1 Introduction
1.1 Polymer adsorption
Understanding of polymer adsorption onto surfaces forms the scientific basis of many biological and technological applications. The ability to describe and control polymer adsorption at various substrates is crucial to establish molecular design principles of antifouling surfaces [1-5], fabricate biosensors [6, 7], prepare low-friction low-wear surfaces and coatings [8], polymer-based technological glues [9, 10], and develop innovative adhesives for biomedical applications [9].
Polymer adsorption is a complex phenomenon, which touches upon both theoretical and experimental areas of research. Numerous studies on polymer adsorption have been published and are directed at determining the influence of polymer and surface charge densities, polymer conformation at the surface, polymer architecture, surface characteristics, and the interaction force of adsorbed polymers at surfaces [4,
11-15]
. With the current developments in atomic force microscopy (AFM) techniques, it has now become possible to tackle polymer adhesion at the true molecular level and open up the possibility to systematically investigate polymer adsorption properties and different intermolecular interactions. For this purpose, single molecule force spectroscopy (SMFS) based on AFM has been developed [14, 16-19]. In SMFS, a polymer chain is firmly attached to the tip of an AFM cantilever and subsequently stretched between the AFM tip and an opposing surface. The force exerted on the cantilever is measured as a function of the distance from the surface as the polymer is pulled perpendicularly to the surface (see Figure 1.1). Force-extension curves then reflect the desorption of a polymer chain from the surface. The principle of the AFM measurement is explained in greater detail in the Chapter 1.4.1.
In desorption experiments, the shape of recorded force curve strongly depends on the dynamics of the system, ranging from saw-tooth pattern to long plateaus [20]. The polymer chains are linked to the substrate either covalently or by non-covalent interactions. In both cases, the rupture of binding sites with the surface leads to extension of the polymer chain by the length of the strand between one and the next binding sites. Depending on the internal dynamics of the probed bonds and the applied force loading rates, the adhesive force acting between the polymer chain and the substrate can be obtained from the force-extension profile as the height of individual unbinding peaks, or from the height of the desorption plateaus (Figure 1.1).This is supported by theory, suggesting that the shape of the force-extension profile for continuous desorption of adsorbed polymer chains from a solid substrate (i.e. unbinding of multiple bonds in series) depends on the force loading rate [21].
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Figure 1.1 Schematic representations of desorption of a polymer chain from a solid substrate. The polymer is coupled to the surface through numerous interaction sites (bonds). Depending on the loading rate and the internal dynamics of the probed bonds, the force-extension profile shows a saw-tooth pattern with individual peaks of distance s corresponding to individual bond rupture (a), or a desorption plateau of constant force with the length L of the desorbing polymer chain (b).
Bond rupture forces are generally nonequilibrium values, depending on the intrinsic lifetime of the bond, the temperature, and on the measurement time [22, 23]. At pulling rates much faster than internal dynamics of the probed bones, each detachment of polymer-surface interaction site provides a peak of a saw-tooth pattern (Figure 1.1a). The rupturing of polymer-surface bonds is an irreversible process and happens under nonequilibrium conditions. These peaks are typically observed for covalent bonds [22], specific receptor-ligand systems [24, 25], as well as for the rupture of protein domains [26, 27]. In case that the distance between the different binding sites on the polymer is decreasing, it becomes more difficult to resolve the single rupture events and the force profile has a plateau-like shape. The measurement still takes place in nonequilibrium, the rupturing of bonds is irreversible and loading rate dependent process [22].
For lower pulling rates, the individual bonds dissociate and reassociate on much faster time scale and the heights of individual peaks related to the consecutive unbinding events decrease. In some cases, one can then observe a desorption plateau of constant force corresponding to the equilibrium desorption of the polymer from the surface segment by segment (Figure 1.1b). The desorption of the polymer is then a reversible process and the measured force is a measure of the polymer-surface adhesion free energy.
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Continuous desorption plateaus are observed when the polymer is only weakly adsorbed, e.g.
polyelectrolytes bound to charged surfaces [12, 14, 28].
During the desorption experiments, plateaus of constant force with several steps can be observed in the force-extension curve [29]. Multiple molecules of different lengths are simultaneously adsorbed on the surface and the different steps represent the desorption of individual molecules one after the other. Each time, a step in the desorption force is recorded when one molecule is completely desorbed, until the moment when the last polymer is fully detached. This means that in the case of multiple events, the last step reflects the detachment of a single polymer from a substrate. The plateau length corresponds to the length of the adsorbed molecule, whereas the height of the plateau to the desorption force that is necessary to desorb one or several polymer chains from the surface.
Not only the dynamics of the system, but also the interaction between the polymer and a solid substrate can affect the shape of the force-extension profile. Based on the polymer-surface interaction, the conformation of an adsorbed polymer chain can go from a train-like structure to a polymer brush. In the intermediate region, a polymer chain can form a loop or tail structure (Figure 1.2) [30]. For some polymer systems, Zhang et al. [20] related the pattern of the force-extension profiles to adsorption conformation of polymer chains on the interface. A force profile showing a single peak corresponded to the detachment of a tail structure, a saw-tooth pattern corresponded to the detaching of several loop structures in series, and a plateau of constant force came from the detachment of a train-like structure. Nevertheless, the important factors determining the adhesion behavior of polymers, and subsequently force-extension profiles, are the nature of the polymer-surface bond and the solution composition [20, 23].
Figure 1.2 Schematic representation of adsorption conformations of a polymer chain.
The nanostructure of materials and surface modifications play an important role in interaction of polymers with solid substrates. The control of surface properties allows one to tune molecular adhesion properties. AFM-based single molecule force spectroscopy has been used to systematically investigate the adsorption process of individual polymers on generic surfaces. Different types of interactions (e.g., electrostatic or hydrophobic interactions) influence the adhesion process on a variety of surfaces [17]. For example, the polymer desorption was studied on self-assembled monolayers (SAMs) with different
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terminal groups [4, 31]. SAMs represent easily accessible systems which allow one to investigate the adsorption-desorption process on well-defined and controlled surfaces. Geisler et al. [12, 16] studied single-polymer adhesion in terms of their adsorption strength on various materials, including the effects of surface composition, hydrophobicity, electrical properties and surface roughness. From a macroscopic point of view, by increasing the surface roughness the effective surface area increases which is supposed to enhance adhesion. Surprisingly, the experiments performed with a molecule on either smooth or rough surfaces show that the surface roughness has no effect on the adhesion of a single polymer [12]. Most material properties such as conductivity, surface potential, and composition hardly influence single-molecule adhesion under equilibrium conditions [16]. Solvent-related properties have greater influence on the adhesion strength but still lead to less than 50% difference [15, 16]. These studies have shown that surface modifications enable the fine-tuning of the surface adhesion of polymers but as long as the polymers are still weakly attached to the substrate, these effects are only marginal [12, 15-17, 32]
. The same conclusion applies also for the effect of molecular architecture on single polymer adhesion [13]. A significant increase in adhesion can be observed when many polymers interact not only with the surface but also with each other via intra- and inter-chain entanglements, for example hydrogels, polymer films and brushes. Adsorption properties of these materials can be also changed by external stimuli [7, 33, 34].
Traditional single molecule approach to investigate the polymer adsorption-desorption process relies on a polymer chain firmly attached to the tip of an AFM cantilever. The force exerted on the cantilever is measured as a function of the distance from the surface as the polymer is pulled perpendicularly to the surface [14, 19, 27, 28, 35-37]. With advances in AFM technology, it has become possible to control the tip position and direction with high precision. This has led to experiments in which the adsorbed polymer can be pulled at different positions along the backbone and also pulled from the surface along different directions [8, 38-40]. For example, a single polymer chain was pulled laterally over the substrate in order to enhance polymer adsorption [38] or to study single polymer friction [8, 39]. There are theoretical and computational studies [41, 42] focusing on the effect of the angle at which the force is applied, ranging from perpendicular to parallel to the surface. These models predict that depending on the angle, the polymer favors either adsorption or desorption. There is a critical angle value beyond which the polymer cannot be desorbed by applying a force. Serr and Netz [38] have shown that pulling the polymer parallel to the surface enhances adsorption, pulling the polymer perpendicular by strengthening the force increases the tendency to desorb.
13 1.2 Single molecule mechanics of polymers
Single polymers show a strongly nonlinear behavior when they are stretched by an external force.
Stretching a polymer molecule causes two kinds of restoring forces. The low force regime (short extensions) is dominated by purely entropic contributions. If a single polymer chain adopts a random coil conformation in solution, the Brownian molecular motion causes a permanent fluctuation of the molecule around a mean equilibrium conformation. Extension of the molecule reduces the number of possible conformations, which causes a loss of conformational entropy. The high force regime is dominated by enthalpic contribution as large chain elongations lead to a tension of the molecular backbone. Bonds become stretched and deformed in the direction of the pulling force, and the corresponding enthalpic elasticity is recorded in addition to the entropic forces. In the medium range, the rupture of salt bridges and intramolecular hydrogen bonds may occur, eventually leading to conformational changes of the polymer. The mean values describing the conformation of a polymer chain in solution can be derived by statistical mechanics [43, 44]. Two models are commonly used for describing the elasticity of a polymer chain: the freely jointed chain model (FJC) [44] and the worm-like chain model (WLC, or Kratky-Porod model) [43, 45].
In the FJC model, a polymer chain is divided into n rigid Kuhn segments of equal length , connected through flexible joints without any long range interactions (Figure 1.3). The segments are freely jointed without restrictions for their spatial arrangement. Each segment is independent of every other, including the nearest neighboring bonds, and can be oriented in every direction with equal probability. The directions of neighboring bonds are thus completely uncorrelated:
i j 0, i j
l l (1.1)
where liand ljrepresent the bond vectors.
The contour length of the polymer chain is given byLn. The partition function Zof a freely-jointed polymer chain subjected to an external forceF, as a function of the extensionx, can be written as:
lnZF x k T R
(1.2)
where k is the Boltzmann constant, and T the absolute temperature. In most cases, it is not possible to derive an analytical expression forZ, therefore an additional term, stretching energyF x , is introduced into chain’s partition function:
14 a given conformation which is a constant as there is no interaction between individual segments in FJC model. The extension xcan be then calculated as a function of the external forceFfrom:
lnZ x k T
F
(1.4)
Based on the Eq. (1.3) and Eq. (1.4), the extension of a polymer chainx can be expressed as a function of the applied force Fby:
This model solely accounts for the entropic elasticity of the chain’s backbone. Since elastic deformations are neglected, the polymer chain cannot be stretched by more than the contour length. This equation is then a good approximation only for small extensions (xL). For large extensions, the deformation of bonds and bond angles will result in an effective increase in the segment length.
Therefore, the enthalpic contribution to the restoring force of the polymer chain needs to be taken into account and the extended FJC model has been proposed [46].
Figure 1.3 Schematic representations of (a) freely jointed chain (FJC) model composed of n rigid segments (with the Kuhn length ) coupled by flexible joints and (b) extended FJC model where the parts of the chain are replaced by elastic springs to include enthalpic effects.
The extended FJC model considers the polymer molecule as n identical elastic springs in series and introduces an additional parameterK, the elasticity constant, to describe each segment [Eq. (1.6)].
x coth F k T F
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The extended FJC model has been successfully used to describe the stretching behavior of various synthetic polymers, such as poly(acrylic acid) [47], poly(ethylene-glycol) [35], poly(vinyl alcohol) [48], polyacrylamide [49], poly(ferrocenyldimethylsilane) [50], dendronized polymers [51], as well as many polysaccharides, including cellulose [52], carboxymethylcellulose [53] and dextran [54].
The WLC model neglects any discrete structure along the chain and describes a polymer as a homogeneous, continuous string r
s of constant bending elasticity B (Figure 1.4) [43, 55]. The elastic bending energy EBis proportional to the square of the curvature and is given by:2 2
ris the unit tangent vector and sis the coordinate measured along the polymer contour.
The molecule is constantly in motion, bending in random directions. The interplay between Brownian motion and rigidity is determined by the persistence length Prepresenting the flexibility of the polymer chain.
Figure 1.4 Schematic representations of the worm-like chain (WLC) model. (a) A polymer chain is described as a
continuous stringr s , with s taking values from s0to sL. The chain direction is preserved on the length scale of the persistence length P. (b) The directional correlation between two segments in a polymer separated by the distance s is given by Eq. (1.9).
The persistence length is defined as the decay length of the directional correlation along the polymer chain and is given by:
P
B
k T
(1.8)
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It is a direct measure of the average local conformation of a polymer chain and below this length the polymer can be considered to be linear. If sis reasonably large, the chain corresponds to a Gaussian chain and the average correlation of the tangent vectors decreases exponentially withs:
between the tangents along the chain separated by the distances. WhensP , Eq. (1.9) leads to cos
s 1, the angle
s fluctuates around zero and the chain segments have nearly same direction. In the case ofP s, Eq. (1.9) results in cos
s 0, indicating that
s can be anything from 0° to 360° with equal probability, i.e. the memory of the chain direction is lost once Pis exceeded.For small extensions, and in the limit of flexible chains (LP), the persistence and Kuhn length are related by 2P[43, 55].
The exact force-extension relation of a wormlike chain can only be determined numerically, but a commonly used analytical approximation is given by the formula of Marko and Siggia [56, 57]:
2
Although entropic and enthalpic contributions are combined in this approach, the extension is limited by the contour length of the polymer [58]. The model does not hold in the high force regime where the segment length increases due to the stretching of the covalent bonds. In analogy to the FJC model, an additional stretching term Kis introduced. The parameter K is appropriate for intrinsic enthalpic contributions and denotes the specific stiffness of the polymer chain. The extended WLC models established by Odijk and Wang offer a good applicability over a wide range of applied forces and can be found elsewhere [59, 60].
The WLC and extended WLC models have been effectively used to describe the force-extension behavior of various polymers, such as DNA [60-62], proteins [62, 63], poly(methacrylic acid) [64], and poly(vinyl alcohol) [65].
In the presence of an external force, polymers often undergo conformational and configurational transitions upon stretching. This is marked by a deviation from the FJC and WLC model in the mid-force regime. The low force regime (below the conformational transition) and the high force regime (above the
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conformational transition) can be fitted separately according to the FJC or WLC model. Typical examples are polysaccharides where high stretching forces bring about conformational transitions in the pyran ring
[52, 54, 66]. An external force can lead to a repeated unfolding of protein domains as reported for titin and tenascin [26, 54]. Furthermore, stretching can induce considerable changes in the secondary structure of single polymer chains. Experiments on poly(ethylene glycol) [35] in water indicated the deformation of the helically folded equilibrium conformation of the polymer due to overstretching the hydrogen-bonded solvation superstructure. Similar transitions were also observed for xantan [67] and PVP [68]. More complex system is double-stranded DNA showing a highly cooperative conformational transition from its natural form (B-DNA) to an overstretched conformation (S-DNA), upon which the length of the molecule is approximately doubled [46].
Changes in the mechanical response of polymers can be also induced by the changes in the environmental conditions, i.e. external stimuli. The stimuli can be chemical (pH, ionic strength, solvent) or physical (temperature, electric or magnetic field, mechanical stress) [28, 47, 50, 61, 69-72].
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
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