Size Dependent Mechanical Properties of Monolayer Densely

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Size Dependent Mechanical Properties of Monolayer Densely Arranged Polystyrene Nanospheres Peng Huang, Lijing Zhang, Qingfeng Yan, Dan Guo, and Guoxin Xie Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b03481 • Publication Date (Web): 21 Nov 2016 Downloaded from http://pubs.acs.org on November 22, 2016

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Size Dependent Mechanical Properties of Monolayer Densely Arranged Polystyrene Nanospheres Peng Huang†‡, Lijing Zhang+, Qingfeng Yan++, Dan Guo†*, and Guoxin Xie†*

†State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China. ‡Sicence and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621908, Sichuan, China. +

School of Chemistry, Dalian University of Technology, Dalian 116024, Liaoning,

China ++

Department of Chemistry, Tsinghua University, Beijing 100084, China.

KEYWORDS: monolayer densely arranged nanospheres, size-dependent mechanical properties, core-shell model, AFM

ABSTRACT: In contrast to macroscopic materials, the mechanical properties of polymer nanospheres show fascinating scientific and application values. However, the experimental measurements of individual nanospheres and quantitative analysis of theoretical mechanisms remain less well performed and understood. We provide a highly efficient and accurate method with monolayer densely arranged honey-comb polystyrene (PS) nanospheres for the quantitatively mechanical characterization of

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individual nanosphere on the basis of atomic force microscopy (AFM) nanoindentation. The efficiency is improved by 1-2 order and the accuracy is also enhanced almost by half-order. The elastic modulus measured in the experiments increases with decreasing radius to the smallest nanospheres (25-35 nm in radius). A core-shell model is introduced to predict the size dependent elasticity of PS nanospheres, the theoretical prediction agrees reasonably well with the experimental results and also shows a peak modulus value.

∎ INTRODUCTION Increasingly more researchers have shown great interests in the mechanical properties of polymer nanospheres due to their extensive applications in self-assembly,1 fuel cell,2 surface coating,3 pharmacology4 and composites.5 All of these applications require the knowledge of the mechanical behaviors of polymer nanospheres, which will be beneficial in controlling the performances of nanospheres in specific applications. For instance, the sphere elasticity could dramatically affect the biodistribution and tissue targeting in the sphere-based drug delivery system.6 Polymer nanospheres and polymer core-shell composites behave rather differently at the nanoscale than at the macroscale.7-14 For example, it was revealed that the elastic modulus of PS nanospheres was closely related to their dimensions especially when the spheres decreased to 200 nm.15 Paik also found that the elastic modulus of polypropylene (PP) nanospheres decreased with the increasing size of PP nanospheres.9 Besides, inorganic nanospheres also show a similar trend. The hardness


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of silicon nanospheres was four times of the bulk value.16 Bian proved that the mechancial properties of PbS nano-crystals was size dependent and verified a peak modulus value with the decrease of sphere size.17 This size dependent elastic modulus of nanospheres was attributed to the relatively large surface-to-volume ratio at the nanoscale.11,16 Surface effects were also alternative explanations for the size dependent phenomena of nano-structures, including the surface stress, the oxidation layer and the surface roughness.9,18 Beside experimental investigations and theoretical analyses, many micromechanic models have been also proposed to predict the overall composite properties but most of them were lack of mathematical rigor and physical realism.19,20 Christensen proposed a composite-sphere model to predict the overall composite properties of isotropic and two-phase composite materials, which has been verified reasonably for metal nanospheres.20 This core-shell model usually contains different elasticities between the surface part and that in the core of a sphere to explain the size dependent mechanical properties. Emulsion polymerization has been a universal method for preparing monodisperse polymer nanospheres.21,22 It is in rapid development and many different technologies emerge, including the emulsifier-free emulsion polymerization, seeded emulsion polymerization, microemulsion polymerization, etc.23 However, the formation and growth mechanisms for the monodisperse polymer nanospheres remain not very clear. Two theories have been employed for explaining the dispersion polymerization process, i.e., oligomer precipitation mechanism and grafting copolymer mechanism.24 There are also two main theories for the emulsifier-free emulsion polymerization: one


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is homogeneous nucleation and the other is oligomer micellar nucleation.25,26 Up to now, the quantitative mechanical analyses of nanospheres are usually with low efficiency and accuracy, and the underlying mechanism for the available data of the mechanical properties of nanospheres remains not well understood either. ● Existing researches on the mechanical characterizations of nanospheres have the spheres scattered on the substrate randomly. It is time-consuming to find out the desired nanospheres and thermal drift will occur before the indentation process. ● The sudden step change in the height of a single nanosphere on the substrate can affect the measurement of force-deformation curves. The probe has an intimate contact with the hard silicon wafer substrate which may lead to severe tip wear, thus resulting in large calculation errors. ● There are still lack of theoretical models for quantitatively analyzing the size dependent mechanical properties of polymer nanospheres. To better investigate the size dependent mechanical properties of nanospheres, it is essential to prepare appropriate specimens and adopt reasonable theoretical models. In the present work, we use the AFM-based nanoindentation method to investigate the mechanical properties of PS nanospheres (25-500 nm in radius) with a 10 nm silicon probe and utilize JKR contact model to calculate the measured modulus values. The monolayer densely arranged samples are prepared and the effects induced by the possible troubles in the measurement of individual isolated nanospheres can be reduced to a large extent. The elastic modulus begins to increase dramatically when the sphere radius reduces to 150 nm and reaches a peak value at approximately 30 nm.


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A core-shell model with different elasticities at the surface layer and in the core is hypothesized to predict the size dependent elasticity of PS nanospheres. The theoretical prediction agrees reasonably well with the experimental results, validating the reliability of the proposed core-shell model.

∎ EXPERIMENTAL METHODS Materials. All the chemicals were purchased from Sinopharm Chemical Reagent Co., Ltd., China, such as the styrene (St, ≥99.0%), potassium persulfate (KPS, ≥ 99.5%), ethanol (≥99.7%), hydrogen peroxide (≥30%), sulfuric acid (95%−98%) and sodium dodecyl sulfate (SDS, 98%). The Deionized (DI) water we used in the experiments has a resistivity of 18.2 MΩ ∙ cm (Ultra Pure UV, China). The one-side polished silicon wafer (p100, 4 in.) was purchased from KYKY Technology Co. Ltd with a resistivity of 1-10 Ω ∙ cm. The silicon wafer was cut into small pieces (1.5 cm × 1.5 cm) before use. Sample Preparation. Monodisperse PS colloidal spheres with the radius ranging from 25 nm to 500 nm were synthesized using the emulsifier-free emulsion polymerization method.27,28 The densely arranged PS monolayer was prepared by using the air-water interface self-assembly method.29,30 Briefly, the glass slide (0.5 cm×0.5 cm) and glass Petri dish (=9 cm) used in this experiment need to be treated by soaking in the piranha solution (H2SO4 and H2O2 in a 3:1 volume ratio) at room temperature for 1.5 hours and then were rinsed with copious DI water. The treated microscopic glass slide was set in the center of the glass Petri dish and then carefully


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added DI water into the dish to the same level as the upper surface of the glass slide. The PS suspension was firstly diluted with equal volume of ethanol and then 5-10 μL of the colloidal suspension was dropped onto the glass slide. The PS spheres would spread rapidly onto the water surface when contacted with the slide, the closely packed monolayer would form after droping the PS suspension for a period. When the PS monolayer nearly covered the whole glass Petri dish, we stopped dropping and added a drop of 1 wt% SDS solution to further consolidate the PS monolayer. The SEM and AFM images of sample are shown in Figure 1.

Figure 1. SEM and AFM images of the PS nanospheres. (a) is the SEM image of the PS monolayer with 400 nm in radius and the spheres are in a good hexagonal distribution. (b) is the AFM image of the PS monolayer sample with 300 nm in radius. The inset is the section curve of the height. The hight change is far less than the sphere diameter.

AFM Experiments. AFM has been widely used to study the nano-mechanical properties of materials and is under rapid development. The mechanical properties of a sample surface can be easily mapped by the peak force QNM mode with high spatial resolution and fast-scanning.31,32 This technology can calculate in real time the


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force indentation curves at each contact point with high surface sensitivity. Hence, this kind of AFM mode was adopted in our research. Dimension Icon (Bruker) AFM was used to accomplish the indentation tests and acquire the force-deformation curves. A standard cantilever holder for operation in the ambient condition was used. The deflection sensitivity of the silicon probe was calibrated on a standard clean sapphire wafer three times at different locations, then the average value was obtained to diminish the accidental error. The spring constants of the cantilevers were obtained by the thermal tune method.33 The probes were observed directly by the scanning electron microscope (SEM) (LYRA3 TESCAN) before and after use to check the wear condition. All the scanning images were collected with a lateral resolution of 256×256 pixels which could ensure that the tops of PS nanospheres were measured during the indentation experiments. At least ten values were calculated for the same dimension, and then we acquired the average data to minimize the accidental error. The spring constants of the AFM probes are at 20 N/m level and the tip radii are about 10 nm. The temperature and relative humidity in the experiment room were 24.5℃ and 14.7%, respectively.

∎ RESULTS AND DISCUSSION Elastic Modulus. The elastic moduli of PS nanospheres are obtained from the AFM indentation experiments by analysing the force-displacement curves with the JKR contact model (Supporting Information).34 Figure 2a shows the representative variation curves of elastic modulus with indentation depth under the same applied


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load. The elastic modulus is very large and unstable at small indentations, and then decreases with the indentation depth and reaches a stable value when the indentation depth comes to relatively large. Figure 2b shows the relationships between the elastic modulus of PS nanospheres and the radius. The elastic modulus of the PS nanosphere is in the range of 2-6 GPa and larger than that of the bulk counterpart, and it remains unchanged and begins to increase dramatically when the radius of the sphere reduces to 150 nm. The modulus also reaches a peak value when the radius reduces to approximately 30 nm and then decreases rapidly.

Figure 2. Elastic modulus obtained with AFM. (a)The applied loads are the same for different PS nanospheres. The elastic modulus is large and unstable at the small indentation depth, and it becomes constant when the indentation depth is large enough. (b) The elastic modulus remains stable for large spheres and increases with decreasing radius to the smallest nanospheres.

Mechanisms for

the Size

Dependent Mechanical Properties of PS

Nanospheres. The size dependent mechanical properties of nanospheres were usually attributed to the large surface-to-volume ratio.11 The structures might also lead to the


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size dependent mechanical properties.9 Surface effects, including surface stress, oxidation layer and surface roughness, were also alternatively responsible for the size dependent phenomena of nano-structures.18 However, the fundamental mechanisms for the size dependent mechanical properties of polymer nanospheres still remain not very clear. The formation mechanism of polymer nanospheres can help to illuminate the size dependent mechanical properties. The PS nanospheres in our experiments were prepared with the soap-free emulsion polymerization method and the oligomer micellar mechanism scheme is illustrated in Figure 3. 25,35,36 The micelles flocculate together to form spheres by the electrostatic repulsion of the negative charged groups located at the end of the micelle indicated by the solid circles in Figure 3. Hence, the molecules in the surface layer are more aligned and denser to stabilize the spheres due to molecular orientation. The polymer monomers in the core are randomly distributed for their neutral properties. The thickness of the surface layer does not vary significantly with the change of sphere size since the oligomeric free radical length almost keeps the same.15 For the very small PS nanospheres, they only contain highly ordered oligomeric free radicals in the surface layer and very few monomers inside the sphere. The distribution density of the oligomeric free radicals differs from each other during the initial formation stage (Figure 3a and 3b). The PS sphere size increases with more monomers diffuse into the sphere to form an unordered core (Figure 3c and 3d). During the enlargement process of sphere size, the length of oligomeric free radicals


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in the shell remain the same leading to a surface layer with a nearly fixed thickness, and the density variation of oligomeric free radicals’ arrangement results in the size dependent elasticity of the surface layer. The elasticities at the surface layer and in the core are different because of the different polymer structures and distributions. The elastic modulus of the surface layer is larger than that of the core part because the oligomeric free radicals in the surface layer are highly-ordered and densely arranged, while monomers in the core are almost randomly distributed. The effective elastic modulus of a nanosphere is a coupling result of the core and surface layer. Therefore, during the initial formation stage of small PS nanospheres, the effective elastic modulus increases rapidly for the compaction of the oligomeric free radicals in the surface layer. With further increase of sphere size, the relative proportion of surface layer tends to decrease and leads to a decreasing elastic modulus. As a result, it is reasonable to expect that the elastic modulus of a nanosphere reaches a peak value at a certain size. Finally, it can be said that the size dependent elasticity of PS nanospheres is as a result of the spatial structures and the polymer chain distributions.15


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Figure 3. Scheme of formation mechanism of PS nanospheres. The oligomeric free radicals form the surface layer with highly ordered arrangement and dense distribution. The monomers diffuse into the core to form a larger sphere. During the initial formation stage of small PS nanospheres, they only contain highly ordered oligomeric free radicals in the surface layer and very few monomers inside the sphere. The distribution density of the oligomeric free radicals differs from each other during the initial formation stage (Figure 3a and 3b). The increasing density in the surface layer can explain the peak modulus value of a sphere.

The existence of a surface layer in the PS nanostructure has also been verified in other researches. Christopher utilized a fluorescence/multilayer method to investigate the distribution of glass transition temperature (Tg) in the PS films and verified a 14 nm surface layer because of the enhanced segmental mobility.37 Similarly, Delorme obtained a 7 nm surface layer of PS thin film by investigating the Tg distribution.38 Although the calculated results are not the same, the thickness of the surface layer is at the 10 nm level and it is strongly related to the molecular weight and polymerization method. Unlike the thin film, the surface layer molecule chain mobility of a sphere is less than the core for its highly ordered distribution because of different synthesis processes. Thus, the highly ordered surface layer stiffens the sphere and leads to the size dependent properties. For the PS nanospheres of 30 nm in radius, the average molecular weight Mw is about 230 kg.mol-1 by the gel permeation chromatography analysis. The gyration . radius ( = 0.0277 ) is about 13.3 nm, which is almost half of the sphere radius,


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so we can assume that the PS nanosphere only contains the highly ordered surface layer and the elasticity comes to a peak value.39,40 Core-shell Model. For the polymer nanospheres, they usually contain a highly ordered surface layer and a randomly distributed core. Hence, a core-shell model based on different elasticities in the surface layer and in the core is hypothesized to predict the size dependent elasticity of polymer nanospheres.17,20 It contains a core with elastic modulus Ec, which we take from the bulk value of polystyrene, and a surrounding shell surface layer with thickness b and a size dependent elastic modulus

Es (eq. 1). Es is an apparent stiffness which is expected to be larger than the bulk modulus Ec considering the formation mechanism of PS nanospheres.25 The thickness of shell is assumed to remain constant with the change of sphere size since the oligomeric free radicals length in the shell almost keeps the same. The arrangement density and charged groups of the oligomeric free radicals in the surface layer are different with the variation of sphere size, leading to a size dependent elastic modulus of the shell. With the increase of sphere size, the denser distribution of oligomeric free radicals in the surface layer brings to an increasing elastic modulus of the surface layer and it comes to the greatest value when being a flat slab. To describe the effective modulus of the surface layer in relation to the radius of a sphere, the size dependent Es is defined as

Es =Es,0 − es /Rn

(1)

where Es,0 is the modulus of the surface layer when being a flat slab, R is the radius of the sphere, is a fitted modulus which is related to the surface area and n is an


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empirical parameter. It is noted that Es,0 ≠ Ec because the molecular alignment in the shell is different from that in the core part. Based on the composite-sphere model, the effective elastic modulus Eeff can be calculated from Es and Ec as

Eeff =Es +c(Ec -Es )/[1+(1-c)(Ec -Es )/(Es +4Gs /3)]

(2)

c=( − ) /

(3)

Gs =3(1 − 2ν)Es /2(1+ν)

(4)

where c is the volume fraction of core, b is the thickness of surface layer, is the shear modulus of surface layer, is the Possion ratio of PS, and b is a fitted parameter. The size dependent

!""

consists of four parameters:

,

, b, n.

According to the fitting results of experimental data, we can obtain that

,

=

11.47 ± 1.01 GPa, = 2461.14 ± 875.86 GPa. nm. , n=2 and = 14.6 ± 0.1nm. Fig.3a compares the effective elastic modulus predicted by the core-shell model with the experimental data. The theoretical model agrees reasonably well with the experimental data and also predicts a peak modulus value when the particle radius comes to approximately 30 nm. The result of n verifies the proportionality of the elastic modulus of the shell to the surface area, and the fitting result of b illustrates the shell thickness of PS nanospheres. The surface layer thickness by theoretical prediction almost matches the data shown in literatures.37,38 The thickness value of 14.6 nm is almost half of the radius of the stiffest sphere and equals to the gyration radius, verifying that the sphere only contains the highly ordered surface layer. Finally, the agreement between the surface layer thickness and the gyration radius proves the rationality of the core-shell model.


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Figure 4a shows that the fitting results by the core-shell model agrees well with the experimental data. Figure 4b compares the elastic modulus of the shell Es with the core Ec. Es increases with the radius monotonically and approaches a constant value. The bigger the nanosphere, the larger the surface layer elastic modulus, because of the more densely arrangement. The effective modulus

!""

is a coupling result of Es and

Ec, and it increases firstly and then decreases to a constant value. For the very small PS nanospheres (/ 17 nm in radius), Es decreases to be less than Ec because the oligomeric free radicals are not compact enough in the initial formation stage. The inset rectangle in Figure 4b shows that

!"" coincides

with Es when the nanosphere

is small, validating that the surface layer dominates the modulus in the initial formation of a nanosphere. Similar to the polymer core-silicon shell composites, the elastic modulus of the nanoparticle increases with the reducing dimension and is strongly related to the proportion of the core-shell sonsittuent.12,14

Figure 4. Theroretical analysis of the core-shell model. (a) Size dependent elastic modulus of PS nanospheres, including the experimental data and the fitting data of the core-shell model. The theoretical fitting results agree reasonably well with experimental data and predict a peak modulus value when the sphere’s radius comes to approximately 30 nm. (b) Elastic moduli of the shell and


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the bulk material. The inset is the scheme of the core-shell model of PS. The surface elastic modulus Es increases with the radius and approaches a constant value asymptotically. The inset black rectangle in (b) shows that

!"" coincides

with Es validating that the surface layer

dominates the modulus in the initial formation of a nanosphere.

Analysis of Tip Wear. The tip influence in the experiments shouldn’t be neglected which may lead to large errors.41 The tip wear is inevitable in the scanning and indentation experiments and the radius would become much larger in previous researches, this might cause a significant deviation of calculation values. Figure 5 shows the errors of evaluated elastic modulus caused by tip wear when calculated with the initial radius of the probe. The error has a remarkable increasing with tip wear and it can reach 50% when the radius increases due to tip wear from the initial 10 nm to 50 nm. In addition, the error also increases with the dimension of PS nanospheres. Assuming that

0

and

.

are the calculated elastic moduli with the tip

radius of the initial value and the wear value, the error can be obtained by the following equation.

Error=

E1 -E2 E1

=1-(

R*2 R*1

-1/2

)

=1-(

Rwear .(10+R) -1/2 10.(Rwear +R)

)

(5)

where Rwear is the radius of the tip after wear while the initial value of tip radius is 10 nm, R is the radius of PS nanosphere, and 0∗ and .∗ are the reduced radii of the initial tip and the tip after wear. Fortunately, in our work we can avoid tip wear as much as possible because of the monolayer densely arranged PS nanospheres samples. The SEM images of the silicon probe before and after use are shown in the inset of Figure 5 and no apparent wear is


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manifested. Hence, we can obtain the accurate and convincing results through our experiments.

Figure 5. Calculation errors of elastic modulus caused by tip wear. The error can reach 50% when the radius varies from the initial 10 nm to 50 nm. The inset shows the SEM images of the silicon probe before and after use in our experiments. No apparent wear is observed.

∎ CONCLUSION In summary, the size dependent mechanical properties of densely arranged monolayer PS nanospheres (25-500 nm in radius) are quantitatively investigated with AFM. The elastic moduli measured in the experiments are in the range of 2-6 GPa and increase with decreasing radius to the smallest nanospheres (25-35 nm) investigated in the present work. A core-shell model is used to predict the size dependent elasticity of PS nanospheres and it agrees reasonably well with the experimental results. It also shows a peak modulus value when the radius decreases to a certain size. The present work sheds light on the quantitative study of size dependent mechanical properties of polymer nanospheres and provides fundamental information for relevant applications


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in surface engineering and biopharmacy, etc.

∎ AUTHOR INFORMATION Corresponding Authors * (D.G.) E-mail: [email protected] , (G.X.) E-mail: [email protected] Author contributions D.G. and G.X initiated this research. P.H. performed the AFM experiments, data analysis and theoretical modeling. L.Z and Y.Q prepared the PS samples. Notes The authors declare no competing financial interest.

∎ ACKNOWLEDGEMENTS We appreciate the financial support from the National Natural Science Foundation of China (Grant Nos. 51375255, 51321092, 51527901) and Foundation for the Author of National Excellent Doctoral Dissertation of PR China (FANEDD No. 201429).

∎ REFERENCES (1) Akcora, P.; Liu, H.; Kumar, S. K.; Moll, J.; Li, Y.; Benicewicz, B. C.; Schadler, L. S.; Acehan, D.; Panagiotopoulos, A. Z.; Pryamitsyn, V.; Ganesan, V.; Ilavsky, J.; Thiyagarajan, P.; Colby, R. H.; Douglas, J. F., Anisotropic self-assembly of spherical polymer-grafted nanoparticles. Nat. Mater. 2009, 8, 354-359. (2) Chai, G. S.; Shin, I. S.; Yu, J. S., Synthesis of ordered, uniform, macroporous carbons with mesoporous walls templated by aggregates of polystyrene spheres and silica particles for use as catalyst supports in direct methanol fuel cells. Adv. Mater. 2004, 16, 2057-2061. (3) Savage, N., Synthetic Coatings Super Surfaces. Nature 2015, 519, S7-S9.


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Boiko,

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J.,

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Size Dependent Mechanical Properties of Monolayer Densely

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