Influence of TMAO on the Dynamics and Gelation of PNIPAm colloids

Influence of TMAO on the Dynamics and Gelation of PNIPAm colloids

Alexander Orlow Matrikel-Nr. 6942052

Department of Physics

Faculty of Mathematics, Informatics and Natural Sciences University of Hamburg

Submitted in partial satisfaction of the requirements for the Degree of Bachelor of Science

in Physics

Supervisor Prof. Dr. Gerhard Grübel Second Supervisor Prof. Dr. Melanie Schnell

Abstract

This thesis studies the dynamics of a colloidal suspension, consisting of concentrated nan- oparticles with a silica core and a polymer shell of poly(N-isopropylacrylamide) (PNIPAm) suspended in water. The thermosresponsive polymer PNIPAm is known for its volume phase transition at a lower critical solution temperature (LCST) of about 32−33^◦C. Below this temperature, the polymer is hydrophilic and therefore swollen with water, whereas above the LCST, PNIPAm transforms into a hydrophobic state, leading to a contraction due to expelled water molecules. This hydrophobic collapse is investigated by the method of Dynamic Light Scattering (DLS) for various particle concentrations with volume fractions up to Φ_eff = 0.27.

All samples are studied in a temperature range around the LCST, i.e. 15^◦C< T < 42^◦C, in a process of heating and subsequent cooling. Thus, the diffusion behaviour of the differently diluted samples is analysed and the hydrodynamic radius of the particles can be determined.

Moreover, the naturally stabilizing osmolyte trimethylamine N-oxide (TMAO), which is known to promote the folding process in proteins, is added as a co-solvent to the colloidal suspension in concentrations of up to 2 mol/l. Increasing concentrations of TMAO are shown to raise the fluids’ viscosity and decrease the size of the particles. Most importantly, TMAO is demonstrated to shift the LCST, at which the PNIPAm shell collapses, to lower temperat- ures as a squared monotonously decreasing function. After presenting a decrease in diffusion behaviour for intermediate volume fractions, TMAO is shown to strongly change the dynam- ics in highly concentrated samples. Here, the intensity auto-correlation functions display the shape of a stretched exponential, induced by the occurrence of differently sized particles, ag- glomerations or distinctive dynamic domains. Through the technique of 3D DLS employed to reduce multiple scattering, the sample is found to be strongly opaque, which, together with the observed arrangement of particles, is interpreted as evidence for the formation of a colloidal gel.

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Kurzfassung

Diese Arbeit untersucht die Dynamik eines kolloidalen Systems, bestehend aus Nanopartikeln mit einem Siliziumdioxidkern (Silica) und einer Polymerschale aus poly(N-isopropylacrylamid) (PNIPAm) gelöst in Wasser. Das auf Temperaturveränderungen reagierende Polymer PNIPAm ist bekannt für seinen Phasenübergang bei der kritischen Temperatur (LCST) von 32−33^◦C.

Unterhalb dieser Temperatur ist das Polymer hydrophil und deshalb mit Wasser vollge- saugt, während es sich oberhalb der LCST in einen hydrophoben Zustand transformiert, was zur Kontraktion des PNIPAm aufgrund des verdrängten Wassers führt. Dieser hydrophobe Kollaps wird mit der Methode der Dynamischen Lichtstreuung (DLS) untersucht, wobei alle Proben über einen Temperaturbereich von 15^◦C< T <42^◦C um die LCST betrachtet werden.

Dadurch kann das Diffusionsverhalten der verschieden stark verdünnten Proben analysiert und der hydrodynamische Radius der Teilchen berechnet werden.

Außerdem wird neben Wasser das natürliche, stabilisierende Osmolyt trimethylamin N-oxid (TMAO), welches für die Unterstützung des Faltungsprozesses in Proteinen bekannt ist, als Zweitlösungsmittel in Konzentrationen bis zu 2 mol/l eingesetzt. Mit höheren TMAO Konzentrationen steigt die Viskosität der Lösung an, während die Teilchengröße abnimmt.

Am interessantesten ist, dass TMAO die LCST, bei der sich das PNIPAm zusammenzieht, in Richtung niedrigerer Temperaturen verschiebt und zwar als eine quadratisch monoton fallende Funktion von der TMAO Konzentration. Nachdem die Verminderung der Dif- fusion für mittlere Volumenbrüche analysiert wurde zeigt sich, dass TMAO die Dynamik hochkonzentrierter Systeme stark beeinflusst. Hierbei stellen die Intensitäts- Autokorrela- tionsfunktionen eine gestreckte exponentielle Funktion dar, welche durch die Existenz von Teilchen unterschiedlicher Größe, Teilchenansammlungen oder verschiedenen dynamischen Domänen hervorgerufen wird. Mit Hilfe der 3D DLS Technik, welche Mehrfachstreueffekte reduziert, wurde eine starke Opazität der Probe entdeckt. Zusammen mit der beobachteten Teilchenanordnung wird diese als die Entwicklung eines kolloidalen Gels interpretiert.

iv

Table of Contents

1 Introduction 1

2 The Sample System 3

2.1 Silica-PNIPAm core-shell Nanoparticles . . . 3

2.2 Trimethylamine N-oxide . . . 4

3 Dynamic Light Scattering 6 3.1 Working Principle of DLS . . . 6

3.2 Dynamics of Diffusive Suspensions . . . 8

3.3 The Experimental Setup . . . 9

3.4 Dynamics of Turbid Samples . . . 10

4 Dynamical Properties 12 4.1 Sample Preparation . . . 12

4.2 Dynamics of Silica-PNIPAm in water solution . . . 13

4.3 Influence of TMAO on Dynamics and Gelation . . . 16

4.3.1 Dynamical Behaviour of PNIPAm with TMAO as co-solvent . . . 17

4.3.2 Gelation of PNIPAM colloids with TMAO as co-solvent . . . 23

5 Conclusion and Outlook 30

References 33

Acknowledgements 37

Eidesstattliche Versicherung 39

vi

List of Figures

2.1 Volume phase transition of a silica-PNIPAm core-shell particle. . . 3

2.2 Structural formulae of TMAO and PNIPAm. . . 5

3.1 Speckle Pattern. . . 7

3.2 Experimental Setup. . . 9

3.3 Experimental Setup of the 3D DLS Mode. . . 10

4.1 Variation of the intensity auto-correlation function with temperature and scat- tering vectorq. . . . 13

4.2 Exponent prelated to the relaxation rate Γ(q). . . 14

4.3 Change in the diffusion coefficient D0 at different levels of dilution. . . 14

4.4 Effective hydrodynamic radius R_H of the silica-PNIPAm colloid at different volume fractions. . . 15

4.5 Relative viscosity to water as a function of TMAO molar concentration. . . . 17

4.6 Hydrodynamic radii R_H for Φ_eff,20 = 0.03 under the influence of TMAO. . . . 18

4.7 Hydrodynamic radii at 15^◦C and 42^◦C for Φ_eff,20 = 0.03. . . 19

4.8 LCST development as a function of TMAO molar concentration. . . 20

4.9 Overlapping of the collapse behaviour for Φ_eff,20= 0.03. . . 21

4.10 Hysteresis in temperature at the hydrodynamic radius ofR_H = 140 nm. . . . 21

4.11 Development of the diffusion coefficientD₀ with TMAO concentration at 42^◦C and temperature from 15^◦C to 42^◦C for Φ_eff,20= 0.11. . . 22

4.12 Development of the diffusion coefficientD₀ with temperature and TMAO con- centration at Φ_eff,20 = 0.27. . . 23

4.13 Intensity auto-correlation functions for Φ_eff,20= 0.27 with 1.0M TMAO between 20^◦C and 30^◦C. . . 24

4.14 Kohlrausch exponentγ for Φ_eff,20 = 0.27 with 1.0M TMAO. . . 24

4.15 Representation ofg₂ functions during the coexistence of differently sized struc- tures in the solution. . . 25

4.16 Domain formation of faster and slower moving particles. . . 26

4.17 Fit for Γ(q) at Φ_eff,20= 0.27 with 1.0M TMAO between 20^◦C and 30^◦C. . . . 26

4.18 Temperature evolution of g₂(q, τ) for Φ = 2x at 1.0M TMAO and q = 20.10 µm⁻¹ around the LCST. . . 27 4.19 Examination of speckle contrastβ and scattering intensityI(q) in colloidal gel

formation. . . 28

viii LIST OF FIGURES

x

List of Tables

4.1 Samples of this investigation. . . 13 4.2 Effective volume fraction Φ_eff. . . 16

Chapter 1 Introduction

Colloidal suspensions consist of nanoparticles, which are dispersed in a liquid, e.g. water. In science, these systems have become powerful models in research for describing the dynam- ics of atoms, as nanoparticles display a similar phase behaviour, however are large enough to be observed by several experimental methods (Yunker et al., 2014). In particular, com- plex liquids as poly(N-isopropylacrylamide) (PNIPAm) colloids are in demand in all parts of natural sciences. Especially in chemistry and biology such thermoresponsive polymers are often used for applications in controlled drug release or as membranes for molecular separa- tion (Reddy et al., 2012). Remarkably, PNIPAm shows a so-called volume phase transition around the lower critical solution temperature (LCST) of about 32−33^◦C, which lets the PNIPAm chains coil up and as a result leads to a decreased particle diameter (Yunker et al., 2014).

This dynamical action can be analysed by Dynamic Light Scattering (DLS), which uses coher- ent laser light to correlate the displacement of the particles at different times. Additionally, the behaviour of PNIPAm can be manipulated by co-solvents such as Trimethylamine N-oxide (TMAO), which is often found in organisms under extreme conditions. The natural osmolyte is known to stabilize proteins to help them cope with the osmotic stress (Yancey, Clark and Hand, 1982). As a part of its effect on PNIPAm, increasing TMAO concentrations have been shown to shift the LCST to lower temperatures, which will be investigated as a part of this thesis. In biomedicine, while TMAO functions as a drug itself for many life-threatening diseases, PNIPAm serves as a drug carrier (Reddy et al., 2012). These colloidal fluids, when injected into patients, can become gels due to the body temperature of about 37^◦C and act as scaffolds for new cell growth or depots for further controlled drug release (Yunker et al.,

2014).

The huge medical applications of thermoresponsive polymers may help to control infectious diseases, which have become more imminent in modern days (Narang and Venkatesu, 2017), as seen this year by the worldwide pandemic of the coronavirus SARS-CoV-2.

In this thesis, the outline is as follows: The sample used for the experiments conducted dur- ing this investigation is introduced and presented together with an overview of the osmolyte TMAO (. Chapter 2). Then the method of Dynamic Light Scattering is explained with its traditional 2D and more sophisticated 3D DLS techniques (. Chapter 3). After that, the experimental results are developed, including basic sample characterization, the influence of TMAO on aqueous PNIPAm and the phenomenon of colloidal gel formation (. Chapter 4).

Here, samples of different volume fractions have been investigated in order to explain various effects. Finally, the results are combined in a conclusion, before an outlook of possible further research is presented (. Chapter 5).

2 Introduction

Chapter 2

The Sample System

2.1 Silica-PNIPAm core-shell Nanoparticles

Subject of investigation was a core-shell structured colloidal nanogel consisting of spher- ical particles with a 55 nm radius silica-core, surrounded by a thicker shell of the thermo- responsive polymer poly(N-isopropylacrylamide), in short PNIPAm. These core-shell particles were dissolved in water, forming a milky white, viscous liquid. The radius of particles in solu- tion generally is referred to as thehydrodynamic radiusR_H and can be tuned by temperature alterations. An interesting property of the polymer is its change of volume around the so- called lower critical solution temperature (LCST) at about 32−33^◦C (Yunker et al., 2014).

At temperatures below the LCST the polymer behaves hydrophilic, meaning it is swollen with water, hence the particles appear larger (Fig. 2.1, left side). At temperatures above the LCST it experiences a sudden decrease in volume due to a transition to a hydrophobic state, implying the nanoparticles oust most of the water (Fig. 2.1, right side). Some wa- ter molecules, however, will still remain in the PNIPAm layer after the so-called volume phase transition, which was shown to be fully reversible (L. S. Frenzel, 2019). Additionally,

Figure 2.1: Volume phase transition of a silica-PNIPAm core-shell particle (L. S. Frenzel, 2019)

PNIPAm nanogels have the unique property, that the volume fraction Φ may be tuned by temperature variations, while the weight fraction as well as the particle number density are not changed. In suspension, the PNIPAm layers interact with each other via short ranged repulsive forces, that prevent the particles from agglomeration, which is known as steric sta- bilization (Löwen, 1995). These repulsive interactions below the LCST, may be overpowered by attractive forces, as e.g. the omnipresent van der Waals interaction, when the temperature exceeds the LCST, thus leading to completely different structure and dynamics. The solution may progress into a gel phase at sufficiently high temperatures and particle concentrations (L. Frenzel, Lehmkühler et al., 2020). Further, due to the polymer’s softness, the shells may be deformed and at very high packing fractions even be compressed or interpenetrate the surface of the other particles, making effective volume fractions of greater than one entirely possible (Conley et al., 2017). The silica-core was implemented in the sample for earlier X-ray experiments in order to create a stronger scattering contrast for the short-wavelength beam and thereby enhancing resolution. Since this thesis is focused on exploring the core-shell system and its tunable interactions, i.e. the dynamical behaviour of PNIPAm, the colloid thereby has been reused.

2.2 Trimethylamine N-oxide

The osmolyte trimethylamine N-oxide (TMAO) is known to naturally stabilize proteins to protect them from hazardous conditions like high pressures or temperatures. It can be found at increased concentrations in e.g. deep sea fish and bacteria (Yancey, Clark and Hand, 1982). Although previous publications demonstrate that TMAO favours the collapsed, or globule state of the PNIPAM layer while the LCST shifts to lower temperatures with increasing TMAO concentration, scientific explanations as to why this is the case do not completely coincide. Whereas researchers agree on the preferential binding of TMAO with water molecules and the nearly nonexistent direct binding of TMAO with PNIPAm, the underlying mechanisms of how TMAO affects aqueous PNIPAm solutions are somewhat controversial. Schroer et al., 2016 as well as Pica and Graziano, 2017 independently found that a preferentialhydrationof PNIPAm takes place with increasing TMAO concentrations

4 The Sample System

due to adsorbed water which is bound to TMAO. This strengthens hydrogen bonds between PNIPAm and water molecules and thereby creates a thin water layer around the polymer, which stabilizes the globule state of the particles. In contrast, the work of Reddy et al., 2012 suggests that the direct hydrogen bonding between water and TMAO reduces the number of available water molecules to bond with PNIPAm, thereby enhancing the dehydration of the polymer which in turn prompts the hydrophobic collapse already at lower temperatures.

Furthermore, TMAO not only decreases the LCST but also reduces the temperature T_gel at which gelation takes place, therefore favouring a colloidal gel state at sufficiently high packing fractions. Very recently, the gelation process of silica-PNIPAm core-shell nanogels was studied by L. Frenzel, Lokteva et al., 2020, who discovered that the volume phase transition at the LCST was necessary to happen prior to reaching T_gel in order for gel formation to be achievable. While colloidal gel formation occurred at lower temperatures with increasing amount of TMAO in the solution, above a critical TMAO concentration no gelation could be observed. Owing to their results, it is suggested that conceivably a 1 : 1 particle ratio of TMAO to PNIPAm units (Fig. 2.2) fosters the collapse of the polymer and suppresses gelation. Here, one single PNIPAm unit is confined to the structure as presented, which

(a) Trimethylamine N-oxide (b) Poly(N-isopropylacrylamide)

Figure 2.2: Chemical structures of (a) TMAO and (b) PNIPAm (L. S. Frenzel, 2019).

is repeated n times in the polymer. As can be already seen from its structure, TMAO is capable of forming hydrogen bonds through a free electron on the oxygen atom. The controversy surrounding the topic regarding the influence of TMAO as a co-solvent displays a great incentive to further research in this area.

Chapter 3

Dynamic Light Scattering

Modern Dynamic Light Scattering (DLS) was implemented in the 1970s and since has been a major asset in studying the dynamics and by that the diffusion, size and aggregation of macromolecules like proteins, nucleic acids and viruses in solution (Stetefeld, McKenna and Patel, 2016). DLS is a fast and non-invasive technique, that delivers precise measurements compared to e.g. transmission electron microscopy and has the prospect of using the same sample multiple times, thus saving lots of time and resources. Moreover the in-situ operation of DLS is a major advantage compared to other electron microscopy techniques (Lim et al., 2013). However, DLS also suffers from limitations such as measurements being sensitive to viscosity and temperature changes or being a comparatively low resolution method (Stete- feld, McKenna and Patel, 2016). Moreover, especially in dense and turbid samples multiple scattering is the main drawback of the DLS technique as the statistics do not reflect mean- ingful results for multiple scattered light (Block and Scheffold, 2010). Modern applications of DLS besides the determination of hydrodynamic radii include biomedical investigations like the exploration of protein-protein or protein-small molecule interactions. For this chapter, the doctoral thesis Structure and Dynamics of Complex Liquids - The Phase Behaviour of Silica-PNIPAm Nanogels by Lara Frenzel (L. S. Frenzel, 2019) served as the main source.

3.1 Working Principle of DLS

In Dynamic Light Scattering the intensity of the scattered light by any particle in the sample is measured over a range of scattering angles θ_r for a given time t (Lim et al., 2013). In more detail, a laser source emits a beam of coherent light, which enters the sample. The particles in the sample scatter this light in all possible directions, but the intensity that is

6

measured in the detector will only be received from the direction of the angle θ_r. When coherent light is scattered by a disordered system, as it is the case for colloidal suspensions, a random interference pattern called “speckle pattern” (Fig. 3.1) is created on the detector.

Here, the figure gives a representation of a speckle pattern resulting from an X-ray source,

Figure 3.1: Left side: speckle pattern resulting from coherent light scattering of an X-ray source on a disordered system, which changes over time t; Right side: representation of incoherent scattered light, which in this case is an average of all times t (Lee et al., 2013).

whereas it looks the same for DLS, since both applications use coherent light. The absolute value of the so-called wave vector transfer q

q = 4πn

λ sin (θr/2) (3.1)

is commonly used as a unified variable for different experimental setups instead of the scat- tering angle θ_r, which makes it easier to compare between various scattering experiments. In equation 3.1, the solution’s refractive index is given by n, whileλ stands for the wavelength of the laser light. Due to the particles non-directional motion the scattered intensity I(q, t) fluctuates in time and therefore varies during the time τ of a measurement, resulting in a different intensity under the same q being I(q, t+τ). At the instant of the measurement (τ = 0 s) the intensities are equivalent or completely correlated, but as the particle moves away from its original location, the scattered intensity will change until there is no correl- ation with the intensity at τ = 0. Through a process called cross-correlation the beam is compared with itself (auto-correlation) at two different points in time, providing information

about the particles displacement. This notion can be quantified by the normalised second order auto-correlation function g₂(q, τ):

g₂(q, τ) = hI(q, t)I(q, t+τ)i

hI(q, t)i² , (3.2)

whereh·idenotes the time average over all timest (Grübel, Madsen and Robert, 2008). Here it is important to note that the light source has to be coherent in order to convey the dynamic information of the colloidal system.

3.2 Dynamics of Diffusive Suspensions

For most soft matter systems, equation 3.2 can be expressed through the Kohlrausch-Williams- Watts (KWW) function as

g₂(q, τ) = 1 +β·exp [−2(Γ(q)·τ)^γ] (3.3)

with the Kohlrausch exponentγ, the relaxation rate Γ(q) and the speckle contrastβ(q), which for DLS mainly depends on the coherence of the light source. The relaxation rate denotes the inverse of the characteristic relaxation time τ_c, that is defined as the time where the g₂ function has decayed to a fraction of 1/e² of its original value and therefore is a measurement for the dynamics of the system. For a diffusive system, equation 3.3 is an exponential with γ = 1, while the relaxation rate is given by

Γ(q) =D₀·q^p (3.4)

with p= 2 and the Stokes-Einstein diffusion constant D₀ D₀ = k_BT

6πηR_H . (3.5)

Here k_B is the Boltzmann constant, η represents the viscosity of the solvent and R_H the hydrodynamic radius of the silica-PNIPAm core-shell particles, which can be rewritten to

R_H = k_BT

6πηD₀ . (3.6)

8 Dynamic Light Scattering

Thus, R_H can be extracted from the information given by the intensity auto-correlation function. Again, these calculations are only valid for diffusive systems, i.e. systems that show Brownian motion and provide solely single scattering information to DLS measurements.

3.3 The Experimental Setup

In this thesis the LS Spectrometer from LS Instruments (LS Instruments AG, 2020) has been employed. Its most prominent features include the automatic angle adaptation over a range from 15^◦ to 150^◦ and the precise temperature control. Additionally, the LS Correlator is responsible for the photon detection as well as the cross- and auto-correlation of the signals. During the experiment, to protect the sample from dust or any other disturbances, it was enclosed in a reservoir filled with the organic compound decalin for the time of the measurement. The experimental setup then included a 100 mW laser, whose beam passed through a pinhole before it hit the sample enclosed in the cylindrical container (Fig. 3.2).

Consequently, the light was scattered by the disordered sample and measured by a detector

Figure 3.2: The experimental setup portraying the beam path of the laser light.

under a certain angle θ_r, or a scattering vector q respectively. The connected computer software converted the intensity signal into the auto-correlation functiong₂(q, τ), while it also saved all characteristics surrounding the measurement as the samples viscosity and refractive indices, the laser intensity and the temperature.

3.4 Dynamics of Turbid Samples

If the system is not diffusive, e.g. a colloidal gel, then the q dependency of Γ(q) is not quadratic and therefore equation 3.4 does not serve to calculate the diffusion coefficient D₀ anymore, neither does equation 3.6 reflect the radius of the particle. Furthermore, the Kohlrausch exponentγ may change for non-diffusive dynamics of the solution. Here, a larger γ signifies a faster than exponential decay of the correlation function, indicating ballistic, hyper-diffusive motion, whereas characteristic sub-diffusive dynamics with γ < 1 influence the slope ofg₂(q, τ) to be a stretched exponential. A value ofγ <1 may also imply the pres- ence of heterogeneities, e.g. particles of different sizes. Moreover, in opaque systems multiple scattering effects are common to occur and can lead to undetectable but significant errors in sample characterization. Therefore an adjustment to 3D cross-correlation needs to be performed, such that two illumination beams are aligned to measure a pair of identical scat- tering vectors in the same sample volume (Fig. 3.3). The initial single-scattering information

Figure 3.3: The experimental setup of the 3D DLS mode portraying two independent laser beams, which are correlated to extract solely the single-scattering information.

is then consistent in both measurements, while multiple-scattering effects are uncorrelated, thus being suppressed in the outcome (Block and Scheffold, 2010). A deficiency of this 3D technique, however, is that while one photon detector is supposed to just measure the scattered light intensity from the corresponding laser beam, it also receives a contribution at a second unwanted scattering vector due to the relative geometry to the second illumination

10 Dynamic Light Scattering

beam (Block and Scheffold, 2010). Since both beams operate at the same wavelength, the detectors encounter these perturbations from the corresponding undesired beam, leading to a reduced intercept β.

Chapter 4

Dynamical Properties

In this chapter it will first be discussed how the intensity auto-correlation function is affected by the temperatureT and the wave vector transferq. After that, the colloidal suspension will be characterized at different volume fractions, before the effects of TMAO on the solution are explored. For the following experiments, the core-shell particles were mixed with water at different ratios and inserted into a thin glass tube. The glass tube was then enclosed in the decalin chamber, which hereby functioned as a thermostat, whose temperature was elevated step-wise from 15^◦C to 42^◦C and consequently decreased again to the initial temperature in steps of 1^◦C. At each temperature step 5 DLS measurements with a time of 5 seconds each were performed under 6 different angles, namely over a range from 45^◦ to 120^◦ in steps of 15^◦.

4.1 Sample Preparation

A for earlier X-ray scattering experiments synthesized silica-PNIPAm core-shell system in a water solution with a weight fraction of 6.5% was diluted with different proportions of water.

The hereby created samples (Tab. 4.1) were to be examined via DLS as previously discussed.

Of each probe one milliliter in total has been filled into a thin glass cuvette, ensuring that all different concentrations are easily comparable in terms of volume fractions. Here, the original sample is referred to as Sample 0.

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Dilution κ weight fraction Volume Sample 0 Volume Water

2× 3.28 % 0.5 ml 0.5 ml

4× 1.65 % 0.25 ml 0.75 ml

5× 1.32 % 0.2 ml 0.8 ml

10× 0.66 % 0.1 ml 0.9 ml

20× 0.33 % 0.05 ml 0.95 ml

40× 0.17 % 0.025 ml 0.975 ml

100× 0.07 % 0.01 ml 0.99 ml

500× 0.01 % 2µl 0.998 ml

1000× < 0.01 % 1µl 0.999 ml

Table 4.1: Different diluted samples created from the synthesized sample 0 with a weight fraction of 6.5%.

4.2 Dynamics of Silica-PNIPAm in water solution

To first gain a perspective on the sample, it was characterized by DLS at different levels of dilution. The g₂ functions were measured at all of the six angles for each temperature (Fig.

4.1), which were examined for (a) all of the temperatures under a fixed angle and (b) all of the angles at a fixed temperature. The intensity auto-correlation functions display a shift to shorter relaxation times τ with both temperature and wave vector transfer q, respectively, indicating accelerating dynamics. To make any statements related to the explanations given

(a) (b)

Figure 4.1: (a)g₂ functions at temperatures from 15^◦C (blue) to 42^◦C (red) under q= 20.10 µm⁻¹ and (b) g₂ functions at T = 20^◦C under different q for a dilution of κ= 40×.

in section 3.2, it is essential for the system to be diffusive. As displayed in figure 4.2, the

Figure 4.2: Exponent p related to equation 3.4 for a dilution of κ= 40×.

exponentpfrom equation 3.4 is roughlyp= 2 for the performed experiments. This indicates, along with γ = 1, a diffusive behaviour, which makes the equations from section 3.2 valid for the system at hand. Through the observed relaxation processes, the principal measured quantity is the diffusion coefficientD₀ (Fig. 4.3). AsD₀ is related to the relaxation rate Γ(q)

Figure 4.3: Change in the diffusion coefficientD0 at different levels of dilution.

by equation 3.4, higher values of the diffusion coefficient imply quicker relaxation processes, i.e. faster dynamics. Interpreted as such, figure 4.3 illustrates that particles apparently move faster in more densely packed systems.

In order to analyze this unexpected observation, the hydrodynamic radius R_H was calculated for all samples by means of the Stokes-Einstein relation (Eq. 3.6), to provide a closer look at a more intuitive quantity (Fig. 4.4). It is noticeable that at low (high) temperatures

14 Dynamical Properties

Figure 4.4: Effective hydrodynamic radius R_H of the silica-PNIPAm colloid at different volume fractions.

the radius seems to be much larger (smaller) for higher particle concentrations than for modest ones. This apparent trend, however, is due to interparticle interactions, perhaps even interpenetration in densely packed systems, resulting in a slowing down of the mixture and thereby does not reflect the true radius of the single particle. Moreover, the solution was observed to be opaque for higher concentrations, which together with the deviating tendency in the radius points to the existence of multiple scattering. The correct size of the PNIPAm shell can only be accurately measured by DLS at more dilute suspensions. A valid result for the hydrodynamic radius is therefore achieved by e.g. the 100× (one hundred times diluted) sample. Hence, with the known weight percentageω of the dissolved particles in the pure sample, the volume fraction Φ_coll for the collapsed state could be determined through equation 4.1 (L. S. Frenzel, 2019):

Φ_coll = V_coll

V_coll+V_H2O . (4.1)

Here, the volume of the collapsed particleV_coll was calculated from the volumes of the silica- core and the contracted PNIPAm layer at T = 42^◦C. The water volume per particle V_H2O was obtained by the difference between total mass per particle (including water) and the raw particle mass (without water) (Eq. 4.2)

VH2O=

mSiP

ω −m_SiP

ρ_H2O . (4.2)

To obtain an effective volume fraction Φ_eff at a given temperature T, the volume fraction Φ_coll has been multiplied with the ratio of the swollen particles volumeV_swoll,T atT toV_coll:

Φ_eff = Φ_coll

κ · V_swoll,T

V_coll , (4.3)

where κ displays the degree of dilution. Three samples that show significant differences in their diffusion coefficients and radii have been chosen for further investigation. With equation 4.3 the different degrees of dilution could be translated to effective volume fractions Φ_eff,20 at room temperature (T = 20^◦C) and are presented in table 4.2. Here, the radius of the

Sample Dilution κ ωeff VH2O Φ_coll Φ_eff,20 original 1× 6.5 % 0.05µm³ 0.0486 1.08

1 40× 0.17 % 2.19µm³ 0.0012 0.03 2 10× 0.66 % 0.55µm³ 0.0049 0.11

3 4× 1.65 % 0.22µm³ 0.0121 0.27

Table 4.2: Effective volume fractions of elected samples for the collapsed state Φ_coll at T = 42^◦C and the expanded state Φ_eff,20 atT = 20^◦C.

collapsed particle was calculated from the sample at κ = 100× to R_coll = 86 nm and the resulting volume amounted to V_coll = 2.7·10⁻³ µm³. The results show that indeed for the original sample an overpacked arrangement with an effective volume fraction of greater than 1 is realized for temperatures below the LCST. Moreover it can be seen, that also the weight fractions of lower concentrations can be derived from the original sample almost by dividing by the dilution, meaning that the density of the solution is very close to that of water.

The dynamical behaviour of the three selected samples will be analysed further under the influence of TMAO in the subsequent section.

4.3 Influence of TMAO on Dynamics and Gelation

As the main part of the investigation, three different volume fractions of silica-PNIPAm particles were mixed with various concentrations of TMAO. As previously discussed, TMAO acts as a stabilizer for the collapsed state of the PNIPAm shell, shifting the LCST to lower temperatures. Here, the objective is to determine the exact correlation between the LCST

16 Dynamical Properties

and the TMAO concentration, while exploring the influence of TMAO on the dynamics of the colloidal suspension.

4.3.1 Dynamical Behaviour of PNIPAm with TMAO as co-solvent

The three volume fractions Φ_eff,20 = 0.03, Φ_eff,20 = 0.11 and Φ_eff,20 = 0.27 from section 4.2 have been mixed with TMAO as a co-solvent. With the addition of TMAO as a solvent besides water, the viscosity of the suspension changes, which has to be taken into account when calculating the hydrodynamic radius according to equation 3.6. In order to perform this correction, the effective viscosity in dependence of TMAO molar concentration with re- gards to pure water was determined from Sinibaldi et al., 2006. Figure 4.5 visualizes the

Figure 4.5: Relative viscosity to water as a function of TMAO molar concentration.

importance of the aforementioned correction, since the highest TMAO concentration of 2.0M used in the experiments already doubles the viscosity of the suspension. As the curve for sample 1 strongly resembles the one of the appointed appropriate dilution ofκ = 100×(Fig.

4.4), its hydrodynamic radius could be determined with the viscosity adjustment from the intensity auto-correlation functions (Fig. 4.6). The particles exhibit a minor decrease in ra- dius at cold temperatures (i.e. 15^◦C) as well as at warmer temperatures of 42^◦C with TMAO concentration (Fig. 4.7). This indicates, that already the mere addition of TMAO extracts water from the PNIPAm layer, thus resulting in a smaller size of the particle, independent from the actual collapse at the LCST. Most notable, however, is the shift in the LCST to-

Figure 4.6: Hydrodynamic radii R_H for Φ_eff,20 = 0.03 under the influence of TMAO.

wards lower temperatures, until the contraction of the polymer layer is not visible anymore in the investigated temperature range, i.e. for 2.0M TMAO. This applies for all TMAO concentrations. To extract a value for the LCST from the data, the mean temperature at R_H = 140 nm was calculated for each TMAO concentration via interpolation. This method is limited to the TMAO concentrations at which the volume phase transition takes effect in the considered temperature range from 15^◦C and 42^◦C. The results show that in fact, the alteration of the LCST does not depend on the volume fraction, but it is one clear correlation solely dependent on the amount of TMAO in the solution (Fig. 4.8). Here, the two lines represent fits to the data. While the purple line displays a model linear fit from literature (Narang and Venkatesu, 2017), the red line demonstrates a fit to the actual data of sample 2, which corresponds to a second order polynomial

LCST(cM) = −1.436c²_M −7.602cM + 33.04 , (4.4)

where the lower critical solution temperature is presented in units of ^◦C and c_M reflects the molar concentration of TMAO in the solution. The linear model was obtained from TMAO concentrations of up to 1.0M in a sample containing pure PNIPAm particles. Although the data and the model from literature give the same value for the LCST without TMAO, i.e.

about 33^◦C, it is clearly visible that for the core-shell system with TMAO concentrations exceeding that of 1.0M a quadratic function conveys a more accurate representation. Addi-

18 Dynamical Properties

(a) (b)

Figure 4.7: Hydrodynamic radii at (a) 15^◦C and (b) 42^◦C at Φeff,20= 0.03.

tionally, the collapse behaviour was investigated through moving all curves back by the LCST shift caused by TMAO, thus aligning the graphs as if the volume phase transition takes place at T = 33^◦C for all concentrations. Figure 4.9 portrays how all curves substantially follow the same course. However, for the highest TMAO concentrations a steeper and more abrupt PNIPAm contraction can be seen, which demonstrates that TMAO provokes the collapsed particle state.

Furthermore, the measurements with increasing temperature from 15^◦C to 42^◦C and the subsequent measurement with decreasing temperature back to 15^◦C in figure 4.6 show an expanding hysteresis with progressive TMAO concentration. To further analyse this obser- vation, the temperature T₁₄₀ at which R_H = 140 nm was extracted for the heating and cooling processes for the various TMAO concentrations. Thereupon, the difference between these temperatures was calculated by subtractingT₁₄₀ for the cooling process from that of the heating process. The results show a non-linear increase in hysteresis (Fig. 4.10) as TMAO is added to the suspension. Here, the data for 0M and 0.1M TMAO concentrations have been excluded from the fit, which is portrayed by the pink dashed line. The hysteresis has been previously observed for poly(N-isopropylacrylamide) and results from the formation of additional hydrogen bonds in the collapsed particle state at temperatures higher than the LCST (Lu et al., 2010). Obviously, the effect is strengthened through the addition of TMAO

Figure 4.8: LCST development as a function of TMAO molar concentration.

to the solution. Moreover, this confirms how TMAO stabilizes the collapsed particle state as PNIPAm stays contracted even for slightly colder temperatures.

For the higher particle concentrations a meaningful radius curve could not be obtained by DLS, hence the diffusion coefficientD₀ serves as a comparative measure. As can be seen from the diminishing D₀ in figure 4.11(a), the particles mobility is reduced with an increasing amount of TMAO in the solution. Moreover, at the highest TMAO concentrations the diffusion coefficient does not show the upturn as it does for lower ones, instead it linearly increases with temperature, indicating that the nanoparticles are already in the globular state. A depiction of D₀ at T = 42^◦C shows, that the reduction in diffusive behaviour with TMAO concentration follows a non-linear model (Fig. 4.11(b)), which results from a combination of changes in radius (Fig. 4.7(b)) and viscosity (Fig. 4.5). As portrayed in the Stokes-Einstein relation 3.5, both R_H and ηbehave inversely toD₀. Since the hydrodynamic radius decreases linearly as seen from sample 1 and the viscosity increases as a second order polynomial, the effects of the viscosity outweigh the ones of the radius, which is why the diffusion coefficient shrinks.

In summary, after contemplating the change in the hydrodynamic radiusR_H with the addition of TMAO as a co-solvent, it has been found that with increasing concentrations of the osmolyte, water is extracted from the PNIPAm shell, resulting in smaller particle sizes.

20 Dynamical Properties

Figure 4.9: Overlapping of the collapse behaviour for Φ_eff,20= 0.03.

Figure 4.10: Hysteresis in temperature T₁₄₀ at the hydrodynamic radius of R_H = 140 nm upon heating and cooling.

This observation coincides with a growing viscosity, while the diffusion D₀ diminishes as TMAO is added to the solution. Moreover, it was discovered that TMAO reduces the lower critical solution temperature, which follows a quadratic model, with an LCST of 33^◦C for 0M TMAO. Additionally, a hysteresis in radius could be identified between the heating and cooling processes. Most likely it results from the formation of additional hydrogen bonds in the collapsed PNIPAm state, which grows stronger under the influence of TMAO.

Furthermore, this conclusion demonstrates the stabilizing effect of TMAO as a co-solvent on globular PNIPAm, in so far that the particles tend to remain in the collapsed state for

(a)

(b)

Figure 4.11: Development of the diffusion coefficientD₀ with (a) temperature and (b) TMAO concentration at 42^◦C for Φ_eff,20= 0.11.

as long as possible during the cooling process. Even slower acclimation is expected in more turbid samples as e.g. for higher volume fractions like Φ_eff,20 = 0.27.

22 Dynamical Properties

4.3.2 Gelation of PNIPAM colloids with TMAO as co-solvent

An interesting behaviour can be seen by examination of sample 3 (κ= 4×). Taking a look at the diffusion coefficient D₀ as for the previous samples, one can recognize, that for low TMAO concentrations the suspension actually seems to accelerate, as indicated by D₀ values above those of 0M TMAO (red line in figure 4.12). At the highest temperature of 42^◦C the suspension apparently slows down as higher amounts of TMAO are realized, as visualized by the D0 below the red line for that temperature. For the highest TMAO concentration of 2.0M the coefficient rises up again, however shows a strong hysteresis between measurements at increasing and decreasing temperatures.

Figure 4.12: Development of the diffusion coefficient D0 with temperature and TMAO con- centration at Φ_eff,20 = 0.27.

Concerning the g₂ functions, it is visible that the q-dependence in figure 4.1(b) is altered for higher temperatures, while it is preserved for figure 4.1(a). Figure 4.13(a) displays the g₂ functions at 20^◦C showing shorter relaxation times with increasing wave vector transfer q, while in 4.13(b) the intensity auto-correlation functions at 30^◦C, are shown to be bundled together instead. This expresses that relaxation times are very similar for all q values at higher temperatures. Moreover, one can notice that the fits of the functions do not perfectly match the data in this example, because the slope is less steep and stretched in time. This observation can be attributed to a diminishing Kohlrausch- or stretching exponent γ, which

(a) (b)

Figure 4.13: Intensity auto-correlation functions for Φ_eff,20 = 0.27 with 1.0M TMAO at (a) 20^◦C and (b) 30^◦C.

is responsible for a stretched (γ < 1) or compressed (γ > 1) exponential (see. Eq. 3.3). As

Figure 4.14: Kohlrausch exponent γ for Φ_eff,20 = 0.27 with 1.0M TMAO. Here the LCST is presented by a vertical red line.

can be examined from figure 4.14, at a temperature which coincides with the LCST of the observed mixture (see Fig. 4.8), the Kohlrausch exponent clearly differs from that of diffusive systems (γ = 1) and is located between 0.6 and 0.85 depending on the scattering angle and temperature. There are numerous possible explanations for this perception, which are all based on the same main idea that structures of different sizes are present in the suspension at the same time. Smaller compounds move quicker than larger ones, which leads to various outputs for g₂(q, τ) with smaller or greater relaxation times τ, depending on the size of the

24 Dynamical Properties

structures. The experiment then averages these functions into one stretched exponential, lowering the γ coefficient (Fig. 4.15). Here, the blue line represents larger and slower com-

Figure 4.15: Representation of g₂ functions during the coexistence of differently sized struc- tures in the solution.

plexes, while the red line portrays smaller, faster structures. The average of the g₂ functions will then lead to a stretched exponential (black) with γ <1.

One possible interpretation displays that some particles are already in the globule state, which is expected beyond the LCST, while other particles still remain in the expanded form- ation. This would obviously lead to differently sized structures in the solution, i.e. individual particles of distinct volumes.

Further, agglomerations of particles, which dominate in the investigated regime of small q values under high densities, might be perceived as larger and therefore slow particles by the photon detector, since the particles are capable of interpenetrating one another. The result is the aforementioned stretched appearance of the intensity auto-correlation function.

There is another possible origin based on previous observations also made in colloidal sus- pensions, which state that for higher packing fractions spatial structural orderings emerge due to dynamic heterogeneity. This means that fast (slow) moving particles cluster together in space with equally fast (slow) moving ones to form domains of different dynamics (Fig.

4.16). This is a typical behaviour for super-cooled liquids and glass formers. The red col- oured grains are displaced by more than their own diameter, while the dark blue colour signifies no movement of the particle at all. Intermediate colours correspond to intermediate displacements (Garrahan, 2011). The figure therefore very well illustrates the formation of

Figure 4.16: Simulation of the equilibrium dynamics of 10,000 particles of a super-cooled fluid mixture over a time comparatively short to the systems relaxation time (Garrahan, 2011).

domains of mobile and immobile particles, respectively. If these domains are detected in the experiment, then the resulting g₂ function would also look like what is suggested in figure 4.15.

The change of g₂(q, τ) thereby leads to equation 3.4 not being valid anymore, since a non- diffusive behaviour of the particles occurs. This can be portrayed by plotting the fit of Γ to q², which should give a linear relation for diffusion (Fig. 4.17), but instead displays a curved line for temperatures above 24^◦C, which is around the LCST for the given sample. This

Figure 4.17: Fit for Γ(q) at Φ_eff,20= 0.27 with 1.0M TMAO between 20^◦C and 30^◦C.

26 Dynamical Properties

indication of non-diffusion points towards the formation of a colloidal gel, which is known to happen for PNIPAm samples at sufficiently high volume fractions once a gelation temperature T_gel is reached. To further investigate this hypothesis, a measurement on the sample with volume fraction Φ_eff,20 = 0.27 and 1.0M TMAO was performed in the 3D DLS mode, to avoid multiple scattering effects, at the cost of a reduced speckle contrast β by a factor of 4 to 5. Here, temperature steps of 0.1^◦C have been used, while each measurement took a time of 100 seconds. Also the temperature range was scaled down to the region around the LCST between 20^◦C to 27^◦C. Interestingly, the contrast of the g₂ functions decreases when

Figure 4.18: Temperature evolution of g₂(q, τ) for Φ = 2x at 1.0M TMAO and q = 20.10 µm⁻¹ around the LCST.

approaching the LCST, until it vanishes completely above this critical temperature (Fig.

4.18). No observable contrast at all, i.e. β = 0, means that the dynamics of the system are either too slow or too fast to be observed in the experiment. However, in this sample system, the dynamics cannot suddenly become too fast, which means they must be very slow. Then, the 3D DLS mode prints out a static signal and the cross-correlation becomes zero, indicating a gelation process. Possibly, an even longer measurement time is necessary to observe the relaxation process of this sample. To verify this discovery, the speckle contrast β has been set up against the time of the measurement and been compared to the change in scattering intensity during the measurement. The LCST is reached after a time of approximately 110 minutes, which is portrayed by the red vertical line. As figure 4.19(a) demonstrates, the

(a) (b)

Figure 4.19: (a) Speckle contrast β and (b) Scattering intensity I(q) normalized to the laser intensity for Φ_eff,20 = 0.27 with 1.0M TMAO and q= 20.10 µm⁻¹ between 20^◦C and 27^◦C.

speckle contrast decreases with the time of the measurement, especially once the LCST is reached, signifying a strong slow down in dynamics. This is confirmed by the scattering intensity falling towards zero for increasing temperatures in exactly the same manner. The shown graph in figure 4.19(b) gives information about the ratio of the photons received by the detector to the power used by the laser. A reduction of this normalized intensity happens when the sample turns opaque, as more laser power is needed for the same amount of photons to penetrate the sample and scatter towards the detector, which is typical for a PNIPAm gel. Thus, to observe the slow dynamics at larger timescales, dynamic light scattering is not sufficient enough, as it is limited to the range of small scattering wave vectors and by its strong deficiency upon the occurrence of multiple scattering. For these investigations short- wavelength beams like X-rays are necessary to detect such prolonged dynamic behaviour as the one found for sample 3. Therefore, X-Ray Photon Correlation Spectroscopy (XPCS) might provide valuable insights in this field of research.

Summarizing, due to curious changes to the diffusion and the intensity auto-correlation function, a reduced Kohlrausch exponent was found for the densest volume fraction of Φ_eff,20= 0.27. It was shown how smaller values for γ influence g₂(q, τ) to become a stretched exponential, through the existence of different particle sizes, agglomerations or various dy- namic domains, which are common indicators for the transition into a colloidal gel phase.

28 Dynamical Properties

Furthermore, it was discovered that for this case the relaxation rate Γ is not related to the diffusion coefficient D₀ for the dense sample, due to multiple scattering effects. Here, the 3D DLS mode was applied in order to extract the single scattering information. Thereby, a rapid decrease of speckle contrast β beyond the LCST indicates very slow dynamics in com- parison to the samples with lower effective volume fractions. Additionally, the normalized scattering intensity decreased during the time of the measurement, which shows that more laser power is needed to traverse the sample, because the dispersion becomes opaque. Such opacity moreover is typical for a PNIPAm gel phase and leads to the conclusion of such a transition. To analyse this in a deeper and more accurate way, one would have to apply scattering techniques, which are less affected by multiple scattering such as XPCS.

Chapter 5

Conclusion and Outlook

In this study, the temperature-dependent dynamics of silica-PNIPAm core-shell nanopartices, especially under the influence of the osmolyte TMAO, have been investigated with Dynamic Light Scattering (DLS). After basic sample characterization and revision of the diffusion behaviour of various dilutions, the hydrodynamic particle radius R_H was obtained from a sufficiently diluted sample.

Three samples of different volume fractions Φ_eff,20 = 0.03, Φ_eff,20 = 0.11 and Φ_eff,20 = 0.27, that have shown diverse developments in the diffusion coefficient D₀, were selected to be examined in a water solution with TMAO as a co-solvent. The results show that TMAO reduces the size of the particles, while it increases the viscosity of the fluid. Moreover, the lower critical solution temperature (LCST) without TMAO was determined to be at about T = 33^◦C, while it decreases as a polynomial function of order two with increasing TMAO concentration. The hysteresis in radius between the heating and the cooling processes can be attributed to the formation of additional (hydrogen) bonds in the collapsed particle state of PNIPAm and it grows stronger as a result of the stabilizing effect of TMAO.

For the highest packing fraction of Φ_eff,20= 0.27 the sample was found to transform into a gel phase at temperatures above the LCST. This observation is associated with differently sized particles, particle accumulations or the formation of distinctive dynamic domains, which are typical for super-cooled liquids or glass formers. To avoid the issue of multiple scattering, the technique of 3D DLS was applied, which displays a decrease of the speckle contrast in g₂(q, τ) for temperatures above the LCST. Furthermore, the scattering intensity decreases during the time of that experiment, which suggests an opaque sample system and supports the interpretation of a present colloidal gel.

30

To investigate the gelation process in more detail, the technique of X-Ray Photon Correlation Spectroscopy (XPCS) can provide valuable insights, since it is capable of operating at a sub- millisecond timescale and less affected by multiple scattering (L. Frenzel, Lokteva et al., 2020). Furthermore, the dynamical properties of PNIPAm could be further analysed under the influence of various co-solvents like e.g. salt (Christau et al., 2017), ethanol (Backes et al., 2017) or the denaturing osmolyte urea, which is known to have the opposite effect to TMAO on proteins (Mondal et al., 2015). To access the exact folding kinetics of PNIPAm and its polymer dynamics, X-Ray Free Electron Lasers (XFELs) could provide more consequential statistics at shorter illumination times by their operation at ultrafast, i.e. sub-nanosecond timescales. Ultimately, it would be wise to validate the experimental findings by theoretical analysis and computer simulations (Micciulla et al., 2016).

32

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36

Acknowledgements

Diese Bachelorarbeit wurde angefertigt über das Deutsche Elektronen Synchrotron DESY.

Ich möchte mich zuerst bei allen Mitgliedern der FS-CXS Gruppe unter der Leitung von Pro- fessor Dr. Gerhard Grübel bedanken. Ich wurde von Anfang an sehr herzlich aufgenommen und konnte von jeder Seite immer auf Rat und Unterstützung zählen, wodurch ich mich sehr wohlgefühlt habe.

Vor Allem Dr. Felix Lehmkühler hat mich bei meiner Arbeit begleitet, mich in das Thema eingewiesen und mir zum Abschluss meines Studiums noch einmal so unglaublich viel beige- bracht. Über physikalische Zusammenhänge, die du auf so einfache Weise erklären kannst, bis hin zur Methodik des wissenschaftlichen Arbeitens und der Auswertung mit MATLAB.

Auch geht mein spezieller Dank an Dr. Wojciech Roseker und Dr. Francesco Dallari, die mir die Funktionsweise des DLS Spektrometers erklärten und somit die Experimente überhaupt erst möglich machten.

Des Weiteren danke ich Dr. Irina Lokteva für die Hilfe im Umgang mit den Chemikalien im Labor.

Ein großes Dankeschön geht an Dr. Lara Frenzel, die mir über ein Proseminar das Thema der kolloidalen Systeme überhaupt erst schmackhaft gemacht hat.

Mein ausgesprochener Dank geht auch an meine Freunde, die ich während des Studiums in Hamburg kennenlernen durfte. Gemeinsam haben wir viele Hürden überwinden müssen, aber letztendlich haben wir es alle geschafft. Mit euch hat das Physikstudium sogar ein bis- schen Spaß gemacht. Danke an Rayan El-Assi, Lukas Judith, Johannes Gebauer, Matthias Czimmeck, Milan Staffehl, Nora Bidzinski, Johanna Lömker, Jan Voß und Leon Weber.

38

Eidesstattliche Versicherung

Ich versichere, dass ich die beigefügte schriftliche Bachelorarbeit selbstständig angefertigt und keine anderen als die angegebenen Hilfsmittel und Quellen benutzt habe.

Die von mir eingereichte schriftliche Fassung entspricht jener auf dem elektronischen Speich- ermedium.

Ich erkläre ferner, dass die von mir angefertigte Bachelorarbeit in gleicher oder ähnlicher Fassung noch nicht Bestandteil einer Studien- oder Prüfungsleistung im Rahmen meines Studiums war.

Ich bin damit einverstanden, dass die Bachelorarbeit veröffentlicht wird.