Elastic Properties of Polystyrene Nanospheres Evaluated with Atomic

Jun 3, 2014 - The compressive elastic moduli of individual nanospheres were obtained ... the size dependence on the elastic modulus of PS nanospheres ...
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Elastic Properties of Polystyrene Nanospheres Evaluated with Atomic Force Microscopy: Size Effect and Error Analysis Dan Guo,* Jingnan Li, Guoxin Xie,* Yuanyuan Wang, and Jianbin Luo State Key Laboratory of Tribology, Tsinghua University, Beijing 10084, China ABSTRACT: The mechanical properties of polystyrene (PS) nanospheres of ca. 50−1000 nm in diameter were evaluated by using an atomic force microscope (AFM). The compressive elastic moduli of individual nanospheres were obtained by analyzing the AFM force−displacement curves on the basis of the Hertz and JKR contact theories. The results showed that the elastic moduli of PS nanospheres of different sizes were in the range of 2−8 GPa. The elastic modulus of PS nanospheres increased with the decrease of the sphere diameter, especially when the diameter was less than 200 nm. The measurement errors due to tip wear and the deformation at the bottom of the sphere were analyzed. Mechanisms for the size dependence on the elastic modulus of PS nanospheres were also discussed.

1. INTRODUCTION In recent years, researchers have shown increasing interests in polymer nanoparticles for their ubiquitous applications in pharmaceutical, microelectronic industry, coating, and other areas.1−3 At nanometer length scales, polymer materials may behave quite differently from their bulk counterparts.4 Understanding the mechanical properties of nanoparticles will aid a lot in controlling their performances in specific applications. For instance, one of the most popular applications of nanoparticles is as abrasives in the chemical mechanical polishing (CMP) technology which is a key technique for wafer global planarization in the manufacturing of very large scale integration (VLSI).5,6 Despite the wide use of silica nanoparticles in the CMP process, polymer nanoparticles have been also demonstrated to have great potentials as abrasives for soft materials, e.g., Cu or dielectrics, to reduce mechanical scratches and improve the planarity.7 Investigating the mechanical properties of these nanoparticles will be helpful for evaluating the role of mechanical abrasion in the CMP process. The microindentation method was used by Steinitz8 in 1943 to measure the microhardnesses of particles. Nanoindentation was then used by Shorey and co-workers9 to determine the elastic properties of magnetic and nonmagnetic abrasives (average size: 5 μm) used in the magnetorheological finishing. Atomic force microscopy (AFM) measurements were conducted by Biggs and Spinks10 to push a polystyrene (PS) sphere (size: 20 μm) attached on the cantilever beam against a mica surface. Since then, methods for characterizing the mechanical characteristics of nanoparticles with AFM have been much developed. Based on these methods, the elastic properties of polymer or composite polymer nanospheres were investigated in some researches.11−13 Tan et al. found that the compressive elastic moduli (thereinafter elastic moduli for © XXXX American Chemical Society

short) of polymer nanospheres (ca. 200 nm in diameter) were less than those of PS bulk materials due to the presence of hydrated ionic functional groups.11 Park et al. found that the elastic moduli of polypropylene (PP) nanospheres (200−500 nm in diameter) depended on the particle size, indentation depth, and applied load.12 Armini determined the elastic modulus of the polymer and composite polymer nanospheres (300−600 nm in diameter) to be 4.3 ± 0.8 GPa using the Hertzian theory, being close to those of the corresponding bulk materials (4 GPa).13 Besides polymer materials, the mechanical properties of silicon nanoparticles evaluated with AFM have been also investigated by Gerberich.14 It was found that the hardness of Si nanospheres (40 nm in diameter) was 4 times greater than that of bulk silicon due to the existence of line defects or dislocations inside the nanosphere, resisting high pressure. Although progresses have been made to measure the mechanical properties of nanoparticles with AFM in the past decades, there has been still no uniform conclusion on the size dependence of the elastic modulus (or hardness) of nanoparticles (especially polymer nanoparticles). Specifically, the elastic moduli of small particles were smaller in some studies while in others they were higher than their bulk materials. Furthermore, only the results of the particles with the size above 200 nm have been reported in most references. Basically, the complexity and difficulty in reliably measuring and accurately analyzing the mechanical properties of nanospheres mainly due to many complicated technical factors involved. For instance, how to prepare uniformly dispersed particles on an extremely stiff substrate; how to locate individual particles Received: April 17, 2014 Revised: May 30, 2014

A

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Figure 1. SEM images of a large area of monolayer polystyrene spheres (diameter: 200 nm) deposited on the Si substrate: (a) mass fraction of 0.3%; (b) mass fraction of 1%. 2.3. Measurements Based on AFM. AFM topographic images and the force−distance curves under ambient conditions (25 °C and 28% relative humidity) were acquired on a Dimension V scanning probe microscope (Veeco, USA). Two types of probes (HA-NC and DCP11, NT-MDT Zelenograd, Moscow, Russia) were employed in this work for investigating the effect of tip shape. The former is a Si tip with a curvature of radius of 10 nm. The latter is a rectangular-shaped Si cantilever with a diamond-coated spherical indenter (tip radius of curvature: 65 nm; estimated with SEM before nanoindentation experiment). The spring constants of the probes were determined by the thermal tune method.15 Some of the technical data of the probes used in this work are summarized in Table 1.

precisely and apply appropriate loads onto the nanospheres; how to measure the minimum deformations caused by the load; and how to calculate the elastic modulus values with the suitable theoretical model. Attempting to take most of these factors into consideration, the size effect on the elastic properties of a series of PS nanospheres with different sizes (50−1000 nm) has been investigated in the present work. Analyses of the measured data based on the Hertz and JKR contact theories were conducted to obtain the modulus value. Moreover, the effects of the AFM tip’s shape and the deformation at the bottom of the sphere which was neglected in other references would be considered.

Table 1. Technical Data of Probes Used in the Present Work

2. EXPERIMENTAL METHODS AND THEORIES 2.1. Materials. All the reagents (analytically pure) were purchased from Nanjing Chemical Reagent Factory (China). All the polystyrene spheres (57.7 ± 2, 89.9 ± 2, 143.7 ± 3, 193.8 ± 5, 456.4 ± 8, and 954.7 ± 13 nm) used in this work were purchased from Nano-Micro Technology Corporation (China), which were prepared by using the well-known soap-free emulsion polymerization method. The spheres were characterized with the dynamic light scattering (DLS) and the scanning electron microscopy (SEM) to check their size, distribution, and stability. Polished single crystal P-type Si (110) wafers were purchased from GRINM Semiconductor Materials Corporation (China) with the roughness less than 2 nm. 2.2. Sample Preparation. Polished single crystal silicon Si (110) wafer substrates were pretreated successively by supersonic rinsing in chloroform, acetone and ethanol for 30 min, and the rinsing process in each organic solvent was followed by thorough rinsing in distilled water (Milli-Q) to remove possible contaminants. The prepared Si wafers were immersed in the piranha solution (98% H2SO4:30% H2O2 = 1:1, volume ratio) heating at 90 °C for 2 h to hydroxylate the surfaces. Besides hydroxylation, any organic/inorganic contaminant can be also removed through the treatment with the piranha solution. The wafers were then rinsed with distilled water and dried by high purity nitrogen gas. The polymer nanosphere solution was diluted with ethanol so that the colloidal solution well wets the Si substrate. After being supersonicated for 30 min to avoid particle aggregation, glass capillaries were used to dip the colloidal solution onto the Si substrate surfaces to ensure that the nanospheres could be dispersedly distributed on the substrate surface. In this way, a large area of monolayer polymer nanospheres could be fabricated, as shown in Figure 1. The distribution density of nanospheres on the surface can be adjusted by changing the polymer sphere solution’s mass fraction. Most of the spheres stay firmly on the substrate due to the adhesion, primarily the capillary force, between the spheres and the Si substrate, since both surfaces are hydrophilic.

probe type

HA-NC

DCP11

resonant frequency force constant tip radius tip materials

153 kHz 8.32 N/m 10 nm single crystalline silicon

255 kHz 20.5 N/m 65 nm diamond-coated silicon

To investigate the mechanical properties of individual nanospheres at the right location, the point and shoot view was used. After scanning an area with individually distributed polystyrene nanospheres, more than 160 nanospheres were randomly selected from the topographic image. And a crosshair on the image could be used to select the specific point (on the right top of nanospheres) to collect the force curves. The point-shoot function in the Veeco Dimension V system was used for the close-loop control. In the experiment, the cantilever deflection was suitably controlled to ensure purely elastic deformation on the sphere. The mechanical properties of the spheres can be obtained by analyzing the force−distance curves centered on the particle. Some of the force−distance curves were excluded: (i) those resulting in especially high stiffness when the tip was not on the right top of the spheres and instead contacted the substrate (E = 169 GPa); (ii) those resulting in unacceptably low stiffness values when the tip contacted the side of the spheres and lateral motion subsequently occurred. Finally, at least 40 effective curves for the PS monolayer spheres of each size were chosen and used for further analyses. Figure 2a shows the typical force−distance curves recorded on the top of a nanosphere. The ramping velocity during nanoindentation investigated in this work was ca. 400 nm/s. The velocity was relatively slow compared with those in some literatures,13,16,17 where the elastic modulus was found to be almost unaffected by the ramping velocity for softer materials than the PS spheres in this work. 2.4. Contact Models of Tip−Sphere. The Hertzian elastic contact theory is the mostly used approach with the simplest expression for modeling the tip−sphere contact.18 The theory has B

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highly adhesive system with low stiffness.19,23,24 The radius of the contact area and the indentation depth has the following forms:23

aJKR 3 =

h JKR =

3R *FJKR (6)

4E*

aJKR 2 R*

−

2πWaJKR (7)

E*

where W is the work of adhesion and can be calculated from the jumpoff contact and P is the force exerted by the tip on the sphere. FJKR is the load between the tip and the sphere:

FJKR = F + 3πWR * +

6πWR * + 9π 2W 2R *2

(8)

Inserting eq 6 into eq 7, the following equation can be obtained:

h JKR = 0.8255R*(−1/3)E*(−2/3)FJKR 2/3 − 0.9532(2πW )1/2 × R *1/6 E*(−2/3)FJKR 1/6

Figure 2. (a) Typical force−distance curves recorded on the top of a polymer microsphere. (b) Relative movements of the AFM tip−sphere system during the indentation process: (i) The AFM tip just comes into contact with the sphere, and no deformation occurs in the sphere; (ii) the cantilever comes to an equilibrium state; (iii) the sphere’s deformation occurs due to the applied force by the tip.

⎛ 3R *F ⎞1/3 ⎜ ⎟ ⎝ 4E* ⎠

where z is the piezo displacement. Considering the deflection offset, d0, due to thermal drift in the system and stresses in the cantilever,25 eq 10 could be modified to eq 12

F = k(d − d0)

1− 1 = E* E1

+

1 − ν2 E2

(2)

h = (z − z 0) − (d − d0)

2

⎛ 9F 2 ⎞1/3 a2 =⎜ ⎟ R* ⎝ 16R *E*2 ⎠

(3)

3. RESULTS Figure 3 shows the relationships between the force as well as elastic modulus and the indentation depth h during an AFM tip (DCP 11) indenting a PS nanosphere (diameter: 57.7 nm). It can be observed that when the indentation depth is less than 2 nm, the elastic modulus is unstable. The variation curves of the elastic moduli with the indentation depth for nanospheres of other diameters are also unstable at small h. The reason for this phenomenon should be ascribed to the destabilizing attractive force gradient in the vicinity of surfaces.26−28 Because of the high local pressure at nanoscale contacts, local yielding might be possible. However, in this experiment, the indentation depths less than 6 nm in the loading process were emphasized for the evaluation of the elastic modulus to avoid the influence of possible plastic deformation happened in the sphere during

(4)

Then the elastic modulus can be derived as E2 =

1/2 3F(1 − ν2 2) ⎛ R 2 + R1 ⎞ ⎜ ⎟ ⎝ R1R 2 ⎠ 4h3/2

(13)

Figure 2b shows the relative movements of the tip−sphere system during the indentation process. The modulus of the sphere can be evaluated from the slope of the loading region on the force− indentation curve.

where E is Young’s modulus, υ is Poisson’s ratio, and R is the radius: the subscripts 1 and 2 denote the tip and the sphere, respectively. Generally, the AFM silicon tip has an elastic modulus of 130−160 GPa and υ1 = 0.27;20,21 the diamond tip has a elastic modulus of 1141 GPa and υ1 = 0.07.22 Poisson’s ratio of bulk PS (0.33) was used in the calculations.11 Hence, the tip deformation could be considered as negligible since the tip modulus is much larger than that of the PS material, and then the deformation of the sphere, h, is h=

(12)

If the height offset z0 is the position where the tip first contacts the sample surface, the force−displacement curve can be transformed into the force−indentation curve to calculate the elastic modulus of these spheres, as expressed by

where R* and E* are the relative radius of curvature and the combined modulus of the two bodies respectively, which are defined as

ν12

(11)

h=z−d

(1)

R + R1 1 1 1 = + = 2 R* R1 R2 R1R 2

(10)

F = kd

where k is the cantilever spring constant and d the cantilever deformation. The tip indentation depth h into the sample surface is

been experimentally demonstrated to be valid for small deformations by a nonadhesive elastic sphere against a plane.19 When the elastic sphere is subjected to an applied normal load (F), there is a circular contact zone of radius a on the sphere−sphere or sphere−substrate interface:18,19 a=

(9)

Then, the elastic modulus can be derived based on eqs 8 and 9. In this work, the elastic moduli of nanospheres obtained based on these two theories would be compared. 2.5. Data Processing. In AFM experiments, the contact radius cannot be obtained directly, but the indentation depth h can be measured. Hence, the indentation depth, rather than the contact area radius, was used to calculate the elastic moduli of the nanospheres. To quantitatively calculate the elastic modulus, the force− displacement curves were converted into the force−indentation curves.11,12 The load, F, applied by the cantilever to the sample surface can be calculated as

(5)

The adhesion force within the contact region is taken account into the Johnson−Kendall−Roberts (JKR) model, which is suitable for C

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Figure 5. Relationship between the sphere diameter and the elastic moduli measured with DCP 11 tip and calculated based on the Hertz and JKR theories.

Figure 3. Variations of the force/elastic modulus with the indentation depth during an AFM tip (DCP 11) indenting into a PS sphere with the diameter of 57.7 nm. Both the elastic moduli calculated with Hertz and JKR theories are shown.

the diameter decreasing. Although the elastic moduli calculated from the JKR theory are lower than that those from the Hertz theory, their variation trends with the sphere diameter are close. Furthermore, most of the elastic modulus values for PS nanospheres are smaller than that of the bulk counterpart (3− 3.5 GPa).4

indentation. Thus, the measured results for the indentation depth from 3 to 6 nm will be emphasized in the following part. It can be seen from Figure 3 that the stable elastic modulus at the indentation depth from 3 to 5.5 nm is about 2.7−3.5 GPa, which was calculated on the Hertz theory. The elastic modulus calculated based on the JKR theory is also shown in this figure, and the value is about 1.7−1.9 GPa, which is lower than that based on the Hertz theory. It is consistent with the results obtained by Chizhik et al.20 that the micromechanical properties of compliant polymeric materials analyzed with the JKR theory were lower than that those with the Hertz theory. In the JKR model, the adhesion work can be obtained from the jump-off contact curve, but the contribution from the capillary force is also included in the curve. Hence, the jump-off contact curve measured in water would be more accurate to get the modulus value with the JKR model. Figure 4 shows the elastic moduli of nanospheres with different diameters (diameters: 57.7, 89.9, 143.7, 193.8, 456.4,

4. DISCUSSION AND ANALYSIS Is the size dependence of the elastic moduli of PS nanospheres intrinsic or due to measurement errors or artifacts? Presumably, possible errors could come from the effects of the tip shape as well as the deformation at the bottom of the sphere, etc. In the following part, these factors will be discussed successively. 4.1. Tip Shape Effect. Figure 6 shows the variations of the elastic moduli of the PS nanospheres of different diameters

Figure 6. Variations of the elastic moduli of the PS nanospheres measured by using the Si tip (HA-NC) with the indentation depth.

measured by using the Si tip (HA-NC) with the indentation depth. Figure 7 shows the direct comparison of the relationships between the sphere diameter and the elastic moduli measured with different AFM tips (calculated based on the Hertz theory). As shown in Figure 7, the moduli measured by using the HA-NC Si tip are larger than those using the DCP-11 tip, although their variation trends with the sphere diameter seem to be close. A new tip was always used for nanospheres of each size, but the Si tips were found to be worn easily, usually changed from 10 nm in radius of curvature (before experiment) to 100 nm (after experiment). In contrast, the radius of

Figure 4. Elastic modulus of spheres with different diameters by DCP 11 tip calculated based on the Hertz model.

and 954.7 nm) at the indentation depths ranging from 3 to 6 nm, and these values were calculated based on the Hertz model. It can be found that the smaller spheres have larger elastic moduli. Figure 5 shows the relationships between the sphere diameter and the elastic moduli, and when the sphere size is smaller than 200 nm, the elastic moduli increase quickly with D

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⎛ R * ⎞1/3 hb = ⎜ T⎟ ht ⎝ RB* ⎠

(15)

where R + R2 1 1 1 = + = 1 * R1 R2 R1R 2 RT

(16)

1 1 1 1 = + ≈ Rs R2 R2 RB*

(17)

where Rs denotes the radius of curvature of the substrate. Thus, the percentage errors of the sphere’s elastic modulus could be written as Figure 7. Relationships between the sphere diameter and the elastic moduli measured by using different AFM tips, and all the calculations were based on the Hertz theory.

Δ = |Ea − E b| /E b

where Ea is the calculated elastic modulus of the sphere after taking the bottom deformation of the sphere into account, while Eb is that without considering the deformation. The percentage errors of the elastic moduli of the spheres with different diameters are shown in Figure 9a. The solid line corresponds to that for the HA-NC tip (10 nm), and the dashed line corresponds to the error for the DCP-11 tip (65 nm). The squares are those spheres of different diameters investigated in this work with the HA-NC and DCP-11 tips, respectively. It can be observed that the bottom deformation obviously affects the results, especially when the sphere size is relatively small. For instance, the error can even reach up to 110% for the HA-NC tip (10 nm) and 160% for the DCP-11 tip (65 nm) in the case of the sphere with the diameter of 57.7 nm. The error decreases when the sphere’s size increases or the tip’s radius of curvature reduces. In spite of this, the errors still cannot be ignored even for the sphere of 4 μm in diameter, where the error is about 27% for the HA-NC tip (10 nm) and 50% for the DCP-11 tip (65 nm). Only for the sphere diameter larger than 500 μm, the errors are less than 10% (4% for the HA-NC tip and 7% for the DCP-11 tip). Then, the elastic moduli of spheres with different diameters were recalculated after taking the bottom deformation into consideration, and the results are shown in Figure 9b. As shown, the modulus values after considering the bottom deformation are obviously larger. The smaller spheres still have larger elastic modulus, and the elastic modulus decreases with the increase of the sphere diameter. The recalculated elastic modulus for the sphere of 57.7 nm in diameter is about 7.9 GPa, which is more than two times the bulk value. In contrast, the modulus value for the sphere of 955 nm in diameter is about 2.4 GPa, close to the bulk value (3 GPa).4 In this case, the question why the measured results of the nanospheres before error analysis without considering the substrate deformation are lower than those of their bulk counterparts could be roughly understood. 4.3. Possible Mechanisms for the Size Effect of Elastic Modulus of Nanospheres. Theoretically, the deformation of the polymer nanospheres and the corresponding elastic modulus could be possibly affected by the glass transition temperature (Tg), the crystalline phase and crystallinity, etc.24 The glass−rubber transition state at the air/PS film interface could result in the elastic modulus of the near-surface region in the film slightly smaller than the bulk value even at room temperature.4 Complex structure changes inside materials at the nanoscale were used to account for the higher elastic modulus of PS nanoparticles (200 nm) than the bulk value.12

curvature of the DCP-11 tip did not change obviously after experiments. Hence, the tip wear should be the cause that the modulus values measured by using the HA-NC tip are larger than those by using the DCP-11 tip. When a tip with the small radius of curvature is used to compress a small sphere, it is very easy to induce location offset on the substrate rather than on the top of the sphere, giving rise to tip wear.29,30 In this sense, the sphere’s modulus could be more accurately determined with a hard tip with not too small radius of curvature. 4.2. Effect of the Deformation at the Bottom of the Sphere. In most cases, the deformation at the bottom of the nanosphere was neglected in the calculation of the elastic modulus of spheres. This could be valid if the sphere is large and the radius of curvature of the tip is relatively small. But when the sphere is at the nanoscale and the tip is on the same scale, the contribution from the deformation at the bottom of the sphere to the indentation depth h should not be neglected. Figure 8 shows the compressive deformation of a sphere

Figure 8. Compressive deformation of the sphere between the tip and the substrate.

between a tip and the substrate. It can be seen that the total indentation depth h includes the deformations at the top part (ht) and that at the bottom part (hb) of the sphere. Then, we have h = ht + hb

(18)

(14)

Using the Hertz theory on both the top and the bottom parts, from eqs 1 and 4, and considering that the elastic modulus of the substrate is much larger than that of the sphere, the following relationship can be obtained E

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Figure 9. (a) Variations of the percentage errors of Young’s moduli with the sphere diameter measured with the HA-NC and DCP-11 tips. (b) Relationships between the sphere diameter and the elastic moduli with and without considering the bottom deformation.

spheres. The results show that the elastic moduli of PS nanospheres of different sizes are in the range of 2−8 GPa, and the elastic moduli depend on the spheres’ size. The possible measurement errors or artifacts due to tip wear and the deformation at the bottom of the sphere were analyzed. The size dependence on the elastic modulus of PS nanosphere is inferred to result from the spatial structure and the distribution of molecular chains in the confined boundary layer of the nanospheres. The present work provides fundamental knowledge to measure the mechanical properties of nanoparticles and elucidate related mechanisms, which are highly relevant to the applications in surface engineering, micro/nanomanufacturing, and nanofabrication, etc.

Besides, the increase of the free energy resulting from the confined growth11 and the surface effect31−33 are alternative explanations to the size dependence on the polymer nanostructures’ elastic modulus. Furthermore, a molecularbased hyperelastic model to simulate the size-dependent mechanical properties of polymer nanostructures was developed by Tan et al.11 Although the underlying mechanism of the size effect of elastic modulus of nanospheres observed in this work is still not very clear, the viewpoints based on the surface energy seem to be more applicable. Hence, in analogue to the results previously reported in refs 11, 31, and 32, the mechanism could be speculated as follows: As mentioned in the Experimental Methods and Theories section, these spheres were prepared by using the method of soap-free emulsion polymerization of styrene, and sphere nucleation would initiate via a micellar mechanism.34 Specifically, the micelles become the nuclei of a growing sphere, which is stabilized by the large numbers of charged groups present in the outer layer. Monomers or shortchain oligomers free radicals preferentially diffuse into the micelles, and the growth of the sphere terminates upon the depletion of most of the monomer and free radicals in the solution. The final sphere would form with many charged groups at the outer surface layer, where molecules are more aligned and denser. This kind of confined growth of nanospheres results in the spatial structure and the distribution of molecular chains in the outer layer being different from those in the core layer inside the sphere,35 and polymer molecules in the core layer are presumably more randomly distributed if the sphere is not too small. In this case, the energy in the surface layer, due to molecular orientation (smaller conformation entropy), as well as defects and inhomogeneity, which were inevitably produced during synthesis,33 could be higher than the core layer inside the sphere. The thickness of the outer surface layer (comparable to the radius of the originally formed micelle) should not change significantly with the change of the particle size, but its proportion in the nanosphere would increase with the decrease of the sphere size. As a result, the compliance of the nanosphere could reduce and correspondingly the elastic modulus increase with the decrease of the sphere size.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail [email protected] (D.G.). *E-mail [email protected] (G.X.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the National Natural Science Foundation of China (51375255), the International Science &Technology Cooperation Project (No. 2011DFA70980), National Key Basic Research Program of China (Grant No 2011CB013102), and the Foundation for Innovative Research Groups from the National Natural Science Foundation of China (51321092).

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REFERENCES

(1) Soppimatha, K. S.; Aminabhavia, T. M.; Kulkarnia, A. R.; Rudzinskib, W. E. Biodegradable Polymeric Nanoparticles as Drug Delivery Devices. J. Controlled Release 2001, 70, 1−20. (2) Gupta, S.; Zhang, Q. L.; Emrick, T.; Balazs, A. C.; Russell, T. P. Entropy-Driven Segregation of Nanoparticles to Cracks in Multilayered Composite Polymer Structures. Nat. Mater. 2006, 5, 229−233. (3) Nayak, S.; Lyon, L. A. Soft Nanotechnology with Soft Nanoparticles. Angew. Chem., Int. Ed. 2005, 44, 7686−7708. (4) Miyakea, K.; Satomi, N.; Sasaki, S. Elastic Modulus of Polystyrene Film from Near Surface to Bulk Measured by Nanoindentation using Atomic Force Microscopy. Appl. Phys. Lett. 2006, 89, 031925. (5) Liu, Y. L.; Zhang, K. L.; Wang, F.; Di, W.G. Investigation on the Final Polishing Slurry and Technique of Silicon Substrate in ULSI. Microelectron. Eng. 2003, 66, 438−444.

5. CONCLUSIONS In summary, the mechanical properties of PS nanospheres were investigated through nanoindentation by an AFM tip into the F

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(6) Swetha, T.; Arun, K. S.; Ashok, K. Tribological Issues and Modeling of Removal Rate of Low-k Films in CMP. J. Electrochem. Soc. 2004, 151, G205−G211. (7) Armini, S.; Whelan, C. M.; Maex, K.; Hernandez, J. L.; Moinpour, M. Composite Polymer-Core Silica-Shell Abrasive Particles during Oxide CMP: A Defectivity Study. J. Electrochem. Soc. 2007, 154, H667−H671. (8) Steinitz, R. The Micro-Hardness Testera New Tool in Powder Metallurgy. Met. Alloys 1943, 17, 1183−1187. (9) Shorey, A. B.; Gregg, L. L.; Romanofsky, H. J.; Arrasmith, S. R.; Kozhinova, I.; Hubregsen, J.; Jacobs, S. D. Study of Material Removal during Magnetorheological Finishing (MRF). In Optical Manufacturing and Testing; Stahl, H., Ed.; SPIE: Bellingham, WA, 1999; Vol. 3782, pp 101−111. (10) Biggs, S.; Sprinks, G. Atomic Force Microscopy Investigation of the Adhesion between a Single Polymer Sphere and a Flat Surface. J. Adhes. Sci. Technol. 1998, 12, 461−478. (11) Tan, S.S.; Sherman, R. L., Jr.; Ford, W. T. Nanoscale Compression of Polymer Microspheres by Atomic Force Microscopy. Langmuir 2004, 20, 7015−7020. (12) Paik, P.; Kar, K.K.; Deva, D.; Sharma, A. Measurement of Mechanical Properties of Polymer Nanospheres by Atomic Force Microscopy: Effects of Particle Size. Micro Nano Lett. 2007, 2, 72−77. (13) Armini, S.; Vakarelski, I. U.; Whelan, C. M. Nanoscale Indentation of Polymer and Composite Polymer-Silica Core-Shell Submicrometer Particles by Atomic Force Microscopy. Langmuir 2007, 23, 2007−2014. (14) Gerbericha, W.W.; Mooka, W.M.; Perreya, C.R.; Cartera, C.B.; Baskesb, M.I.; Mukherjeec, R.; Gidwanic, A.; Heberleinc, J.; McMurryc, P.H.; Girshickc, S.L. Superhard Silicon Nanospheres. J. Mech. Phys. Solids 2003, 51, 979−992. (15) Hutter, J.L.; Bechhoefer, J. Calibration of Atomic-Force Microscope Tips. Rev. Sci. Instrum. 1993, 64, 1868−1873. (16) Tripathy, S.; Berger, E. J. Measuring Viscoelasticity of Soft Samples using Atomic Force Microscopy. J. Biomech. Eng. 2009, 131, 094507. (17) Rico, F.; Roca-Cusachs, P.; Sunyer, R.; Farre, R.; Navajas, D. Cell Dynamic Adhesion and Elastic Properties Probed with Cylindrical Atomic Force Microscopy Cantilever Tips. J. Mol. Recognit. 2007, 20, 459−466. (18) Hertz, H.; Reine, J. On the Contact of Elastic Solids. Angew. Math. 1882, 92, 156−171. (19) Johnson, K. L. Contact Mechanics; Cambridge University Press: New York, 1985. (20) Chizhik, S. A.; Huang, Z.; Gorbunov, V. V.; Myshkin, N. K.; Tsukruk, V. V. Micromechanical Properties of Elastic Polymeric Materials as Probed by Scanning Force Microscopy. Langmuir 1998, 14, 2606−2609. (21) Yaralioglu, G. G.; Degertekin, F. L.; Crozier, K. B.; Quate, C. F. Contact Stiffness of Layered Materials for Ultrasonic Atomic Force Microscopy. J. Appl. Phys. 2000, 87, 7491. (22) Kracke, B.; Damaschke, B. Measurement of Nanohardness and Nanoelasticity of Thin Gold Films with Scanning Force Microscope. Appl. Phys. Lett. 2000, 77, 361. (23) Johnson, K. L.; Kendall, K.; Roberts, A. D. Surface Energy and the Contact of Elastic Solids. Proc. R. Soc. London A 1971, 324, 301− 313. (24) Guo, D.; Xie, G.; Luo, J. Mechanical Properties of Nanoparticles: Basics and Applications. J. Phys. D: Appl. Phys. 2014, 47, 013001. (25) Touhami, A.; Nysten, B.; Dufrêne, Y.F. Nanoscale Mapping of the Elasticity of Microbial Cells by Atomic Force Microscopy. Langmuir 2003, 19, 4539−4543. (26) Guo, D.; Li, J.N.; Chang, L.; Luo, J.B. Measurement of the Friction between Single Polystyrene Nanospheres and Silicon Surface using Atomic Force Microscopy. Langmuir 2013, 29, 6920−6925. (27) Wang, X.D.; Yu, J.X.; Chen, L.; Qian, L.M.; Zhou, Z.R. Effects of Water and Oxygen on the Tribochemical Wear of Monocrystalline

Si(100) against SiO2 Sphere by Simulating the Contact Conditions in MEMS. Wear 2011, 271, 1681−1688. (28) Chizhik, S.A.; Huang, Z.; Gorbunov, V.V.; Myshkin, N.K.; Tsukruk, V.V. Micromechanical Properties of Elastic Polymeric Materials as Probed by Scanning Force Microscopy. Langmuir 1998, 14, 2606−2609. (29) Hsu, S.; Ying, C.; Zhao, F. The Nature of Friction: A Critical Assessment. Friction 2014, 2, 1−26. (30) Broitman, E. The Nature of the Frictional Force at the Macro-, Micro-, and Nano-scales. Friction 2014, 2, 40−46. (31) Cuenot, S.; Frétigny, C.; Demoustier-Champagne, S.; Nysten, B. Surface Tension Effect on the Mechanical Properties of Nanomaterials Measured by Atomic Force Microscopy. Phys. Rev. B 2004, 69, 165410. (32) Jing, G.Y.; Duan, H.L.; Sun, X.M.; Zhang, Z.S.; Xu, J.; Li, Y.D.; Wang, J.X.; Yu, D.P. Surface Effects on Elastic Properties of Silver Nanowires: Contact Atomic-Force Microscopy. Phys. Rev. B 2006, 73, 235409. (33) Jing, G.Y.; Zhang, X. Z.; Yu, D. P. Effect of surface morphology on the mechanical properties of ZnO nanowires. Appl. Phys. A: Mater. Sci. Process. 2010, 100, 473−478. (34) Goodall, A.R.; Wilkinson, M.C.; Hearn, J. Mechanism of Emulsion Polymerization of Styrene in Soap-Free Systems. J. Polym. Sci., Polym. Chem. Ed. 1977, 15, 2193−2218. (35) Tang, S.; Greene, S.; Liu, W.K. A Variable Constraint Tube Model for Size Effects of Polymer Nano-structures. Appl. Phys. Lett. 2011, 99, 191910.

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dx.doi.org/10.1021/la501485e | Langmuir XXXX, XXX, XXX−XXX