pucci, focusing once again on the equilibrium between the dispersed and aggregated forms of the dye.

By using a SNOM probe, we studied the impact on this equilibrium of the local surface topog-raphy of the sample.

The experimental set-up, in fact, was able to collect and register, with a spatial resolution below 100 nm, the fluorescence emission of the very small excited portion of the sample in the red and green spectral regions at the same time: we are going to refer to the resulting maps as “red maps” and “green maps”, which, as mentioned in the Introduction, are indicative of the

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The aim of the work was to provide some insight on the mechanisms that regulate the phenomenon at the core of the thermochromism for this type of polymeric smart materials, as well as proof that, on a nanoscopic scale, the distribution of the various aggregation forms of the dye molecules is not homogeneous. Such general goals were not so different from those of the present work, except for the enhanced possibilities in terms of spatial resolution, unfortunately accompanied by a lack of flexibility and an inherently cumbersome operation.

To the best of our knowledge, this was the first experiment of this kind performed on this type of materials.

3.1 The experiment

Giving a detailed description of the experimental set-up employed during the experiment is beyond the aim of this summary; nevertheless, in this section we will describe the key aspects of the instruments used, so as to give a clearer picture of the experiment and pinpoint advantages and disadvantages of the selected approach.

In order to study the behaviour of dye molecules within a polymeric matrix on a nanoscopic scale, one can take advantage of a microscope capable of sub-diffraction limit resolution. This limit is given by the Rayleigh criterion and represents the maximum resolution obtainable with conventional microscopy [41]:

d = 0.61λ

NA (3.1)

where d is the resolving power, λ is the excitation laser wavelength and NA is the numerical aperture of the objective used. Being NA ∼ 1, d in the visible range amounts to hundreds of nm.

A key aspect of our experiment was the ability to acquire topographic and fluorescence maps of the sample at the same time, as enabled by SNOM.

Therefore, simultaneous maps of optical properties and sample’s surface can be acquired; this represents, along with the high spatial resolution, a unique added value of the technique.

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There are, however, several counterparts for such beautiful features.

The first one deals with the complicated operation of the instrument. If, in fact, one were to change the portion of sample investigated, a very straightforward operation in a confocal set-up, here one would have to move the probe further from the sample, remove the microscope head, change sample position, reassemble the system, and finally re-start the approach proce-dure, where a stepper motor is used for the coarse motion of the probe towards the sample. Furthermore, repeatability of the scans is hampered due to the kind of piezoscanner used, a simple hollow PZT cylinder (the geometry allows for placing a detector inside the cylinder, as required for measurements in transmission), and, due to the typically low level of the acquired signals, scans are slow (over an hour long for a few µm side scans).

Apart from the above technical concerns, there are also more fundamental obstacles relating to using SNOM for the purposes of our research. Clearly, analysing thermochromic materials takes advantage of the possibility to control and modify the sample’s temperature. Unfortunately, integrating a temperature controlled stage into a SNOM is a truly difficult task, not only for physical interferences with its components, but also for the circumstance that any variation of temperature induces thermal expansion (in the sample, in the probe holder, in the whole microscope head, and in the environment where the probe oscillates), which can severely affect the tip-to-sample distance control (details will be given in the following), eventually leading to crashing the fibre onto the specimen.

Indeed, the only possible way to perform temperature resolved scans, which has been explored and demonstrated very poor reliability, is to move the tip further from the sample, modify the temperature, wait for stationary conditions, re-approach the tip, and make a new scan. In doing so, however, for the intrinsic mechanical compliance of the system, the new scanned region tends to be different from the previous one, hampering any chance to compare the behaviour of similar portions, as required in our analysis.

Furthermore, excitation intensity is a clear issue in the study we intend to perform. While generally improving the signal-to-noise ratio, an increase of laser power may lead to local heating of sample caused by absorption, and even to photobleaching effects (see Sec. 5.1.3), clearly unwanted in our investigations.

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Excitation intensity depends on laser power and on the size of the region concerned by the electromagnetic field, two quantities that are difficult to evaluate with a SNOM. While power can be estimated by measuring the residual far-field leaving the probe (typical values are in the tens or hundreds of nW range), the actual lateral extension of the near-field is unknown, the only available estimation being the expected extinction range of the near-field (assumed in the hundred of nm range). Therefore, intensity can’t be easily determined and small variations of the operating conditions, e.g. an increase of tip aperture size due to wearing, may produce uncontrolled effects in terms of intensity coupled to the sample.

Finally, the high spatial resolution offered by SNOM, while being certainly appealing for many applications, is probably not strictly required in our study. As a matter of fact, SNOM scans revealed occurrence of “islands”, or “domains” of fluorescence, intended as regions with almost constant optical properties (emission intensity, spectral features, etc.), with a transverse size above 150-200 nm, i.e. in a range close to the one accessible with a conventional confocal microscope.

In addition to that, since the near-field is confined to a very small range out of the aperture (tens of nm), SNOM measurements are strictly limited to surface properties. Although this was useful in order to relate optical and topographical features, the very superficial nature of the investigation may hamper depicting the true behaviour of the investigated samples, since it completely leaves out all of the processes happening in the bulk of the material.

On the other hand, as already anticipated, the SNOM investigation was essential in finding out out specific topography-related trends.

An aperture SNOM probe, such as the one used in the experiment, consists of a tapered optical fibre with a very small aperture (50÷100 nm of diameter) [42], which, in a fluorescence microscopy set-up, serves to produce a near-filed being coupled to a laser source (an Oxxius 405 nm diode laser in our case).

When a plane wave passes through an aperture much smaller than its wavelength, it gen-erates a very intense and localised evanescent electric field, which is confined to a region with dimensions comparable to the diameter of the fibre’s aperture (50 nm in our case). The non-propagating nature of the evanescent field makes it not subject to the diffraction limit,

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which, in conjunction with the extremely localised excitation region, allowed our microscope to have a nominal resolution even below 100 nm.

In order for the aperture to be kept in the proximity of the sample’s surface, methods borrowed from conventional scanning probe microscopy were used. In these methods, the fibre is glued to the side of one of the prongs of a quartz tuning fork, which is forced to oscillate, in the direction parallel to the specimen’s surface, at the resonance frequency of the system by a piezoelectric transducer (the so-called dither piezo).

When the tip of the fibre approaches the sample’s surface, a force dependent on the distance between the two, called the shear-force, arises; this force decreases the oscillation amplitude, which is constantly monitored by a feedback system driving the vertical displacement of the piezoscanner holding the sample and being responsible of its in-plane scanning.

The aim of this system is to maintain a constant gap of less than 10 nm between the fibre and the surface of the sample: if the amplitude of the oscillation is lower than its reference value (registered with the probe far away from the specimen), the system sends a signal to the piezoscanner on which the sample is placed, changing its length until the reference value is established. A more detailed description of this process can be found in [43].

By raster-scanning the specimen and keeping track of the vertical movements of the translator imposed by the feedback system, topographic maps of the sample’s surface are obtained. In Fig. 3.1, we report a schematic representation of the probe of a SNOM microscope like the one used in the experiment.

One of the most important features of the experimental set-up was the ability to register the fluorescence emission of the sample in the two relevant spectral regions at the same time. The light collection apparatus that allowed us to do so was composed by a Mitutoyo 10x microscope objective (NA: 0.28, working distance: 3.4 mm) placed at a 45° angle with respect to the sample’s surface, behind which was a 50:50 beam-splitter; each of the two beams coming from it passed through a series of filters (a long-pass filter at 600 nm for the red spectral region and a combination of a long-pass filter at 550 nm and a short-pass filter at 600 nm for the green one) and towards two distinct detectors (Hamamatsu R9880 miniaturised photomultipliers). In Fig. 3.2, we show a scheme depicting this part of the set-up, for better clarity.

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Figure 3.1:Schematic representation of an aperture SNOM microscope (details of the probe). Image adapted from [44].

Figure 3.2: Schematic representation of the light collection system employed during the experiment. Image adapted from [45].

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3.2 Results

In this section, we report the results of the different measurements carried out during the experiment.

3.2.1 Topographic and fluorescence measurements

The first type of measurements carried out during the experiment consisted in simultaneous scans of the topography of the sample’s surface and of the fluorescence emission in both the red and green spectral regions, while keeping constant the power of the laser injected into the SNOM fibre (around 1 mW). The aim of these measurements was to correlate shifts in the equilibrium between the monomeric and aggregated forms of the dye, represented by the emission intensity in the two spectral regions, to the local morphology of the polymer’s surface. These raster scans resulted in maps a few µm2 wide, a set of which we report in Fig. 3.3 as an example.

Each acquired fluorescence map was subjected to a pixel-by-pixel normalisation process with respect to its minimum value: this operation produced maps normalised between 0 and 1 (in arbitrary units), in order to enable a straightforward comparison of fluorescence and topography features by removing the dependence on the spectral response of the detectors.

In order to better visualise the dominant aggregation form in each part of a scanned portion of the sample, we created what we called “difference maps”, which are the result of a pixel-by-pixel subtraction of the red maps from the corresponding green ones (Fig. 3.3d): according to the hypothesis described in the Introduction, the areas of these maps with higher positive values are those in which the disaggregated form is favoured, and vice versa. We also produced figures where a contour plot of each difference map was superimposed to the respective topographic one (Fig. 3.3e), so as to make it easier to compare these two types of maps at a glance.

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Figure 3.3: Example of a full set of maps resulting from a topographic measurement. (a): topographic map. (b): normalised red map. (c): normalised green map. (d): map resulting from the difference between map (c) and map (b). (e) contour plot of map (d) superimposed to map (a). Image adapted from [5].

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with regard to the local morphology of the sample, we extracted line profiles from these topog-raphy and difference maps, of which we show two examples in Fig. 3.4.

Figure 3.4: Line profiles extracted from two difference maps and from the corresponding topographic maps, along the segments shown in the maps on the right. The black curves (left axis) represent the topography, while the green curves (right axis) represent the values of the difference map along the line. Graphs adapted from [5].

The graphs show a qualitative correlation between the difference between the normalised signals in the green and in the red spectral regions and the topography of the sample, with local maxima (minima) of the difference map generally corresponding to local maxima (minima) of the topographic map. This, in turn, can be interpreted as a tendency of the monomeric form of the dye to be favoured in correspondence to a “hill” on the sample’s surface, while the supramolecular aggregates tend to be favoured within a “valley”.

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inward superficial pressure in correspondence to a valley, which, in turn, would favour the aggregation of the chromophores.

In light of the results of our latest experiment, however, we have hypothesised another expla-nation for this phenomenon, backed up by the model developed in this work, which will be described in Chapter 7.

Another feature that can be easily seen in the graphs is that the values of the difference maps tend to overall diminish greatly in the presence of a pronounced topographic hill, only to recover after its peak. An explanation for this behaviour could be found in the particular light collection set-up, more specifically in the objective being at a 45° angle with respect to the sample leading to a sort of shadowing effect.

When the probe is exciting a portion of the polymeric surface right before a height, the emitted light will have to pass through it before reaching the objective (see Fig. 3.5); since the material’s absorbance is higher in the green spectral region than in the red one (see Fig. 6.10 for detailed absorption spectra), more “green” photons will be absorbed than “red” ones, thus decreasing the value of the difference map corresponding to the considered point.

Given the situational nature of this “artefact” and the fact that we are more interested in the correlation between local minima or maxima of the curves analysed in the graphs, however, this peculiar behaviour does not invalidate our conclusions.

3.2.2 Variable power measurements

As already mentioned, playing with excitation intensity in the near-field is a cumbersome task, due to the combined effects of a difficult measurement of the power in it and of the practical impossibility to measure its lateral extension, which can only be estimated.

Nonetheless, assuming that near-field extension does not change during a scan (which means assuming negligible tip wearing), relative behaviours of difference maps as a function of the power of the laser injected into the fibre probe can be investigated.

The rationale for the experiment described in this section was indeed to analyse such a behaviour in selected portions of the sample in the shape of lines. Therefore, sample scanning along a direction, the one appearing in the vertical axis of the scan, was inhibited and the power of the

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Figure 3.5:Schematic representation of the fluorescence light path before a pronounced hill on the sample’s surface.

laser continuously varied according to a triangular modulation centred in the middle of the map.

To this aim, we acted on the voltage control of the laser, which was fed by a triangle wave with a peak-to-peak voltage of 5.56 V, minimum voltage of ∼0 V, and half-period set as to match the duration of the scanning process (3396 s). This meant that the laser power entering the fibre started at 0 W and reached a maximum value of ∼3 mW.

The results were “pseudo-maps”, since a single line was scanned back and forth during each scan. With that in mind, we are going to refer to them simply as maps for brevity.

The aim of this kind of measurements was to correlate the dominance of an aggregation form over the other to the laser power and, consequently, the excitation intensity, an increase of which could also lead to local heating of the sample through local absorption.

The measurement process consisted in the simultaneous acquisition of a topographic scan (Fig. 3.6a), fluorescence scan in the red (Fig. 3.6b) and green (Fig. 3.6c) spectral regions, and

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Figure 3.6:Variable power pseudo-maps resulting from the variable power measurements. (a): topographic map. (b): red map. (c): green map. (d): map resulting from the difference between (c) and (b). (e): map resulting from the difference between the green and red maps normalised with respect to the transmission maps. Image adapted from [5].

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so-called “transmittance scan”, which is proportional to the laser power; the relevant signal for the latter type of scans was coming from a detector faced behind the sample and placed inside the hollow PZT tube of the scanner.

In Fig. 3.6d, we show the difference between the green and red maps, in which a clear increase in values in the central region can be seen. Given the shape of the wave fed to the laser generator, this corresponds to a more pronounced increase in emission for the monomeric form of the dye compared to the aggregated one with higher laser power.

Both the red and green maps were also subjected to a normalisation process, this time with respect to the transmission map: the difference between the normalised green and red maps is shown in Fig. 3.6e. This was done in order to remove the direct increase in emission due to higher laser intensity, thus making its secondary effects more visible.

This map depicts a slightly different scenario: the signal is still increasing with higher laser power, but its decrease with decreasing power is much less pronounced.

This behaviour could be ascribed to an increase in the sample’s temperature, which tends to favour the monomeric form of the dye [7], [8], with the inability of the polymer to effectively dissipate the built-up heat during the second half of the scan causing the signal to remain overall higher. This explanation is also consistent with the increase in average height of the sample in the middle portion of the scan (see Fig. 3.6a), which is indicative of a swelling of the sample due to thermal expansion.

Clearly, the methodology used for the presented analysis did not allow us to draw detailed and truly reliable conclusions.

The unknown intensity values, in fact, made it impossible for us to make even rough estimates of the temperature increase related to local laser absorption, a task already extremely complex to accomplish in the best of circumstances.

Furthermore, occurrence of thermal expansion implies, as already stated, a variation of the operating conditions of the SNOM probe, possibly leading to modifications of the tip-to-surface distance and, consequently, of the effective near-field intensity coupled to the sample.

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reported in the next section. The proven scarce reliability of such measurements was one of the main motivations behind the work of the present thesis, where the use of a confocal microscope did enable reliable temperature dependent analyses at the expenses of a (slightly) reduced spatial resolution and, obviously, of the impossibility to acquire simultaneous topography data.

3.2.3 Temperature varying measurements

Near-field microscopy, despite its unique spatial resolution, is not a technique particularly well suited for situations in which the sample undergoes changes in shape or volume, especially if the experiment requires to scan the same portion of the specimen multiple times, as was our case.

As already mentioned in Sec. 3.1, the swelling of the sample due to thermal expansion leads to a great deal of technical difficulties, going as far as a serious risk of damaging the SNOM probe, in case of it crashing onto the polymer’s surface.

These drawbacks greatly affected our ability to reliably acquire a good amount of maps; for this reason, the results of this type of measurements are mostly qualitative and refer to very small temperature variations, obtained by heating the sample with the current flowing through a wire resistor wound on the sample holder.

In Fig. 3.7, we report an example of a full set of maps acquired for two different temperature values; these maps are much smaller compared to the ones from the other types of measurements, since we had to cut them significantly in order to only keep the same region of the sample’s surface for the two consecutive scans.

For this type of measurements, we did not apply any normalisation to the resulting maps, since we were interested in studying the emission of the material, without correlating it to the local topography.

As we can see from the figure, the scanned portion of the surface experiences a higher overall increase in the emission in the green spectral region, which is especially noticeable by comparing 3.7g and h. This trend was also confirmed by line profiles extracted from the same difference maps over the same line on the sample (Fig. 3.8).

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Figure 3.7:Example of a full set of maps resulting from a variable temperature measurement. (a) and (b): topographic maps. (c) and (d): red maps. (e) and (f): green maps. (g) and (h): difference maps. In order to make them easier to compare visually, we used the same colour scale for the emission maps of the same type, as well as the difference ones. The maps on the left were recorded at a sample’s temperature of 40 °C, while the ones on the right at a temperature of 42.5 °C. Image adapted from [5].

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This behaviour is consistent with studies conducted on the same material on the macroscopic scale [7], [8], which show a shift in the equilibrium between the two aggregation forms of the dye towards the disaggregated one with increasing temperature.

Figure 3.8: Line profiles extracted from Fig. 3.7g (blue curve) and 3.7h (black curve). The bottom axis represents the position on the segment superposed on the map, while the left axis is the corresponding value of the difference map. Image adapted from [5].

3.2.4 Conclusions

In the experiment briefly analysed, clear indications of the inhomogeneity in the distribution of the aggregation forms of the considered dye as part of a host-guest system were observed on the local scale. The fluorescence emission is spatially organised in domains, or islands, with typical transverse size in the hundred(s) of nm range that, to the best of our knowledge, were reported in this study for the first time.

First of all, we showed that there is a correlation between the local topography of the sample’s surface and the prevalence of an aggregation form of the dye over the other, with hills favouring the disaggregated form and valleys favouring the aggregated one.

We also observed a peculiar behaviour of fluorescence as a function of the laser power, which could be tentatively attributed to local sample heating subsequent to absorption. Moreover,

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attempts were made aimed at verifying the fluorescence response of the material as a function of temperature, but their reliability was strongly hampered by the difficulty in ensuring constant operating conditions related with thermal expansion.

All of these aspects are at the basis of the study presented in this thesis. The typical size of the observed fluorescence domain is, in fact, compatible with the spatial resolution of confocal microscopy, a technique which, on the other hand, enables reliable control of the sample temperature and a more straightforward estimation of the laser intensity.

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4

Experimental set-up

In this chapter, we explain in detail the experimental process behind our work on the macro-and meso-scale.

4.1 The material

The material under study, provided by Prof. A. Pucci, is a host-guest system composed of a dispersion of 0.02 wt.% of R-Pery in a Linear Low-Density PolyEthylene (LLDPE) matrix and it comes from the same batch described in [5] and [7]. For convenience, we report here the main fabrication steps used to obtain it after the synthesis of the dye.

First, and the polymer and the dye were mixed together in a Brabender plastograph mixer under nitrogen atmosphere at 180 °C with a rotation speed of 50 rpm; the amount of LLDPE introduced was 20 g, with the amount of R-Pery added constituting its 0.02 wt.%.

After 10 minutes of mixing, the material was then ground at room temperature in an analytical mill; the obtained powder was then compression-moulded between two aluminium foils at 180 °C for 5 minutes. The obtained film, with typical thickness of around 100 µm, was then slowly

cooled at ∼5 °C per minute until it reached room temperature.

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and could easily be cut into small and easy to handle samples with a pair of scissors.

Figure 4.1:A picture of the polymeric film from which we cut the studied samples. .

4.2 Macro-scale spectroscopy

The spectroscopic measurements on the macro-scale have been carried out with a Jobin Yvon-SPEX/Horiba TRIAX 320 monochromator (focal length: 320 nm, grating: 1200 g/mm, blaze: 550 nm, slit width: 0.1 mm) in conjunction with an Hamamatsu R955 phototube.

The sample was illuminated with a Changchun New Industries MBL-III-473-150 mW laser with a wavelength of 473 nm and a spot size of ∼2 mm, controlled by a PSU-III-LED controller by the same manufacturer. The laser power reaching the sample was around 1 mW.

The fluorescence emission was collected and sent to the monochromator by a multi-mode quartz optical fibre (core diameter: 125 µm) coupled to a 10 mm converging lens.

The temperature was controlled via a current-regulated PID controller designed and produced at the Department of Physics of the University of Pisa, driving an NiCr spiral (total resistance:

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∼10 Ω), and measured by a PT100 thermoresistance.

After changing the temperature on the controller, we have always waited around a minute before registering the spectrum, in order to let the sample reach thermal equilibrium with the hotplate.

4.3 Meso-scale confocal microscopy

In the following section, we examine the experiment on the meso-scale.

4.3.1 Confocal microscopy

As already mentioned in the Introduction, our experiment on the meso-scale makes use of a confocal microscope: in this section, we will briefly discuss the principles behind this kind of microscopy.

In confocal microscopy, a lens or an objective is used to focus a point-like light source, e.g. a laser beam, onto a sample. The light reflected or, as it is our case, emitted by the specimen is then focused through the same or another lens or objective towards a detector; in front of this, on the image plane of the microscope, a pin-hole is placed.

In Fig. 4.2, we report a schematic representation of a typical confocal microscope.

As highlighted in the figure, the presence of a pin-hole in front of the detector is the key factor in the operation of a confocal microscope, since it allows the instrument to only (or mostly) collect light coming from the focal plane, while blocking that generating from any other plane on the sample. This feature, if combined with a scanning technique over the different planes of the specimen, allows the acquisition of a three-dimensional image of it with highly enhanced contrast, since most of the stray-light is blocked [46].

Furthermore, the effective rejection of light scattered from regions located outside of the focal plane is a key factor for improving the spatial resolution along the in-plane direction, up to the

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Figure 4.2: Scheme representing the basic principle behind a confocal microscope. Image adapted from [46].

level allowed by the Rayleigh criterion (see Sec. 3.1).

This, however, comes at a price: the presence of a small pin-hole in front of the detector also means that most of the light coming from the sample is lost, greatly diminishing the strength of the acquired signal with respect to ordinary fluorescence microscopy.

4.3.2 Confocal scanning microscope

The confocal microscope employed in this work has been personally designed and implemented by the candidate during the thesis work.

The microscope used was a Nikon Eclipse Ti-U/B inverted microscope with a Nikon LU Plan Fluor 50x/0.8 Dry objective (magnification: 50x, numerical aperture: 0.8, infinity- corrected) and two easily swappable tube lenses (one without magnification and the other with 1.5x magnification) required to operate with infinity-corrected objectives; during our fluorescence

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measurements, we used the one without magnification.

The microscope had five ports, which we used in part for different tasks:

• Back port: by using a beam-splitter (75% reflection, 25% transmission) on an adjustable support mounted on a custom-made rail system, we managed to have both the laser beam and the illumination of an LED lamp enter this port. This was necessary in order to be able to use our set-up as both a confocal microscope and a conventional one, the latter part proving very useful when pre-selecting which area of the sample to scan. • Left port: it had a Canon Eos 1100D camera (sensor: CMOS APS-C 22.2×14.7 mm2, fov

with a 50x objective and 1x tube lens: 0.44×0.29 mm2_{) mounted in it, which let us take} pictures of the samples upon LED illumination and monitor in real time the polymer’s surface.

• Front port: the view port, where the user could look through the oculars of the microscope. • Right port: the signal coming from the samples was directed from this port towards the

rest of the confocal set-up. • Bottom port: not used.

The microscope had a series of mirrors and beam-splitters inside of it, so that it was possible to select which “output” port to use, while the back port was always used as the “input” one. In addition to that, the microscope was equipped with a carousel system on which different filters could be mounted and selected one at a time.

As previously stated, the laser beam entered the microscope through the back port, then it impinged on the filter on the carousel, which was one of the following:

• Beam-splitter filter: a beam splitter with 50% in reflection and 50% in transmission. • A Thorlabs FITC filter cube: one of the key component in a fluorescence microscopy

set-up, this system is composed of an excitation filter, a dichroic beam-splitter, and an emission filter (see Fig. 4.3).

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excite the sample; this also gives the particular filter box its name, based on the common dye which can be excited in the transmitted spectral range (in our case, FITC stands for Fluorescein IsoThioCyanate).

The dichroic beam-splitter, placed on an angle of 45° with respect to the direction of the excitation beam, has the aim of reflecting it towards the objective, while letting the fluorescence light emitted from the sample pass through it and towards either the ocular or one of the two lateral ports. It is, in fact, a dichroic mirror designed to reflect the excitation wavelengths and transmit those expected to be emitted by the specimen. The emission filter, similarly to the excitation one, has the aim of letting only the wave-lengths of the fluorescence or excitation light pass through it.

We anticipate that, in our set-up, we removed the emission filter: since the one mounted on our FITC cube cuts the wavelengths above ∼560 nm, in fact, keeping it on would have filtered out the fluorescence emission we wanted to measure. The role of emission filter has been played by additional filters placed in front of the detector.

It is easy to notice how both of the filters employed were either a straight up beam splitter, or had a beam-splitter as a component: this is not a coincidence, but a key part of developing our confocal microscope, since it required the laser beam to be directed upwards to the sample and the fluorescence emission towards one of the two lateral ports, which could not have been achieved by simply using mirrors.

By using this set-up, we were able to achieve our aim: the laser could effectively excite the sample and the light emitted or reflected from it, after passing through the selected filter on the carousel and the selected tube lens, was successfully directed towards the chosen lateral port by a system of mirrors and beam-splitters. The same objective served for both illumination and collection.

The carousel filters led to some power loss for the excitation laser effectively impinging on the sample, highly dependent on the selected filter: while the FITC filter led to a decrease in power of around 6%, the use of the beam-splitter, as expected, introduced a power loss of ∼50%.

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Figure 4.3: A schematic representation of a fluorescence filter. Our set-up is upside-down compared to the scheme presented, since the objective was placed above the filter cube, due to the inverted configuration of the microscope; furthermore, below it, the light emitted or reflected from the sample could be directed either to the ocular, the left port or the right port. Image adapted from [47].

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4.3.3 Laser

The laser and its controller employed were the same as in the experiment on the macro-scale: a Changchun New Industries MBL-III-473-150 mW laser (wavelength: 473 nm, spot size: ∼2 mm) and PSU-III-LED controller by the same manufacturer. The latter features a knob to adjust the current of the pump diode and, consequently, the power of the laser.

We noticed that the power output of the laser presented an hysteresis loop with regard to the current set on the controller, but only if fed with a current greater than 1.1 A.

We also noticed that the power output was subject to not negligible fluctuations when the generator was set to higher currents (∼1 A and above); this was probably due to a non-optimal thermal dissipation of the laser mount, which led to the laser building up heat and being less stable.

All of these problems, however, were solved by setting the generator to the current value of 0.67 A (corresponding to an output power of ∼90 µW) and by constantly measuring the part of laser power transmitted by the beam-splitter in front of the input port of the microscope during our fluorescence measurements (see the next section).

4.3.4 Optical table

Our optical table set-up consisted of various components; we present a scheme depicting it during our fluorescence measurements in Fig. 4.4.

The laser beam exited the laser and impinged on a Standford Research Systems SR540 optical chopper, used in conjunction with a lock-in to suppress noise (see Sec. 4.3.6). The controller of the chopper was set to around 990 Hz, avoiding any frequency multiple of 50 Hz (the frequency of the power network). The beam then encountered a first mirror, which sent it towards a second mirror in a beam-steering configuration, which directed it upwards to the beam-splitter mounted on a rail system; from here, the laser beam entered the microscope. When the right port was selected, the light emitted from the sample was directed to the detector

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Figure 4.4:Scheme of the optical table during our fluorescence measurements, with the blue line representing the laser beam and the red-green dotted line representing the fluorescence emission. Before entering the microscope, the beam was directed upwards by a mirror and then towards the input port by a beam-splitter: this part of the set-up is shown from side and front view (with their point of views indicated by the arrows) in the red rectangle for better clarity.

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through the filter holder placed outside the microscope. This could house the filters used to select the spectral region for the measurement: a combination of a Edmud Optics high performance OD4 long pass filter at 550 nm (LPF550) and an Edmund Optics TECHSPEC OD2 short pass filter at 600 nm (SPF600), which we are going to refer to as “green filter”, for the green spectral region, and a CVI/Melles Griot LPF-600-0.50 at 600 nm (LPF600), which we are going to refer to as “red filter”, for the red spectral region. The nominal spectral response graphs for the LPF550, SPF600, and LPF600 filters are reported in Fig. 4.5, 4.6, and 4.7, respectively. In order to reduce any spurious signal, we also placed a small piece of black cardboard with a hole poked in its center in front of the filters.

Figure 4.5:Spectral response graph of the LPF550 filter (and others). Graph adapted from the Edmud Optics online catalogue.

Once the emitted light was properly filtered, it impinged on a Thorlabs P50D 50±3 µm diameter pin-hole, a fundamental part of any confocal set-up. This was mounted on a Thorlabs ST1XY-S translator with micrometer drives, which was itself mounted on another micrometric drive translator, allowing for movement along the three axis.

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Figure 4.6:Spectral response graph of the SPF600 filter (and others). Graph adapted from the Edmund Optics online catalogue.

Figure 4.7:Spectral response graph of the LPF600 filter (and others). Graph adapted from the CVI IDEX Optics and Lasers catalogue.

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affects both the spatial resolution and the intensity of the acquired signal. As already mentioned in Sec. 4.3.1, the main function of the pin-hole is to prevent light emitted from out-of-plane points to reach the detector: by looking at Fig. 4.2 it is apparent that, by increasing its diameter, light emitted from planes further away from the focal plane will be accepted, thus reducing the spatial resolution of the microscope [46].

On the other hand, reducing the amount of light passing through the pin-hole inevitably leads to lower signals and, consequently, lower signal-to-noise ratios: in experiments where the intensity of the light to be analysed already tends to be very low, e.g. in confocal fluorescence microscopy like the one performed in our work, this could represent a serious problem. It is important, then, to strike the right balance between resolution and signal intensity: this is generally achieved by choosing a pin-hole diameter equal to or slightly larger than the size of the Airy disk in the image plane [48], [49], which, in our case, is simply the dimension of the Airy disk (see Eq. 3.1) multiplied by the objective magnification [48]; this is often referred to as an Airy Unit (AU), which, for our set-up, is ∼18 µm.

This simple calculation would suggest us to use a 20-25 µm pin-hole, but, because of the very low signal intensities typical of our measurements (see the next section), we decided to sacrifice a higher resolution for a better signal-to-noise-ratio, and chose a 50 µm pin-hole instead.

After the fluorescence light had passed through the pin-hole, it finally reached a Hamamatsu C4777-01 Avalanche PhotoDiode (APD) module (gain: ∼5×107 V/A), which converted the intensity of the impinging light into a voltage signal. This piece of equipment mounts an Si APD 3.0 mm diameter detector, two stage thermoelectrically cooled (operating temperature: 0 °C), coupled to a current to voltage converter leading to a peak photosensitivity above 109_V/W (bandwidth: ∼5 kHz) and a nominal Noise Equivalent Power (NEP) of a few fW/√Hz.

The lamp depicted in Fig. 4.4, a Thorlabs MCWHL5-C5 LED lamp, was another important piece of our design, since it allowed us to image the sample from “white light” illumination. In Fig. 4.8, we report the spectrum of the lamp, adapted from its datasheet [50]. The lamp was powered by a current-controlled supply, enabling varying illumination power.

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Figure 4.8:Performance plot of the LED lamp used in the experiment. Image adapted from [50].

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4.3.5 Nanopositioner and temperature controller

A fundamental requisite in any scanning microscopy set-up is the ability to change the position of the probe beam with respect to the sample, and our confocal microscope is no exception. In conventional confocal microscopy, typically the laser beam is scanned, whereas, in our set-up, we preferred to scan the sample position instead. This choice eliminated the restriction of using specific (telecentric) objectives, not available in our labs, while maintaining an excellent spatial resolution in sample positioning. It came, however, with its drawbacks, namely a rather long measuring time, which could easily stretch into 30 or 40 minutes for a single scan, due to the slow speed of the scanner. This, however, did not constitute much of an issue for us, since the scanning speed we could reliably use in our measurements would have been limited anyway (see Sec. 5.1.2).

In our experiment, the sample’s scanning process was achieved by using a Physik Instrumente P-517.2CL piezo scanner, equipped with an integrated capacitive sensor for closed-loop op-eration along two axis with 100 µm maximum travel, 1 nm resolution (3×10−4 _{max relative} linearity error), and ±5 nm repeatability.

Nanopositioner operation was accomplished via a controller (Physik Instrumente E-500, equipped with a two direction module) enabling closed-loop operation. The controller accepts as its input a voltage (0-10 V, separately for each direction) which linearly drives the travel with the specified resolution.

Therefore, in order to produce a confocal map, a computer-controlled system able to sweep a voltage (that is, to control sample position along the two directions and to perform the scan) and simultaneously acquire the signal of interest (typically the emission signal, but also a signal representative of the laser power) is needed.

For the sake of efficiency, rather than developing an independent pc-controlled system, we preferred using a commercial controller (RHK SPM 100) conceived for driving scanning probe microscopes, therefore including components for the feedback operation not used in the present work. The controller allowed us to have two independent voltages, in the range of 0-10 V, used to raster scan the sample and acquire the signal of interest in order to produce maps, with

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widely adjustable scan speed and size.

Furthermore, maps were acquired during both forward and backward displacement along the x direction (fast scan axis) that could be used to check the repeatability of the process and to identify possible artefacts due to the integration time.

The temperature controlled stage was based on Peltier elements enabling heat transfer from one side of the element to the other, depending on the current sign.

During our measurements, we only set temperatures above the room value, both in order to prevent water vapour condensation onto the sample surface (being the humidity of the environment uncontrolled, dew points above 15 °C can occur) and because of the temperature interval we were interested in studying. Although the temperature controlled stage has been usually employed as a heater, the use of Peltier elements strongly improved stability of the operating point. To this aim, the temperature was read by a Pt-100 thermoresistance (calibration error: 0.3 °C, see Sec. 5.1.4) in thermal contact with the stage, and a PID controller, developed in our Department (nominally able to maintain temperature within better than 1/100 °C), was employed to current drive the Peltier elements. The stage comprised of two Al plates (size: 7.5 cm × 2.5 cm × 2 mm) with two Peltier elements connected in series, each one with a maximum electrical power of 10 W, sandwiched in between. Thermal contact between Peltier and plates was achieved by putting a small quantity of silicon paste able to withstand high temperatures (up to 200 °C).

In Fig. 4.9, we show a picture of the stage.

The sample was placed in contact with one plate with the aid of small stripes of kapton adhesive tape, while the other plate was used as a thermal sink.

Since the whole stage was scanned, an excess in its mass could have led to an increase in the inertia of the system, thus reducing the response time of the nanopositioner and imposing a limit on the effective scan speed (which, however, was limited by other experimental factors, see the next section). As a result, we had to use a small heat mass as thermal sink, furthermore located in proximity of the heated plate (the entire stage is, in fact, 6.3 mm thick).

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Figure 4.9:Picture of the temperature controlled stage used in the experiment.

the Al plates, eventually limiting the maximum temperature difference between them and, consequently, the maximum temperature of the sample.

In principle, such a difference for a Peltier element is rated as 70 °C (maximum), which, as-suming the heat sink duly thermalised with the lab environment, means a maximum sample temperature around 90-100 °C. We noticed, however, that temperature stability was difficult to achieve for sample temperatures set to above 60 °C, which required a driving current close to the maximum rated value for the used Peltier elements (1 A). Therefore, we decided as a comfortable compromise not to exceed 60 °C as sample temperature.

Clearly, being the temperature measured by the Pt-100 sensor in contact with the stage, actual sample temperature may differ from the one set on the PID controller, because of diffusion issues and convection: for this reason, we performed a calibration procedure, by using a second Pt-100 sensor put in thermal contact with the surface of the stage where the sample was going to be placed (see Sec. 5.1.4).

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Mechanical stability against temperature variations is, in principle, also a strong issue of the setup, although it likely led to negligible effects, thanks to the possibility to finely adjust the focus of the instrument and compare map features acquired at different temperatures. Owing to the size of the elements (thickness of sample and plates), even in the presence of relatively large relative linear expansion coefficients (2×10−4 _°C−1 _{for LDPE at 20 °C, 2×10}−5 _°C−1 _for Al), negligible effects are expected compared with the Rayleigh range, or with the axial spatial resolution, of our set-up.

Another crucial aspect deals with the possibility for the sample to start detaching from the plate because of temperature-induced modifications of the mechanical conditions involved in holding it in place (e.g. modifications in the adhesive film of the kapton tape). This problem might have been avoided by placing a duly fixed coverslip in between the sample and the objective. However, being our objective optimised for use in air, aberration effects due to the presence of the glass coverslip would have prevented proper operation of the confocal setup. For this reason, we decided to simply carefully place more kapton tape along all of the borders of the sample.

4.3.6 Signal acquisition

The signal collected from the avalanche photodiode, a voltage proportional to optical power, was sent to a Standford Research Systems SR830 lock-in amplifier, which had the important task of clearing it from the noise. This operation is particularly crucial in a confocal fluorescence microscope such as ours, because of the typically weak signal amplitude.

The reference signal was fed to the amplifier by the chopper controller, so as to cut any compo-nent of the signal whose frequency was different from the one set on it.

For all of our fluorescence measurements, the lock-in was set to a time constant of 10 ms and a sensitivity of 10 mV.

Since the RHK SPM 100 controller used to realise the maps acquires as input an analog signal (voltage), we used the analog output of the lock-in amplifier for the confocal maps. The

Inhomogeneity at the surface: multi-scale study of the optical properties of a smart polymer