Force Spectroscopy Measurements on Poly(Methyl Methacrylate) Nanoparticles

To study if the addition of a cross-linking agent results in particles with a higher rigidity, which should prove advantageous for mechanical manipulation, force spectroscopy on cross-linked and non-cross-linked particles was performed. The polymer dispersions were diluted and spin coated onto silica substrates. Figure 56 displays a typical force-distance curve taken on the silica substrate (left) and a typical force-distance curve taken on a non-cross-linked PMMA particle (right), measured in contact mode, respectively.

Figure 56. Typical force-distance curves measured on a silica substrate (left). 1: Approach of the tip from far distance. 2:

Snapping of the tip to the surface. 3: Retraction of the tip from the surface while overcoming adhesive interactions.

Typical force-distance curves measured on a non-cross-linked PMMA particle with a diameter in the range of 40-80 nm (right). A: Tip-sample contact point. B: Slope of the approach curve used for determining the Young’s modulus. C:

Increase in repulsion due to close proximity to or direct contact with silica substrate. C-A: Indentation depth. FAdh: Maximum force of adhesion between tip and particle.

(3, blue line). The adhesion can be probably attributed to the presence of a water meniscus on the tip and the silica surface.¹⁸⁰

A typical force-distance curve derived from studying a non-cross-linked PMMA particle is depicted in Figure 56 (right). The tip approaches the surface from far distance without any attractive interaction at short distances. As soon as the cantilever hits the surface (A, red line), the vertical deflection increases, translating to a repulsive interaction. The slope of this curve is a measure for the rigidity of the material (B, red line). After the tip has covered a certain height while compressing or penetrating the sample, the slope of the approaching curve rises significantly and reaches a similar value as observed for the tip in contact with the silica substrate (C, red line).

The retract curve features a similar trend as observed for silica, with a steep decline in vertical deflection while the tip is retracted form the surface. The main difference is the missing adhesive interaction, probably because there is still a polymer layer between the tip and the substrate. The difference between the approach and retract line (hysteresis) indicates a viscous and plastic behavior of the particle, meaning that it is not only reversibly deformed (C-A, shaded area). By fitting the slope of the first increase in vertical deflection with a Hertz model implemented in the AFM software, the elastic modulus of the studied material can be extracted (data processing is described in the experimental section, Chapter 7.8). Exemplary force-distance curves fitted with the Hertz model for a cross-linked, a non-cross-linked particle and for the silica substrate can be found in the appendix (Figure A 32, Figure A 33, Figure A 34).

To study the difference between cross-linked and non-cross-linked PMMA particles, both dispersions were spin coated onto a silica substrate and were analyzed by force spectroscopy. PMMA particles and the silica substrate were analyzed alternately, and the Young’s modulus obtained for silica was used as a reference to be able to compare the results obtained for non-cross-linked and cross-linked particles. Figure 57 depicts a typical region of a spin-coated dispersion with five positions at which a polymer particle was examined (1-5) and five positions at which the silica substrate (6-10) was analyzed.

5.2 Results and Discussion

Figure 57. Typical area on a silica substrate with PMMA particles spin coated on it. The numbers indicate positions at which a minimum of five force-distance curves were recorded, either on a PMMA particle (1-5) or on the silica

substrate (6-10).

In total, a minimum of 15 cross-linked and 29 non-cross-linked particles were studied. To ensure comparability of the results, the samples were analyzed by the identical cantilever.

Figure 58 depicts typical force-distance curves measured on the silica substrate (left), on a non-cross-linked PMMA particle (center, (Chapter 5.2.1, Table 6, Entry 1)) and on a non-cross-linked PMMA particle (right, (Chapter 5.2.1, Table 6, Entry 9)). Every measurement was repeated at least five times and in all three graphs, the five curves are very similar, underlining the good reproducibility of the measurements.

The left image of Figure 58 depicts the force-distance curves obtained from measuring the substrate surface. A small attractive interaction between the tip and the substrate is visible and the slope of the curves at negative tip-sample separation is very steep, underlining the expectable high rigidity.

The force-distance curves for non-cross-linked and cross-linked particles look similar (Figure 58, center & right). In both, the vertical deflection increases as soon as the tip contacts the surface. After a compression of approx. 40 nm of the particle, the slope increases to a value similar as observed for silica. This is probably because the particle is not further compressible. Alternatively, it is conceivable that the tip penetrates the particle and hits the silica surface at some point. However, in this case one would expect to observe an adhesive force between the sample and the tip when the latter is retracted as observed in measurements on the silica substrate (Figure 58, left), which is not the case.

From analyzing several cross-linked and non-cross-linked particles, it can be concluded that the increase in vertical deflection with increasing penetration depth of the tip is significantly higher for cross-linked particles, indicating these particles to feature a higher rigidity. The results are summarized in Table 7.

Table 7. Young’s modulus extracted from force spectroscopy measurements on PMMA particles and silica substrates.

Entry No. of

Non-cross-linked PMMA 64 0.070 0.072

Silica surface (cross-linked

sample) 25 4.530 4.500

Cross-linked PMMA 45 0.223 0.222

a The value obtained for silica was set to 4.500 GPa and was used as reference to allow for comparison of the values obtained for the respective PMMA particles.

Analysis of non-cross-linked particles and the underlying substrate afforded a Young’s modulus for the particles of 0.072 GPa (referenced, Entry 2) and 4.349 GPa (Entry 1) for the silica substrate.

For the cross-linked sample, a value of 0.222 GPa (referenced, Entry 4) for the polymer and 4.530 GPa (Entry 3) for the substrate is derived.

It has to be denoted that the AFM tip was not calibrated, which explains why the obtained values are significantly lower by approximately a factor of 10 compared to literature reported values for PMMA (1.8 – 3 GPa) and silica (50 – 90 GPa). Furthermore, the Hertz model is only valid when the penetration depth is smaller than 5 – 10% of the sample thickness. This limit is exceeded, as the tip penetrates or compresses the particles to a significant extent. Additionally, the used cantilever has a triangular and rather sharp tip, which might result in sample penetration and in an underestimation

5.2 Results and Discussion

values derived for the silica surface as a reference (set to 4.500 GPa, column 4), the moduli obtained for PMMA and cross-linked PMMA can be compared because all measurements were performed with the same cantilever under equal conditions.

The following conclusions can be drawn from the results listed in Table 7. The obtained moduli for the substrate are very similar for both samples (4.349 GPa vs. 4.530 GPa), indicating a good reproducibility. This additionally underlines that the cantilever is not damaged by the measurements and that there is no significant pick-up of polymer material. Pick-up and or damage of the cantilever would result in an altered spring constant and in a different Young’s modulus for silica for the two samples. The observed elastic modulus of cross-linked PMMA is significantly higher by a factor of three compared to the modulus of non-cross-linked PMMA (according to a t-test, the difference between both moduli is significant (p-value: 8 × 10^-7)).

In conclusion, the addition of cross-linker resulted in particles with a significantly higher rigidity.

This should prove advantageous in manipulation experiments and should result in less pick-up.

Additionally, the cross-linking of the polymeric shell is beneficial for the quantum yield of the emitters.

5.2.3 Encapsulation of Organic/Inorganic Semiconductor Hybrid Particles into Polymer