1 Introduction
1.3 Dendronized polymers
Dendronized polymers (DPs) represent nanostructured molecular objects with high level of structural complexity at the interface between materials and biosciences. In recent years, DPs have attracted considerable interest for their potential application in biology and material sciences, including the development of optical devices [73, 74], biosensors [75], supports for enzymes or nucleic acids [76, 77], and drug delivery systems [77, 78]. They comprise linear backbones carrying repeatedly branched dendrons of varying generation as the side chains. Free ends make up more than 50% of the monomers in a dendronized polymer, with the spatial distribution favoring the exterior envelope of the chain. A large number of end groups permits then the control of solubility as well as further chemical modifications [79]. There are two principally different synthetic approaches to dendronized polymers, i.e. “attach-to”
route and macromonomer route [79, 80] (Figure 1.5). In the attach-to route, two types of trifunctional building blocks, polymerization (P) and dendronization (D) units, are used. P units with two blocked functionalities are polymerized thus forming a first generation of DP PG1 (Figure 1.5a and b). The resulting polymer is deblocked (Schema 1c) and reacted with D units to create a second generation PG2 (Figure 1.5d). Higher generations are created by repeating the de-protection step followed by reaction with blocked D units. In the macromonomer route, the P units already carry a dendron of generation in question (Figure 1.5e) and their polymerization leads directly to this generation of DP (Figure 1.5f). The stepwise addition, “attach-to” route, allows the production of long high generation DP whereas the
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polymerization of dendronized monomers, the macromonomer route, only creates short DPs of higher generation, due to the bulkiness of the P units.
Figure 1.5 The two synthetic routes to dendronized polymers, “attach-to” route and macromonomer route [80]. The homologous series of different generations of DPs relies on the same chemistry but differs in the number of monomers in the side chain [81]. Therefore, DPs allow systematic, generation-dependent study of the variation in thickness, persistence length and other physicochemical properties. The thickness of DPs allows distinguishing between species of different generation using atomic force microscopy when coadsorbed onto a single substrate. DPs adsorb as weakly deformed cylinders, the degree of deformation varying with generation. Compared to dendrimers and bottle brushes of linear chains, the cylindrical geometry of DPs provides smaller volume to a side chain, thus leading to stronger chain stretching and weaker deformability. The highly crowded DPs are close to their maximum extension, thus the higher the generation is, less deformable coronas and higher backbone rigidity is expected [81]. Numerous studies on DPs have addressed their responsive behavior [51, 82-84], their conformation [85], the dimensions of adsorbed chains [81], self-folding of single charged polymer chain [86], and their interaction with surfaces [37].
19 1.4 Surface sensitive techniques
1.4.1 Atomic force microscopy
The atomic force microscopy (AFM) is the principal technique used in this study to investigate the conformation of DPs on solid substrates, their interaction with surfaces and mechanical response of individual polymer chains at the single-molecule level.
Since the invention of AFM in the mid 1980s by Binnig et al. [87], the technique has developed into a powerful and versatile tool intensely used for the study of the surface topography at atomic and nanometer scale, the chemical structure of a molecule [88], the high resolution imaging of DNA, proteins and polymers [89-91], the inter- and intramolecular interactions in surface-immobilized systems [27, 54, 92-94], the mechanical properties of polymers [28, 95-97], and more. In this thesis, AFM was employed to measure forces and surface topography; both approaches are discussed in the following.
Figure 1.6 (a) Schematic drawing of a force microscope and (b) illustration of a deflection-displacement (piezo position) experiment.
Typically AFM is carried out under ambient conditions, but a great advantage of AFM is the possibility to image the sample in almost any environment, ranging from vacuum, trough gas, to liquid.
AFM probes the surface of a sample with a sharp tip which is located at the free end of a cantilever spring. The cantilever acts as a sensor for the interaction between the tip and a sample (Figure 1.6a). The sample is mounted on a piezoelectric device, which allows the sample to be moved in the vertical direction (z-direction) and scanning the surface in the x-y direction. While the tip scans over the sample,
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the forces between the tip and the sample surface cause the cantilever to bend or deflect. The deflection of the cantilever is detected optically by the deflection of a laser beam focused at the back of the cantilever and reflected to a position-sensitive photodiode.
AFM force measurements. In a force measurement, the x-y position is fixed, while the sample (or tip) is moved up and down by applying a voltage to the piezoelectric device. The cantilever deflection and displacement of the piezo are recorded (Figure 1.6b). During an experiment, the tip is initially far away from the surface, forces are absent and the cantilever is not deflected (Figure 1.6b, Position 1).
Subsequently, attractive surface forces become apparent as the tip approaches the surface and eventually jumps into a close repulsive contact with the surface (Figure 1.6b, Position 2). While the tip and the sample are in contact, the pressure that the tip exerts on the surface increases with the sample displacement. In this region (Figure 1.6b, Position 2-3), known as the constant compliance region, the signal of the photodiode (voltage) and sample displacement are proportional, and the voltage can be directly converted into the cantilever deflection. Upon retraction of the tip and the substrate, the repulsive forces decrease continuously followed by the complete separation of the tip from the surface (Figure 1.6b, Position 4).
These deflection-piezopath data have to be transformed into force-distance curves. The measured piezo position (z0) can be converted into the real distance (z) between the AFM tip and the surface according to Eq. (1.11):
1
zz0s D (1.11)
Here, D is the measured cantilever deflection and s is the slope [voltage/length] of the linear part of the curve reflecting the bending of the cantilever upon contacting and indenting the substrate surface. The force F is then obtained by applying Hooke’s law [Eq. (1.12)] [98]:
0
F kc z z (1.12)
where kc is the spring constant of the cantilever. The minus sign in the equation transforms the negative deflection into a positive force signal. Finally, the force acting on the cantilever is plotted against cantilever-surface distance (z), giving the true force-distance curve.
The cantilever spring constant kc is normally determined from the thermal oscillation spectrum of the cantilever [99, 100], but many other methods [101], such as vibrational based on the geometry of the cantilever
[102], method measuring the resonance frequency of the cantilever before and after adding end masses [103], can be used.
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In the work reported in this thesis, the spring constant was obtained by thermal method in air [99]. The cantilever is positioned far away from the surface, is not affected by long range forces and only vibrates around its equilibrium position due to the thermal fluctuations. If a system is in thermal equilibrium, the ground oscillation of the cantilever has a mean energy equal to 1
2k T (kis the Boltzmann constant, Tis the absolute temperature). Due to thermal motion, the cantilever oscillates with an amplitudex. If the cantilever is modeled as a harmonic oscillator, its resonance frequency is:
0 kc
m (1.13)
where 0is the resonance frequency, kcthe spring constant, and mthe effective mass of the cantilever.
Considering just one degree of freedom for the cantilever (it can move only up and down) and the equipartition theorem:
2 2 2
0
1 1 1
2m x 2kc x 2k T (1.14)
where x2 is the mean square of the thermal cantilever fluctuations. The spring constant can be subsequently obtained as Eq. (1.15):
2 c
k k T
x (1.15)
To exactly determine x2 , it requires integration over the ground oscillation in the power spectrum of the cantilever measured over all frequencies [104].
AFM topography. AFM modes are generally classified as static or dynamic modes, based on the oscillation of the tip during the imaging [105].
In the static mode, the tip does not oscillate and the topography of the surface is generated from the cantilever deflection. There are two basic ways of operation, constant height and constant force. In the constant height mode, the cantilever deflection is detected without a feedback control as the height of the scanner is fixed as it scans and it is used directly to obtain the topographic data. This mode is applicable to very smooth, atomically flat surfaces where the variations in the cantilever deflections (i.e., in applied force) are small. In the constant force mode, the cantilever deflection is kept constant by moving the
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scanner up and down in z direction, generating the image from the scanner motion. Constant force mode is generally preferred as the total applied force to the sample is constant and well controlled.
In the dynamic modes of AFM, the system vibrates the cantilever at or near its free resonance frequency. According to the parameter used to establish the feedback mechanism, two major dynamic modes of AFM are amplitude modulation and frequency modulation AFM [105, 106]. In amplitude modulation AFM, the oscillation amplitude changes as the tip approaches the sample surface and is used as a feedback parameter to obtain the surface topography. On the other hand, in frequency modulation, the cantilever is kept oscillating with a fixed amplitude and the feedback parameter is a frequency shift between the resonance frequency far from the surface and the resonance frequency closer to the surface.
The resonance frequency depends on the forces acting between tip and sample surface. The dynamic (oscillating) AFM modes became widely popular, taking advantage of the signal-to-noise benefits associated with modulated signals. The imaging can be carried out with a small probe-sample force, thus preserving both the sample and the AFM tip.
Figure 1.7 Schematic illustration of the amplitude change as a function of the tip-surface separation.
Throughout this thesis, the amplitude modulation (AC) mode of AFM was used to image the topography of the sample. The cantilever is oscillated (with free oscillation amplitudeA0) typically at or near its resonance frequency with an additional piezoelectric element. When the oscillating cantilever approaches the surface, the forces between the tip and the surfaces cause changes in the oscillation, a damping in the cantilever oscillation (Figure 1.7). The damping leads to a decrease in the resonance frequency and in turn in the amplitude of the oscillation. The feedback loop maintains the amplitude constant. This process involves comparison between the instantaneous value of the amplitude Aiwith respect to a reference value, the set point amplitudeA. An error signal is generated. The goal is to keep
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this error signal as small as possible. Based on the error signal, an integral differential system moves the piezo scanner in zdirection in order to minimize the difference between A and Ai.
Depending on the oscillation amplitude used, AFM can be operated in different regimes, i.e. non-contact, and intermittent-contact regime (Figure 1.8). The interatomic force between the tip and the surface is either repulsive (contact mode) or attractive (non-contact mode). Using a small oscillation amplitude, the cantilever can be held in the attractive regime only. On the other hand, if a large oscillation amplitude is applied, the tip can move from ‘zero-force’ regime, through the attractive regime where is no tip-sample interaction, to the repulsive regime in each oscillation cycle. This technique is known as intermittent-contact AFM (IC-AFM). The cantilever tip, which vibrates at or near its resonance frequency, is brought closer to the sample surface and at the bottom of its travel it just barely hits the sample. IC-AFM has become an important technique as with its introduction it became possible to image soft structures such as polymers, since it is less likely to damage the sample than contact AFM by eliminating lateral forces and is more effective than non-contact AFM by overcoming its fundamental instability in air.
Figure 1.8 Different operating regimes for oscillating AFM modes. Force versus tip-to-sample separation curve illustrating the attractive and repulsive regimes.
1.4.2 Reflectometry
Reflectometry is a simplified form of ellipsometry, which is cheaper, with rather simple setup and uses surfaces easy to prepare and to further functionalize. It enables continuous and quantitative measurements of the polymer or particle adsorption onto flat solid substrates [107-110]. A continuous
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measurement is obtained over short time scales, therefore reflectometry is highly suitable for the measurement of the adsorption kinetics on the time scale of seconds to minutes [110, 111]. With the developments in the reflectometry setup, the technique has even proven to be efficient for probing the ions at a water-silica interface during the formation of the electrical double layer [112], and in biomolecular sensing [113, 114]. A schematic representation of a reflectometry setup is shown in the Figure 1.9.
Figure 1.9 Schematic representation of reflectometry setup.
In this technique, a linearly polarized laser beam is reflected on a surface through an optical prism at a fixed angle of incidence. The beam reflected off the surface passes through a beam splitter (Wollaston prism), and is split into its parallel (p) and perpendicular (s) components with respect to the plane of reflection. Two separate photodiodes continuously measure the intensities of parallel (Ip) and perpendicular (Is) polarized light. Changes in the refractive index close to the surface due to polymer or particle adsorption lead to a change in the ratio of these intensities. The reflectometry signal Ris given by:
p s
R I
I (1.16)
The intensities are proportional to the reflectances RpandRs, respectively, and related to the reflectometry signal Rthrough an unknown instrumental constantC:
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p s
R CR
R (1.17)
The instrumental constant can be eliminated by normalizing signal to its initial valueR
0 as:
This reflectometry signal S t
is directly proportional to the adsorbed mass per unit area according to:
t S t( ) A (1.19)
where
t is the adsorbed mass per unit area at timet, andAis the sensitivity constant.The sensitivity constant is system dependent and one should evaluate the effect of the adsorption on the value of the reflectometry signal in order to quantify the sensitivity constant. For polymers or very small particles, a homogeneous four-slab model can be applied to calculate the effect of the adsorbed mass on the value of the reflectometry signal, with the use of Fresnel equations and Abelès matrix formalism [107, 115]. Every layer on the surface is assumed to be homogeneous and characterized by the thickness and the refractive index of that layer (Figure 1.10). The adsorbed polymer layer is treated as the topmost slab with a certain refractive index nL which can be calculated, assuming the validity of the perfect mixing law, as:
where nsis the refractive index of the solvent, dn
dcis the refractive index increment of the adsorbed material, anddLis the thickness of the adsorbed film.
The refractive indices and the thicknesses of each layer in the given multilayered system can be obtained from an ellipsometric measurement and the refractive index increment from a measurement by a differential refractometer. Using the Fresnel equations and Abelès matrix formalism, one obtains a theoretical calibration curve which slope determines the sensitivity constantA. Knowing then all the optical characteristics of the substrate, one can obtain the adsorbed mass.
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Figure 1.10 Schematic representation of the surface structure used for the optical modeling. Polymers are adsorbed on the Si wafer with a SiO2 layer. Each layer is considered to be homogeneous and is characterized by its thickness and refractive index.
1.5 Outline of the thesis
Adhesion and mechanics of dendronized polymers adsorbed on solid substrates were investigated by means of surface sensitive techniques, namely atomic force microscopy and reflectometry. The thesis is divided into 7 chapters. The first chapter provides the theoretical background of polymer adhesion, single polymer mechanics and describes the principle of the surface sensitive techniques used.
The second chapter describes the desorption of individual DPs of different generations from various surfaces studied by AFM-based single-molecule force spectroscopy (SMFS). By combining the AFM imaging and force measurements, the effects of surface hydrophobicity, ionic strength, and polymer generation on the adhesion behavior of DPs were investigated at the single-molecule level. Depending on the surface modification, solution conditions and polymer in question, the polymer-surface interactions can be tuned at the molecular level.
The third chapter focuses on the measurement of force-extension profiles of individual DP molecules.
A novel nano-handling technique based on AFM was developed allowing the investigation of the mechanical properties of the polymers on truly single molecule level. This is ensured by coupling of imaging and force measurements in one experiment. One single polymer molecule is hold between the AFM tip and the opposing surface and can be stretched many times back and forth. Using this technique, the force response of individual DPs in electrolyte solution of different ionic strengths was recorded and described by the freely jointed chain model, showing that the mechanical response of DPs can be tuned by the solution composition.
The fourth chapter reports on a SMFS investigation of the stretching response of DPs. Various methods have been proposed to obtain a single molecule response from the pulling experiments, namely nano-handling, classical pulling, and fishing technique. The nano-handling technique identifies a single polymer molecule on the surface by AFM imaging, and this molecule is subsequently probed during the
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force measurements. The force response can be then directly attributed to a single polymer molecule. The classical pulling and fishing methods, however, do not provide such a direct way to identify if the pulling event originates from a single or several polymer molecules. This chapter demonstrates that not all the methods are suitable to obtain a single molecule stretching response, and this response is for some techniques substrate and solution conditions dependent.
The fifth chapter discusses the polymer physics of DPs adsorbed onto various surfaces. The persistence length of DPs in electrolyte solution of different ionic strengths was obtained from AFM images using the decay of the bond-bond correlation function and the internal end-to-end distances. This investigation showed that the persistence length of DPs increases with increasing generation and decreasing ionic strength. The magnitude of the persistence length strongly varies with the surface, suggesting that the specific polymer-surface interactions affect the molecular conformation.
The sixth chapter extends the study of adsorption of DPs onto a solid substrate. Reflectometry and AFM were employed to investigate the adsorption process of DPs at different salt levels. Combination of these two techniques allowed to follow the adsorption process of DPs in greater detail, to obtain the adsorbed amount, and to explore conformational changes of adsorbed DPs. It was demonstrated that with increasing ionic strength and generation, the adsorbed amount significantly increases. AFM imaging supports well the results obtained from reflectrometry. Furthermore, AFM image analysis shows that the conformation of adsorbed polymer chains is dependent on the surface coverage.
The seventh chapter presents the basic conclusions of the thesis.
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2 Interactions between Individual Charged Dendronized Polymers and Surfaces
*2.1 Introduction
Since their discovery in the eighties, dendtritic architectures continue to capture the imagination of chemists [79, 116-119]. Globular dendrimers consist of several dendrons attached to a central core, and they represent the most widely investigated structures. While dendrimers of lower generation have relatively loose inner structure, higher generations are rather densely packed and uniform, even though this packing may be influenced by changing the solvent quality [117, 120-122]. Dendrimers have unusual properties, for example, their specific viscosity goes through a maximum with increasing molecular mass [123] or their charge may build up in even-odd shell fashion [124]. At higher concentrations, they assemble in liquid-crystalline structures [125, 126]. Dendrimers have been proposed for interesting applications, for example, as gene vectors [127, 128], drug delivery systems [129-131], or catalysts [116, 132, 133].
Dendronized polymers (DP) carry dendrons at each backbone repeat unit and they represent the other important class of dendritic architectures [79, 119]. The properties of these polymers have been studied in lesser detail than dendrimers so far. Their radial density profile resembles the one from dendrimers,
Dendronized polymers (DP) carry dendrons at each backbone repeat unit and they represent the other important class of dendritic architectures [79, 119]. The properties of these polymers have been studied in lesser detail than dendrimers so far. Their radial density profile resembles the one from dendrimers,