Results and discussion

Individual amino-functionalized DPs were investigated by AFM adsorbed on three different surfaces, namely bare mica, hydrophobized mica, and gold. They were investigated at pH 4 at which the amino groups are fully ionized normally in 10 mM KCl electrolyte solution, unless indicated otherwise. In particular, images of the adsorbed molecules were acquired and single molecule force experiments were carried out.

Figure 2.1 Adsorbed dendronized polymers (DPs) of different generations on mica imaged by AFM in 10 mM KCl electrolyte of pH 4. (a) Structural formulas of the polymers and images of (b) a mixture PG1, PG2, and PG3 and (c) a mixture PG3, PG4, and PG5. The pearl structure of PG5 distinguishes it from PG4.

Imaging. Different generations of DP adsorbed on mica were imaged with AFM in solution in the intermittent contact mode. Overview images of samples, where different generations were mixed, are shown in Figure 2.1. For generations up to PG4 one observes a uniform envelope of the adsorbed chains.

However, PG5 features a characteristic pearl-necklace structure.

Figure 2.2 compares high resolution images of adsorbed PG4 and PG5 chains obtained with very sharp AFM tips. These images clearly illustrate the different structures of the charged chains. Since very similar

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structures were also observed for chains adsorbed on hydrophobized mica and gold, we hypothesize that these structures exist in solution too. One should note that uncharged PG5 does not show any pear-necklace structure ^[154].

Figure 2.2 Adsorbed DPs on mica imaged by AFM in 10 mM KCl electrolyte of pH 4. Normal resolution images (top row) and high resolution images (bottom row). PG4 (left column) and PG5 (right column).

A large number of similar AFM images were analyzed quantitatively. The average heights and apparent lengths of the molecules were recorded. By applying a deconvolution algorithm, volumes of the individual molecules were estimated too. Table 2.2 summarizes the resulting number averaged molecular mass M_nand of the polydispersity index (PDI) defined as M_w/M_n where M_wis the weight averaged molecular mass. The density of 1.3 g/mL was used for these molecules as reported earlier for neutral analogs ^[81]. Dividing their volume by the apparent length furnishes the cross sectional area. This area is converted to a width at the base of the molecule by means of a parabolic cross-section, which turned out to represent a good approximation of the actual profile.

The corresponding values are summarized in Table 2.2. Since we report the maximum heights for PG5, their width is probably somewhat underestimated due to their pearl-necklace structure. No dependence on the salt level of the heights and volumes of the single molecules could be established.

Identical pearl structures for PG5 could be observed at different salt concentrations.

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The numbers reported in Table 2.2 compare relatively well with independent estimates. For the PG4 sample, the number weighted molecular mass M_nand PDI of 6.8×10⁶ g/mol and 2.0 were determined by multiple-detection gel permeation chromatography and they are in reasonable agreement with the present estimates. The somewhat smaller value of the molecular mass obtained by AFM is probably due to errors in the deconvolution process. The average height and width of similar but neutral DP was studied with AFM in dry state and with cryo field emission scanning electron microscopy ^[81]. The presently reported heights compare very well with these values, while the observed widths are somewhat larger. The latter difference is probably due to the fact that the measurements are carried out on isolated molecules, while in the mentioned reference they were measured from the repeat distance between several aligned molecules. The average height of the PG5 molecule reported here is somewhat smaller than the one for PG4. This discrepancy has to do with the fact that the PG5 shows the pearl-necklace structure, while the unprotected polymer rather has a cylindrical form. The peak-to-valley height difference along the backbone is about 3 nm.

Table 2.2 Average Properties of the Dendronized Polymers (DP) Used.

no. of

PG2 125 (8.0±0.9)×10⁵ 1.6±0.2 1.65±0.04 5.0±0.5

PG3 188 (2.9±0.3)×10⁶ 1.5±0.1 3.57±0.04 10.8±0.4

PG4 104 (5.8±0.5)×10⁶ 1.3±0.1 6.12±0.05 13.2±0.5

PG5 73 (3.9±0.6)×10⁶ 1.6±0.2 5.55±0.09 17.6±0.7

We have also counted the number of pearls in all PG5 molecules imaged. By dividing the volume of each molecule by the corresponding number of pearls we find an average volume of each pearl. Assuming a spherical shape, we find that the average diameter of a single pearl is about 11 nm. Given the known molecular mass of a monomer and its density we find that there are approximately 71 monomers per pearl. The pearls appear larger in the normal resolution AFM images due to convolution with the cantilever (see Figure 2.2, top). This analysis procedure of the normal resolution images does not provide any accurate information on the size distribution of the pearls. To obtain this information, we have analyzed the high resolution images, where tip convolution effects are almost negligible (see Figure 2.2, bottom). By estimating the volumes of about 100 pearls in such images, we found that each pearl contains about 63 monomers on average, which is in good agreement with the value quoted above. This number

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suggests that the contour length of polymer backbone within one pearl is about 16 nm on average. We further find that the volume distribution of the pearls is relatively broad, and can be characterized by a PDI of about 1.2. Because of the limited set of high resolution images available, these numbers only represent approximate estimates.

The mechanism of pearl formation is probably related to the hydrophobic nature of the backbone, which is known to generate pearl-necklace structures in synthetic linear polyelectrolytes. With increasing hydrophobicity of the backbone, the polyelectrolyte undergoes a coil-to-globule transition whereby the intermediate structures have a pearl-necklace structure. For synthetic polyelectrolytes, this effect is well established by AFM imaging ^{[157, 158]} and with computer simulations ^{[159, 160]}. How this mechanism could be extended to dendronized polymers is not known yet in detail.

Single Molecule Force Experiments. Typical experimental results with single DP molecules adsorbed on hydrophobized mica are shown in Figure 2.3. The polymers are adsorbed on the surface and imaged in solution with the AFM with a silanized tip in intermittent contact mode. After the selection of a part of a suitable molecule (arrow) a series of about 300 approach-retract force profiles was recorded. After this experiment, the same region of the sample is imaged again. This procedure that was carried out within the same fluid cell assures that force profiles are recorded truly for individual molecules. Any eventual lateral displacement of the molecule that may have occurred during the force scan can be detected.

Figure 2.3 Single molecule force profiles on retraction for the molecule shown above before and after the experiment on hydrophobized mica. PG3 (left) and PG4 (right).

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The individual force profiles vary substantially from one approach-retraction cycle to another. Rather frequently, no events are recorded at all during a cycle. For PG3, 96.3% of all cycles did show no events on average. In the remaining 3.7% of all cycles, single molecule events were observed. For PG4, events were observed more frequently, namely with a frequency of 23.7%. These events occur since the polymer is bridging the tip and the substrate, and when the tip is retracted the polymer is progressively stretched.

Two major types of events are observed, namely peeling and pulling.

Peeling events are characterized by a constant plateau in the force curve, and they were observed in 3.0% of all retract curves for PG3, and in 20.9% for PG4. In this case, the molecule is more weakly attached to the substrate, and when the tip is retracted, the molecule is being peeled away. In the present case, the peeling force is about 25 pN. Note that only single plateaus are observed, and several plateaus were not detected. Several plateaus would be characteristic for peeling events involving loops within individual molecules or originating from several polymer chains. Sliding of the polymer on the surface might also lead to plateaus in the force profiles ^[39]. Since the polymer images were mostly identical before and after the force experiments, we suspect that sliding of the polymer on the surface is unimportant.

Pulling events were observed in 0.7% of all cases for PG3, and in 2.8% of all cases for PG4. They are associated with a characteristic spike and result when a molecule is strongly attached to tip and substrate.

At larger extensions, the force increases strongly with the extension in a non-linear fashion. The pulling force becomes at one point so large that the molecule detaches from the tip, and this event leads to the characteristic spike in the force curve. By imaging the polymer on the surface after the force experiments, one can assure that the molecule has again detached from the tip. Detachment of an entire molecule from the surface was never observed, since single molecule events always occurred at a distance that was much smaller than the contour length of the molecule. Pulling of DP was investigated earlier and was shown to be sensitive to the salt level ^[137]. This issue is complicated by the fact that DP may form duplex bundles

[85, 86], and their presence could affect the force extension relationships. We will address these aspects in a forthcoming article.

Peeling from Different Surfaces. PG3 was used to investigate the differences in the peeling behavior involving various surfaces, namely bare mica, hydrophobized mica, and gold. Typical force curves are shown in Figure 2.4 (top). Histograms of the peeling forces for the three different surfaces shown in Figure 2.4 (left column) reveal that their distribution is approximately Gaussian. One also observes that the nature of the surface influences the magnitude of the peeling force substantially. The average peeling forces and the corresponding standard deviations are summarized in Figure 2.4a (right column). The

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peeling force increases in the sequence bare mica, hydrophobized mica, and gold. The contact angle and thus the hydrophobicity of the surface increases in the same sequence (see Table 2.1). The relative width of the distributions is about 25%. The present results are well comparable to peeling of other polymers, including poly(vinyl amine) ^[28], poly(allyl amine) ^[152], poly(acrylic acid) ^[29], cellulose ^[153], or single stranded DNA ^[161]. These polymers show average peeling forces in the range of 50–100 pN and comparable widths of the corresponding distributions.

Figure 2.4 Peeling of PG3 from different substrates in 10 mM KCl at pH 4 with typical force curves shown on the top. Left column shows histograms of the peeling forces for (a) bare mica, (b) hydrophobized mica, and (c) gold.

Right column shows some characteristics of the peeling forces. (a) Average peeling force with error bars, (b) probability of events, and (c) relative probability of peeling and pulling.

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The probability to observe an event shown in Figure 2.4b (right column) also increases in the same sequence. Both trends indicate that the forces responsible for the adsorption are principally of hydrophobic character. The relative probability to observe peeling versus pulling events as shown in Figure 2.4c (right column) does not indicate any clear trends, however. Hydrophobized mica shows the largest tendency for peeling. For bare mica, the probabilities to observe peeling or pulling are about comparable, while pulling is much more likely for gold. The polymer attaches to gold the strongest, which rationalizes its tendency to generate more frequent pulling events.

Generation Dependence of Peeling Forces. The generation of DP has also a substantial effect on the peeling forces. Figure 2.5a shows peeling events for different generations from hydrophobized mica, and one observes that the peeling force increases with increasing generation. Moreover, for PG5 one observes two rather distinct magnitudes of peeling forces. This situation is more clearly evident in the histograms of the force curves shown in Figure 2.5 (left column). PG3 and PG4 show the usual Gaussian distribution of peeling forces, while the distribution for PG5 shows two maxima. More detailed analysis of PG5 indicates that large peeling forces correspond to relatively short chains, while the smaller peeling forces include short as well as longer chains. We suspect that the smaller peeling forces originate from the unwrapping of the individual pearls, while the larger peeling forces correspond to the peeling of the polymer from the surface.

Average peeling forces and the corresponding standard deviations are shown in Figure 2.5a (left column). One observes that the peeling force increases with increasing generation. This trend can be understood since the polymers flatten in the adsorbed state, and this deformation leads to an increase in the number of contact points with increasing generation. This aspect can be also illustrated by considering the work of adhesion, which equals to the ratio between the peeling force and the width of the polymer.

One obtains about 3.3±0.6 mJ/m² and this value is independent of the generation. Interestingly, this value is about one order of magnitude lower than reported for synthetic polyelectrolytes ^[14]. This fact is also reflected in the adsorption energy per monomer, which was reported to be about 3–6 kTfor synthetic polyelectrolytes, where kT refers to the thermal energy. For DPs this number is substantially lower as it lies in the range of 0.7–2.9kTand it increases with the generation. This difference is probably related to the fact that only a part of the DP is exposed to the surface.

The two values plotted for PG5 indicate the position of the two peaks in the histogram. This aspect is related to pearl-necklace structure of PG5 and will be discussed in the next section. Figure 2.5b (left column) shows the probability of all types of events versus the generation. While this probability roughly increases with increasing generation, PG3 shows the lowest probability among all. Figure 2.5c (left

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column) illustrates that peeling is much more likely than pulling for DP up to generation 4, while pulling becomes more frequent for PG5.

Figure 2.5 Peeling of DP of various generations from hydrophobized mica in 10 mM KCl at pH 4 with typical force curves shown on the top. Left column shows histograms of the peeling forces for (a) PG3, (b) PG4, and (c) PG5.

Right column shows some characteristics of the peeling forces. (a) Average peeling force with error bars, (b) probability of events, and (c) relative probability of peeling and pulling.

Salt Dependence of Peeling Forces. The salt concentration was found to have a substantial effect on the observed peeling forces. Figure 2.6 summarizes these results for PG3. The histograms of the force plateaus are shown in the left column and the average peeling force increases strongly with increasing salt

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concentration, as shown in Figure 2.6a (right column). The probability to observe an event also increases with increasing salt concentration (Figure 2.6b, right column). At low salt concentrations peeling is observed exclusively, while at high concentrations peeling and pulling events are roughly equally probable, see Figure 2.6c (right column). A similar increase of the peeling force with the salt concentration was also observed when bare mica was used as a substrate.

Figure 2.6 Peeling of DP PG3 at various salt concentrations of KCl at pH 4 from hydrophobized mica. Typical force curves are shown on the top. Left column shows histograms of the peeling forces for (a) 1 mM, (b) 10 mM, and (c) 100 mM. Right column shows some characteristics of the peeling forces. (a) Average peeling forces with error bars, (b) probability of events, and (c) relative probability of peeling and pulling.

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The increase of the peeling force with increasing salt level may seem surprising at first. When only electrostatic forces would be present, one expects that the peeling force of a charged polyelectrolyte adsorbed at an oppositely charged substrate decreases with increasing salt level due to an increased screening of the electrostatic interactions by the salt ions. Such dependence was indeed observed for simple polyelectrolytes, such as poly(vinyl amine), poly(acrylic acid), or cellulose [28, 152, 153] and could be semi-quantitatively explained with a simple Debye-Hückel model. However, a substantial non-electrostatic contribution to the peeling force could be also identified, which may strongly depend on the substrate. In the present case, the non-electrostatic contribution seems to dominate and even lead to the reversed trend. This trend is probably due to the hydrophobicity of the DP backbone. Since the hydrophilic charged amine groups are screened with increasing salt level, hydrophobic interactions between DP and the substrate are expected to become more important. However, it was also shown that shifts in ionization equilibrium upon adsorption of the polymer may also lead to a similar reversed salt dependence ^[152].

Figure 2.7 Typical peeling force curves for PG5 together with the corresponding images of the molecules investigated. The arrow indicates the position of the force measurements. (Left top to bottom) Peeling events illustrating the two different force plateaus, and multiple pulling event, and a single pulling event. (Right) Combination of different pulling and peeling events.

Consequences of the Pearl-Necklace Structure of PG5. The highest generation polymer PG5 shows substantially different peeling behavior than all lower generations. We suspect that these differences are due to the pearl-necklace structure of PG5. Recall that the histogram of the peeling forces shows two

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maxima (see Figure 2.5). Another important difference between PG5 and the lower generation DPs is the presence of the complex multiple pulling events for PG5 shown in Figure 2.7. Such events are only observed for PG5 and not for lower generation polymers. Similar single molecule force events involving numerous spikes were reported for muscle and other proteins [26, 27, 162]. These proteins show a very regular sequence of spikes, while the sequence of PG5 is random. Nevertheless, we suspect that the mechanisms are similar. While the spikes observed for proteins correspond to unwrapping of individual sub-domains, those observed for PG5 probably correspond to unwrapping of individual pearls. The irregular sequence likely originates from the random coil structure of the individual pearls and random entanglement of the chain. Note that events involving multiple spikes have also been observed when several polymer molecules have been pulled at the same time ^[36]. However, one can exclude this possibility since our method of imaging before and after the force experiments ensures that we deal with individual chains only.

Figure 2.8 Distribution of the distances between the spikes in the force curves for PG5.The inset shows a sample force curves with the distances indicated. The threshold to detect a spike was set at 50 pN.

Figure 2.8 shows the distribution of the distances between individual spikes exceeding 50 pN. The distribution is relatively broad, and has an average of about 16 nm and a standard deviation of 14 nm.

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This value is exactly the same as the estimated average contour length of the polymer within one pearl given above. The broadening of the distribution reflects most likely the polydispersity of the pearls. Based on the AFM images, we have concluded above that the pearls have a PDI of 1.2. The spike-to-spike distribution shown in Figure 2.8 suggests a PDI of 1.9. The fact that the distribution of spikes is wider than the distribution of the pearl volumes probably reflects the length distribution of segments attached to the substrate or our inability to resolve very small pearls with the AFM. Two different peeling forces reported in Figure 2.5 are also likely related to the pearl-necklace structure of PG5. Unwrapping of a single pearl may lead to a smaller peeling force, while desorption of an adsorbed polymer chain to a larger peeling force.