Nonlinear Viscoelasticity of Highly Ordered, Two-Dimensional

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Interface-Rich Materials and Assemblies

Nonlinear Viscoelasticity of Highly Ordered, Two-Dimensional Assemblies of Metal Nanoparticles Confined at the Air/Water Interface Shihomi Masuda, Salomé Mielke, Federico Amadei, Akihisa Yamamoto, Pangpang Wang, Takashi Taniguchi, Kenichi Yoshikawa, Kaoru Tamada, and Motomu Tanaka Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b02713 • Publication Date (Web): 28 Sep 2018 Downloaded from http://pubs.acs.org on October 1, 2018

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Nonlinear Viscoelasticity of Highly Ordered, Two-Dimensional Assemblies of Metal Nanoparticles Confined at the Air/Water Interface

Shihomi Masuda1,2,#, Salomé Mielke1,#, Federico Amadei1, Akihisa Yamamoto3, Pangpang Wang2, Takashi Taniguchi4, Kenichi Yoshikawa3,5, Kaoru Tamada2,*, and Motomu Tanaka1,3,*

1

Physical Chemistry of Biosystems, Institute of Physical Chemistry, Heidelberg

University, D69120 Heidelberg, Germany 2

Institute for Materials Chemistry and Engineering (IMCE), Kyushu University, 819-

0395 Fukuoka, Japan 3

Center for Integrative Medicine and Physics, Institute for Advanced Study, Kyoto

University, 606-8501 Kyoto, Japan 4

Department of Chemical Engineering, Graduate School of Engineering, Kyoto

University, 615-8510 Kyoto, Japan 5

Faculty of Life and Medical Sciences, Doshisha University, 610-0321 Kyotanabe,

Japan #

*

Equal Contribution Corresponding

Authors:

[email protected],

heidelberg.de

ACS Paragon Plus Environment

tanaka@uni-

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ABSTRACT In this study, we investigated the viscoelastic properties of metal nanoparticle monolayers at the air/water interface by dilational rheology under the periodic oscillation of surface area. Au nanoparticles capped with oleylamine form a stable, dense monolayer on a Langmuir film balance. The stress response function of a nanoparticle monolayer was first analyzed using the classical Kelvin-Voigt model, yielding the spring constant and viscosity. The obtained results suggest that the monolayer of nanoparticles is predominantly elastic, forming a two-dimensional physical gel. As the global shape of the signal exhibited a clear nonlinearity, we further anayzed the data with the higher modes in the Fourier series expansion. The imaginary part of the higher mode signal was stronger than the real part, suggesting that the dissipative term mainly causes the nonlinearity. Intriguingly, the response function measured at a larger strain amplitude became asymmetric, accompanied by the emergence of even modes. The significance of interactions between nanoparticles was quantitatively assessed by calculating the potential of mean force, indicating that the lateral correlation could reach up to the distance much larger than the particle diameter. The influence of surface chemical functions and core metal has also been examined by using Au nanoparticles capped with partially fluorinated alkane thiol and Ag nanoparticles capped with myristic acid. The combination of dilational rheology and correlation analyses can help us precisely control twodimensional colloidal assembly of metal nanoparticles with fine-adjustable localized surface plasmon resonance.

Keywords:

dilational

rheology,

colloidal

addembly,

viscoelasticity, lateral correlation ACS Paragon Plus Environment

nanoparticle,

nonlinear

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INTRODUCTION A number of studies have demonstrated that micrometer-scale particles form twodimensional (2D) colloidal assemblies,1 whose phases can be modulated by salts, surfactants, and polymers.2-4 To date, 2D assemblies of nanometer-scaled particles have been investigated mostly using metal or semiconductor nanoparticles taking spherical or rod-like structures.5 Highly ordered assemblies of these nanoparticles have been drawing attentions towards the optoelectronic device applications utilizing localized surface plasmon resonance (LSPR).6-9 Although the precise control of interparticle distance is crucial for the fabrication of LSPR materials, the fabrication of macroscopically uniform 2D sheets of Au or Ag nanoparticles remained challenging. Recently, Tamada and co-workers succeeded in the fabrication of 2D sheets of Ag10 and Au nanoparticles.11 Monodispersive metal nanoparticles capped by organic molecules form an ordered monolayer at the air/water interface, which can be transferred onto a transmission electron microscopy (TEM) grid by LangmuirSchaefer method. Such nanoparticle monolayers can be applied not only for understanding the fundamental principle of LSPR but also for various applications, such as high resolution imaging in the close proximity of the surface.12,13 Like other surfactant molecules, nanoparticles risiding at the air/water interface reduce the surface tension and makes the interface more elastic. Here, the mechanical properties of interface depends on the phase behavior and hence the lateral correlation between particles. The lateral correlation and phase behavior of nanoparticles at the interface are expected to be different from micrometer-scale particles. For example, nanoparticles have much larger surface area against their volume compared to micrometer-scale particles, where the surface chemical functions strongly modulate inter-particle interactions.6,14 In fact, previous studies have demonstrated that the capillary force and hence the wettability determines 2D ACS Paragon Plus Environment

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phase behaviors of particles and proteins.15-18 Consequently, the modulation of interparticle interactions by surface chemical functions results in the significant change in mechanical properties of 2D colloidal monolayers. However, to date, little has been understood how surface chemical functions and core metals modulate the lateral correlation and thus the mechanical properties of colloidal assemblies of metal nanoparticles at the interface. Recently, we studied the linear viscoelasticity of self-assembled domains of fluorinated surfactants by interface shear stress rheology19 and dilational rheology.20 The latter is especially useful in case the film has high viscoelasticity moduli near or beyond the instrumental limitation of shear stress rheology. In this study, we synthesized three metal nanoparticles capped with organic molecules, and found that these nanoparticles form highly elastic 2D gels at the air/water interface. Therefore, we investigated the viscoelastic properties of these nanoparticle monolayers by dilational rheology and calculated the lateral correlation between nanoparticles. MATERIALS AND METHODS Synthesis of Metal Nanoparticles As presented in Figure 1A, the following metal nanoparticles capped by organic molecules were synthesized in this study: Au nanoparticles capped with oleylamine (AuOA) and Ag nanoparticles capped with myristic acid (AgMy) were synthesized according to the procedure reported in our previous study.21,22 Au nanoparticles capped with fluorinated thiolate (AuF6) were synthesized by a two-phase Brust’s reduction method.23 [AuCl4]– ions in an aqueous solution (30 mM, 4.3 ml) were extracted into a toluene phase by tetraoctylammonium bromide (TOAB) (50 mM, 11.4 ml) as a stabilizer. A 20 mg of 11-(3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluoro-1-octyloxy)-


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1-undecanethiol (ProChimia, Gdansk, Poland) was then added into the organic phase together with a NaBH4 aqueous solution (0.4 mM, 3.6 ml). The mixture was stirred for 12 h at room temperature. The color of the solution turned to dark-brown when AuF6 particles were successfully produced. The obtained AuF6 were purified by ethanol several times and re-dispersed in toluene. Interfacial Dilational Rheology The interfacial dilational rheology of nanoparticle monolayers (Figure 1B) was measured at room temperature (T ≈ 293 K) using a KSV Nima film balance (Helsinki, Finland) with two movable barriers. A 600 µl portion of metal nanoparticles suspended in toluene (3.0 mg/ml) was deposited on the water subphase. After the evaporation of solvent, the film was compressed to π = 15 mN/m, and the sample was equilibrated by additional compressions until the drop of surface pressure becomes less than 1 mN in 10 min. The area per particle A was sinusoidally oscillated at a defined frequency (f = 50 – 125 mHz), = 1 + sin .

(1)

A0 is the initial area per particle, and u0 the strain amplitude, which coincides with the relative change in the area. As the lateral compressibility of the monolayer calculated from the pressure-area isotherm (Supporting Information Figure S1) is κ =

− < 58 m/mN, the amplitude of strain was kept at u0 = 0.01 unless stated

otherwise in order to minimize the risk to induce the collapse of films. = 2 stands for the frequency of oscillation. The stress response of the system π(t) of the linear viscoelastic body is given by: = + sin + , ACS Paragon Plus Environment

(2)

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where π0 is the initial surface pressure, π1 the stress amplitude, and the phase shift. The classical Euler’s equation for the viscoelastic body should read: ∗ = ′ + ′′ =

!"

cos +

!"

sin .

(3)

E* is the complex viscoelastic modulus, E’ the elastic modulus, and E” the viscous modulus.

Figure 1. (A) Chemical structures of ligand molecules on metal nanoparticles; oleylamine (OA) for 10 nm gold nanoparticles (AuOA), 11-(3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluoro1-octyloxy)-1-undecanethiol (F6) for 4 nm gold nanoparticles (AuF6), and myristic acid (My) for 5 nm silver nanoparticles (AgMy). (B) Schematic illustration of the dilational rheology measurements with sinusoidal oscillation of the barrier position after compressed film formation. Once the stock solutions were deposited on a water subphase, all the particles formed stable Langmuir monolayers at the air/water interface.

Surface Potential Measurements Surface potentials were recorded simultaneously with π-A isotherm using a Kibron µSpot mini trough (Espoo, Finland), equipped with a vibrating Kelvin probe Au


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electrode. The nanoparticle suspension was deposited in the close vicinity of the barriers to avoid ripening of the water subphase by solvent displacement. Transmission Electron Microscopy (TEM) The collective order of nanoparticles was evaluated by atomic resolution analytical transmission electron microscopy (TEM) images taken by JEOL JEM-ARM200F (Tokyo, Japan). The monolayers of metal nanoparticles were transferred onto a TEM grid (EM Japan, Tokyo, Japan) by Langmuir-Schaefer (LS) technique. The images of an AuOA, AuF6 and AgMy monolayers were captured with an accelerating voltage of 200 kV. Radial Distribution Function The radial distribution function %& was calculated from the TEM images of nanoparticle monolayers, %& =

)*

( +,*-*

(4)

where .& represents the number of pairs of two particles that has the distance between & and & + /& and 0 is the number density of particles. Here, not only the pair correlation with the nearest neighbors but also “all” the pair correlations are taken into consideration. In the following discussion, we used the dimensionless radial distribution function %1 by replacing the distance r by the dimensionless one normalized by the diameter of the metal core D, i.e. 1 = &⁄2. By assuming that the radial distribution function %1 follows Boltzmann distribution, the normalized potential of mean force 4 1 can be calculated from %1 as 4 1 ⁄56 7 = − ln%1 ACS Paragon Plus Environment

(5)

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where T is the absolute temperature and 56 the Boltzmann constant. The potential of mean force 4 1 in the vicinity of the first order minimum at 1 = 1 can be well approximated as a harmonic potential. Thus, the second derivative of the potential is the potential curvature V” representing the sharpness of the potential confinement: 4" =

-:

-; :

?

;@;"

.

(6)

RESULTS AND DISCUSSION Viscoelastic Response of AuOA Monolayer Figure 2A represents the typical stress and strain signals of an AuOA monolayer, measured at 100 mHz. The oscillatory change in the area per particle (red curve) is ∆A ≈ 2 Å2, corresponding to 1 % area change (u0 = 0.01). Throughout the experiments, we confirmed that the data subjected to the analysis exhibited no distinct drop of the surface pressure during 4 cycles. As the global shape of the response function suggests that the viscoelastic response of AuOA monolayer is strongly nonlinear, the data analysis followed the Fourier series expansion, = + ∑)=@ = sin5 + =

(7)

where = is the amplitude of mode k and = the corresponding phase shift. In the first step, we analyzed the amplitude of response function and phase information using only the first mode. As presented in Figure 2B, the phase difference between the strain and stress, = tan

EFF EF

, remained smaller than /2 under all

measurement conditions, indicating that AuOA monolayer is predominantly elastic. A monotonic increase in by the increase in frequency coincides with the increasing viscous contribution at high frequencies. Moreover, the fact that the phase difference


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did not converge to zero even at low frequencies suggests that there is an intrinsic onset phase shift originating from the experimental setup, H)IJK ≈ 0.4 at f ≈ 50 mHz. In our previous study on self-assembled domains of semifluroalkane monolayers, we reported the onset level of H)IJK ≈ 0.28 at f < 10 mHz.20 As far as the analysis is performed up to the first mode, it is possible to apply the classical Kelvin-Voigt model for predominantly elastic bodies (Figure 2C): L = %M + N

-

-K

M,

(8)

where L is the stress, % the spring constant, M the strain, and N the viscosity. Here, the complex dilational modulus E*1 can be represented as: ∗ =

OK PK

= % + N = F + ′′.

(9)

The elastic modulus E'1 (ω) and viscous modulus E''1 (ω) of AuOA monolayer are presented in Figure 2D. The symbols are the mean values and standard deviations out of more than 3 measurements, while the solid lines are the fitting results with the Kelvin-Voigt model, yielding the spring constant and viscosity, g = (81.6 ± 2.2) mN/m and N = (235 ± 27) µNs/m, respectively. The spring constant of AuOA monolayer is about 2 times smaller, and the viscosity was by 5 times larger compared to the corresponding values of self-assembled domains of partially fluorinated alkanes. Kawaguchi and co-workers performed dilational rheology measurements of polymer particles with sub-µm size and reported that the monolayer of latex particles prepared by disperse polymerization of styrene and diacetone polyacrylamide is predominantly viscous

while

those

of

polyvinylalcohol

and

polymethylmethacrylate

are

predominantly elastic.24 Safouane et al. have also demonstrated that the viscoelastic


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properties of fumed silica nanoparticles modified by organic silanes are strongly modulated by the surface hydrophobicity.14

Figure 2. (A) Surface pressure (black) and the corresponding area change (red) of AuOA monolayer at 100 mHz during the barrier oscillation. The strain amplitude was kept at u0 = 0.01 to avoid the collapse of the monolayer. (B) Phase shift between stress and strain plotted as a function of the frequency . (C) Schematics of the Kelvin-Voigt model. (D) Dilational elastic modulus E’ and viscous modulus E’’ of AuOA monolayer measured at = 50 – 125 mHz, at = 0.01. The error bars present the standard deviations out of more than three independent measurements. Solid lines coincide with the fitting results with Kelvin-Voigt model. The calculated spring constant and viscosity are g = (81.6 ± 2.2) mN/m and η = (235 ± 27) µNs/m respectively.

Nonlinear Viscoelasticity of AuOA Monolayer Figure 3 represents the surface pressure π of AuOA monolayers plotted as a function of time t (left) and area per particle A (right), measured at (A) 50 mHz, (B) 75 mHz, and (C) 100 mHz. As shown in the left panels, the global shape of response functions shows a clear deviation from the linear response function, such as flat portions in the left panels and kinks in the right panels (Lissajous plots). Note that the x-axis of Lissajous plot is area per molecule but not commonly used dilational strain.25 This clearly indicates that the viscoelasticity of AuOA monolayer distinctly contains nonlinear components. Therefore, we analyzed the nonlinear viscoelasticity of AuOA


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monolayers by fitting the measured data with the higher modes in the Fourier series expansion. The red lines in the figure coincide with the fitting results including up to the 5th mode, showing apparently good agreement with the experimental data. The “flat” parts in the Lissajous plots suggest either the buckling of interfaces or yielding of microstructures at the interface, but these scenarios can be excluded, as this features appear repeatedly over several cycles. Therefore, considering the large E’ and E” values, it might be possible that AuOA particles form interfacial mesophases. For example, oligofructose ester layers at the air/water interface under exhibited a qualitatively similar result but only under a high strain (30 %), which was attributed either to the soft glass phase of saccharide moieties or to the crystalline phase of fatty acid chains.26

Figure 3. Stress response function (surface pressure π) of AuOA monolayer plotted as functions of time t (left) and area per particle A (right). The fitting curves (red solid lines) include up to the 5th mode. The measurements were performed at = 50 mHz (A), 75 mHz (B), and 100 mHz (C) at strain amplitude = 0.01. Note that the x-axis of Lissajous plot is area per molecule but not dilational strain.

Figure 4A and Figure 4B represent the real and imaginary parts of the Fourier transformed response functions of AuOA monolayers measured at 100 mHz,


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respectively. The spectrum in the real part implies that the odd modes have a much larger proportion than the even modes. The amplitudes of the even modes are comparable to the instrumental limit. This suggests that the system is highly isotropic. In the imaginary part, the intensity of m = 3 was very prominent, suggesting that the contribution from the viscous component of the system is dominant. It should be noted that the nonlinear elastic response should be odd (m = 1, 3, ..) under reflection due to the mirror symmetry. Figure 4C shows R + of the fitting results plotted as a function of the highest mode included in the fit, confirming that the expansion up to m = 5 is sufficient. The significance of nonlinearity of the response function was further assessed by total harmonic distortion (THD): 7S2 =

T

+. U∑XW@+ VW

(10)

VW is the amplitude of the mth Fourier mode. The calculated THD of AuOA monolayer is THDAuOA = (16.2 ± 0.6) %, which is larger than the values we obtained from selfassembled domains of semifluroalkane monolayers (11 – 13 %).20 Following Ewoldt et al.,27 we also assessed the nonlinearity parameter S=

Z[ Z\ Z[

.

(11)

As indicated in the figure, GM is the tangent of the Lissajous plot at zero strain, while GL the secant modulus at the maximum strain. It is notable that the nonlinearity parameter obtained from the Lissajous plot at = 0.01 (Figure 4D) are S0.01 ≈ − 0.23, suggesting the symmetric shear softening during the compression and relaxation.


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Figure 4. Real part (A) and imaginary part (B) of the Fourier transformed response function of AuOA NP monolayer at = 100 mHz ( = 0.01). (C) The corresponding values of the fit quality R + plotted as a function of the number of Fourier modes included in the fitting. (D) Lissajous plots of AuOA monolayer measured at = 100 mHz.

To understand how a clear nonlinear viscoelastic rheology emerges, we also measured the response function at = 0.03 ( = 100 mHz). Figure 5A shows the stress response function of AuOA monolayer plotted as functions of time (left) and area per particle (right). As shown in the right panel of Figure 5A, the global shape of the curve becomes clearly asymmetric at = 0.03 compared to the one measured at = 0.01 (Figure 4D). The nonlinearity parameters obtained from Eq. 11, S0.03,comp = 0.07, clearly indicated that the system undergoes the "stress hardening" during the compression and a "stress softening (S0.03,relax = − 1.31)" during the relaxation.28 The asymmetric responses containing the shear hardening during compression and the shear softening during relaxation at u = 0.03 can also be seen from the emergence of even mode signals in the Fourier transformed response functions. Figures 5B and 5C show the real part and imaginary part of Fourier transformed response functions, respectively.


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Since the elastic part of the system is mostly represented by the linear part (m = 1, Figure 5B) and the imaginary part shows signals in the Fourier spectrum at m > 1, the response function can be well described with an extended nonlinear Kelvin-Voigt model, including the nonlinear terms only in the dissipative components: = %M + N + ^ F M_ + ^′′M_ + M_, where

-

-K

M ≡ M_.

(12)

Taking our oscillatory strain function, ϵ = , we obtain = %M + N M − + ^ F M + − b ^ F ′M b ,

(13)

which explains the appearance of the third mode in the imaginary part of the Fourier spectrum. Here, the motion of fluids due to the particle movement results in the dissipative term. Since this dissipation is different from the conventional Stokes drag and reflects the motion of many nanoparticles and fluid, the effective viscous dissipation increases when the change in the interfacial area and hence the strain amplitude becomes larger. The appearance of even mode peaks also clearly indicates that the deformation is no longer symmetric during compression and relaxation at = 0.03. This is in contrast to interface shear rheology experiments, where the shear deformation is perfectly symmetric. It should also be noted that the strain amplitude sweep over a wider range is practically difficult for our experimental systems. The experiments at small amplitudes (u0 < 0.01) are limited by the accuracy of oscillating barriers, while the measurements at u0 > 0.03 often cause the destabilization of the film.


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Figure 5. (A) Stress response function (surface area π) of AuOA monolayer plotted as functions of time t (left) and area per particle A (right) measured at = 100 mHz and = 0.03. Red line: the fit including up to the 5th mode. The real part (B) and the imaginary part (C) of the Fourier transformed response function of AuOA monolayer.

Lateral Correlation between AuOA Particles The dilational viscoelasticity of 2D particle assemblies depends on the significance and the range of particle-particle interactions, which is modulated by the interplay of van der Waals interactions, electrostatic interactions, hydration repulsion, and entropic contributions from organic molecules deposited on the particle surface.29 Since the experimental quantification of all individual contributors is practically impossible for nanoparticle systems, the potential of mean force that includes all pair correlations was introduced. In case of microparticles that are visible by optical microscopy, this can be assessed by analyzing the fluctuation of particle positions30 and radial distribution function.2,4,31 However, since our AuOA particles (DAuOA ≈ 10 nm) on the water surface cannot be visualized by optical microscopy, we transferred AuOA monolayer on a TEM grid by LS technique and visualized them by TEM (Figure 6A).13 Figure 6B shows the normalized radial distribution function calculated from Figure 6A, implying peaks at the position of R ≈ 1.4, 2.6, 3.9, 5.1, and 6.4, ACS Paragon Plus Environment

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suggesting that the particle-particle correlation can reach not only to the nearest neighbors but can act over the distance more than 6 times larger than the diameter of metal core, r > 64 nm. The normalized potential of mean force V1 ⁄5d 7 calculated from g(R) is shown in Figure 6C. As indicated by the red line, the potential in the vicinity of the first minimum can be well approximated as a quadratic function, " yielding the potential curvature of 4efge = 24.6 ± 1.9. As suggested by the g(R), the

potential minima can be identified up to the fifth order minimum, verifying the longrange correlation between AuOA particles.

Figure 6. (A) TEM image of AuOA monolayer. (B) Radial distribution function %1 calculated from panel A, plotted as a function of normalized distance, 1 = &⁄2 (2efge = 10 nm). (C) Normalized potential of mean force 41/56 7 of AuOA monolayer plotted as a function of R. The red curve in panel (C) indicates the fitting result around the first minimum by a harmonic approximation, yielding " the dimensionless potential curvature 4efge = 24.6 ± 1.9.

Influence of Surface Chemical Functions To modulate the strength of particle-particle interactions, Au nanoparticles capped with fluorinated thiolate (AuF6) were synthesized (Figure 1A). Figure 7A and Figure


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7B represent the surface potentials Ψ (red) and surface pressures π (blue) of AuOA and AuF6 monolayers plotted as a function of area per particle A, respectively. The onset of pressure increase for AuOA appears at a larger area per particle compared to AuF6, which can be attributed to a difference in the diameter of Au core; DAuOA ≈ 10 nm and DAuF6 ≈ 4 nm, respectively. The compression of AuOA monolayer to π = 15 mN/m leads to a slight increase in surface potential ∆ΨAuOA ≈ + 60 mV due to the condensation of CH3- chain termini. In contrast, the compression of AuF6 monolayer to π = 15 mN/m is accompanied by a prominent decrease ∆ΨAuF6 ≈ − 200 mV. This can be understood from the opposite dipole moment carried by CF3- chain termini, reported previously.32,33 Thus, the obtained results confirmed the successful capping of Au cores with fluorinated thiolate molecules. The TEM image of AuF6 monolayer (Figure 7C) suggests that the particle core is less contrasted due to the smaller core size (/efhi = 4 nm), and AuF6 particles is more heterogeneous in size compared to AuOA (Figure 6A). Intriguingly, the calculated potential (Figure 7D) seems much softer than that of AuOA. The first minimum is clearly identified at around R = 1.5 (r = 6 nm), but the second and higher order minima can hardly be determined. This finding suggests that the lateral correlation between AuF6 particles is rather limited within a short range. The harmonic approximation near the first minimum (red) yields the potential curvature " 4efhi = 2.2 ± 0.2, which is almost by an order of magnitude smaller than that of

AuOA, indicating the softening of particle-particle interactions in AuF6 monolayer.


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Figure 7. Surface pressure π (blue) and surface potential Ψ (red) of AuOA monolayer (A) and AuF6 monolayer (B), plotted as a function of area per particle A. The compression to π = 15 mN/m resulted in changes in surface potentials; ∆ΨAuOA ≈ + 60 mV and ∆ΨAuF6 ≈ − 200 mV, respectively. (C) TEM image of AuF6 monolayer, suggesting the size distribution of AuF6 is more heterogeneous than AuOA. (D) Normalized potential of mean force 41/56 7 of AuF6 monolayer plotted as a function of 1. " The harmonic approximation (red) yields the dimensionless potential curvature 4efhi = 2.2 ± 0.2.

In Fig 8A, the dilational elastic modulus E’ and viscous modulus E’’ of AuF6 monolayer are plotted as a function of frequency ( = 0.01). Compared to the corresponding data of AuOA monolayer (Figure 2D), the error of each data point from more than three independent measurements is much smaller. The fitting with the linear Kelvin-Voigt model (Figure 2C) yields the spring constant and viscosity, g = (97.1 ± 0.2) mN/m and η = (210 ± 1.9) µNs/m, respectively. The spring constant is about 20 % larger whereas the viscosity is slightly smaller compared to AuOA monolayer. This finding can be attributed to an increase in repulsive interactions caused by the stronger dipole contribution from CF3- termini. As shown in Figure 8B, the surface pressure π plotted as a function of time t (left) and area per particle A (right). The global shape of response functions of AuF6 looks very similar to that of AuOA, but the plateau parts in both curves are narrower than those of AuOA, ACS Paragon Plus Environment

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suggesting that the nonlinear viscoelasticity of AuF6 monolayer is less pronounced compared to AuOA. In fact, the nonlinearity parameter obtained from the Lissajous plot at = 0.01 is very small S0.01,AuF6 ≈ − 0.005, suggesting the symmetric shear softening during the compression and relaxation. As presented in Figure 8C, the intensity of the third mode peak in real part is comparable to the corresponding peak of AuOA monolayer, but the intensity of 3ω0 peak in imaginary part looks clearly weaker compared to that of AuOA monolayer (Figure 4B). This was also reflected to the global shape of Lissajous plot measured at = 0.03 (Figure 8D), showing a symmetric stress softening (S0.03,AuF6 ≈ − 0.57). Actually, the global shape Lissajous curve is clearly different from the one of AuOA monolayer measured at = 0.03 (Figure 5A), exhibiting a strain hardening during the compression and a strain softening during the relaxation.

Figure 8. (A) Dilational elastic modulus E’ and viscous modulus E’’ of AuF6 monolayer measured at = 50 – 125 mHz, at = 0.01. The standard deviations out of more than three independent measurements are smaller than the size of symbols. Solid lines coincide with the fitting results with Kelvin-Voigt model. The calculated spring constant and viscosity are g = (97.1 ± 0.2) mN/m and η = (210 ± 1.9) µNs/m, respectively. (B) Stress response (π) of AuF6 monolayer measured at = 0.01, = 100 mHz, plotted as functions of time t (left) and of area per particle A (right). The fit (red) includes the Fourier expansion up to m = 5. (C) Real part (left) and imaginary part (right) of the Fourier transformed response functions of AuF6 monolayer at = 100 mHz. (D) The Lissajous plots of AuF6 measured at = 0.03 and = 100 mHz.

Influence of Core Metal


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The influence of the core metal was further investigated by synthesizing Ag nanoparticles capped with myristic acid (AgMy, DAgMy ≈ 5 nm, Figure 1A). Figure 9A represents the TEM image of AgMy monolayer, and Figure 9B shows the normalized potential of mean force 4 1 /56 7 plotted as a function of 1. AgMy particles look more uniform than AuF6, and 41/56 7 exhibited its first minimum at R = 1.6 (r1 = 8 nm). The potential curvature obtained by a harmonic approximation near the first " minimum (red) is 4ejkl = 21.4 ± 0.7, which is slightly lower than that of AuOA. The

higher order peaks could be detected distinctly up to the fifth order, corresponding to the distance of r ≈ 37 nm. Fig 9C represents the dilational elastic modulus E’ and viscous modulus E’’ of AgMy monolayer as a function of frequency ( = 0.01). The spring constant and viscosity obtained from the Kelvin-Voigt model are g = (24.5 ± 3.5) mN/m and η = (237 ± 38) µNs/m, respectively. The viscosity is comparable to those of Au nanoparticles, since the dilational strain is applied to highly packed particle monolayers. On the other hand, the spring constant is by a factor of 4 smaller than AuOA and AuF6 monolayers, implying that the significantly weaker repulsive interaction between Ag nanoparticles compared to Au nanoparticles. What causes a significant change in particle-particle interactions between Au and Ag nanoparticles? The influence of electrostatic interaction (dipole moments) from the organic molecules does not seem to play major roles, because AuOA and AgMy are both terminated with hydrocarbon chains with CH3− termini. Another possible scenario is the penetration of strong electromagnetic fields through the organic capping layer. Using alkanethiols with different chain lengths, we previously reported that the local plasmon field near the surface of Ag nanoparticles can penetrate out to the solvent when the length of alkanethiol is shorter than 1-decanethiole.21 On the ACS Paragon Plus Environment

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other hand, the local plasmon field near the surface of Au nanoparticles is much weaker compared to Ag. Therefore, although the chain length of AgMy (C14) is longer than decanethiol (C10), the contribution from strong local surface plasmon near Ag surfaces cannot be excluded. Another major factors modulating particle-particle interactions is van der Waals (vdW) interaction, which includes the Hamaker constant of metal cores and the thickness of organic monolayers. As bulk materials, both Ag and Au possess large Hamaker constants in water, AAg = 30 × 10−20 J and AAu = 20 × 10−20 J, respectively. However, the contribution of vdW forces might be retarded for nanoparticles. When the separation distance x between two neighboring particles is much smaller than the particle radii (R1 and R2), the vdW force scales with mn-o = −

; ;:

.7,34 However,

+p : ; q;:

this assumption becomes invalid for AgMy, as the distance between the metal surface (x = 3 nm) is comparable to the particle radius of (R1 = R2 = 2.5 nm). Last but not least, Pinchuk et al. has shown that the Hamaker constant is significantly modulated by the size of nanoparticles, because the imaginary part of the dielectric permittivity distinctly increases with decreasing the particle size.35 A more recent study demonstrated that the stability of Au nanoparticles capped with organic monolayers can be predicted by taking the effect of nanoparticle size on the Hamaker constant as well as the tilt angle of hydrocarbon chains into consideration.36,37 Unfortunately, our current data do not enable us to nail down if the thickness of organic layers, the size-dependent Hamaker constant, or another unconsidered factor causes the difference between AuOA and AgMy due to the practical limitations for the synthesis of uniform nanoparticles. As presented in Figure 9C, the response function of AgMy monolayer is clearly nonlinear, and the nonlinearity coefficient calculated from the Lissajous plot analysis ACS Paragon Plus Environment

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(S0.01 = − 0.20) suggested the strain softening both under compression and relaxation. It should also be noted that AgMy monolayer exhibited a higher nonlinear total harmonic distortion, THDAgMy = (19.9 ± 0.6) % compared to AuOA monolayer. The data measured at a larger strain amplitude (u0 = 0.03) exhibited in a strain hardening during the compression (S0.03,comp = 0.08) and a strain softening during the relaxation (S0.03,relax < − 0.70). The fitting including the Fourier expansion up to m = 5 (Figure 9D, red) can represent the global shape of the stress response function. Like the other systems, a clear signal in the imaginary part at m = 3 was also observed in the Fourier transformed response function (Figure 9E).

Figure 9. (A) TEM image of a transferred AgMy monolayer. (B) The normalized potential of mean force 41/56 7 plotted as a function of 1 (/ejkl = 5 nm). The red curve indicates the fitting result of the quadratic function around first minima. (C) Dilational elastic modulus ′ and viscous modulus ′′ for AgMy monolayer measured at = 50 – 125 mHz, at = 0.01. The error bars present the standard deviations out of more than three independent measurements. The fitting results with Kelvin-Voigt model are shown with solid lines. The calculated spring constant g and viscosity η are (24.5 ± 3.5) mN/m and (237 ± 38) µN/m, respectively. (D) Stress response curves of AgMy monolayer plotted as functions of time (left) and area per particle (right). Real part (left) and imaginary part (right) of Fourier transformed response function of AgMy monolayer at = 100 mHz.

It is notable that the particle-particle interactions assessed from the TEM images of “transferred” monolayers should be handled with care, although the translational


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motion of particles is highly suppressed at high surface densities.38 On the other hand, it is not technically possible to precisely determine the “wetting property” of nanoparticles capped with organic molecules, as it is not possible to “visualize” the position of meniscus in the vicinity of nanoparticles. For this purpose, the determination of structure factor S(q) from grazing incidence X-ray scattering measurements at the air/water interface39,40 allows the quantitative assessment of the radial distribution function of nanoscopic colloidal assemblies confined at the air/water interface. CONCLUSIONS Although two-dimensional (2D) assemblies of metal nanoparticles have been drawing increasing attention for the optoelectronic device applications based on localized surface plasmon resonance (LSPR), little is understood how the interactions between nanoparticles modulate the viscoelasticity of 2D colloidal sheets when the particles are assembled at the air/water interface. In this study, we measured the viscoelastic properties of three types of nanoparticles by using a dilational rheometer; Au particle capped with oleylamine (AuOA, DAuOA ≈ 10 nm), Au particle capped with partially fluorinated alkanethiol (AuF6, DAuF6 ≈ 4 nm), and Ag particle capped with myristic acid (AgMy, DAgMy ≈ 5 nm). As the global shape of the stress response function under the sinusoidal oscillation of the area per particle (frequency f = 50 – 125 mHz, strain amplitude u0 = 0.01) suggests that the viscoelasticity of AuOA monolayer is clearly nonlinear, the response function was analyzed by Fourier series expansion. In the first step, we analyzed the amplitude of response function and phase information using only the first mode. This enables us to apply the classical Kelvin-Voigt model, yielding the spring constant g = (81.6 ± 2.2) mN/m and viscosity N = (235 ± 27) µNs/m. When the ACS Paragon Plus Environment

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response function of AuOA monolayer measured at u0 = 0.01 was fitted with the higher modes in the Fourier series expansion, we found that the imaginary part has a much larger proportion than the real part. The dominant contribution of the imaginary part implies that the nonlinearity mainly arises from the viscous and thus dissipative part of the system. Furthermore, the fact that the nonlinearity appeared only in odd modes suggests the mirror symmetry of the system. The significance of nonlinearity was assessed by total harmonic distortion, yielding THDAuOA = (16.2 ± 0.6) %. Intrestingly, the response function measured at a larger strain amplitude (u0 = 0.03) exhibited a clear asymmetry; stress hardening during compression and a stress softening during the relaxation. Such an asymmetry in response functions is accompanied by the emergence of even modes (m = 2, 4,..). The lateral correlation between AuOA nanoparticles was evaluated by calculating the radial distribution function and normalized potential of mean force V⁄5d 7 from the TEM image of AuOA monolayer transferred onto a TEM grid. The potential in the vicinity of the first minimum can be " well approximated as a harmonic potential, yielding the potential curvature of 4efge =

24.6 ± 1.9. Remarkably, the potential minima could be detected up to the fifth order minimum, corresponding to the distance of 64 nm. To highlight the influence of surface chemical functions on the particle-particle interactions, we synthesized AuF6 particles (DAuF6 ≈ 4 nm) and measured the dilational rheology. Prior to the rheology measurements, the surface potential measurement at the air/water interface confirmed the grafting of partially fluorinated thiolate molecules, whose dipole moments point the opposite direction from those of alkyl chains. We found that the lateral correlation between AuF6 particles is rather limited within a short range with a shallower potential confinement compared to " AuOA, 4efhi = 2.2 ± 0.2. The global shape of stress response functions of AuF6


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resembles to those of AuOA, but the nonlinear viscoelasticity of AuF6 monolayer is less pronounced. To further understand the influence of the core metal, we examined the lateral correlation and dilational rheology of AgMy nanoparticles (AgMy, DAgMy ≈ 5 " nm), where the potential of mean force analysis yields a potential curvature of 4ejkl

= 21.4 ± 0.7. Intriguingly, the lateral correlation between AgMy particles could reach the distance of 37 nm, which is distinctly shorter compared to AuOA. The spring constant obtained from the Kelvin-Voigt model, g = (24.5 ± 3.5) mN/m, is by a factor of 4 smaller than AuOA and AuF6 monolayers, suggesting that the correlation between Ag nanoparticles is distinctly weaker compared to Au nanoparticles. Further characterization of 2D colloidal sheets at the air/water interface, such as grazing incidence X-ray scattering study on a Langmuir film balance will enable to calculate the structure factor S(q) and hence the radial distribution function of 2D colloidal assemblies of nanoparticles at the air/water interface. The obtained results have demonstrated that the dilational rheology combined with the radial distribution function analysis enables one to quantitatively determine the influence of core metal and surface chemical functions on the lateral correlation and mechanical properties of 2D colloidal assembly of metal nanoparticles capped with organic molecules. This approach opens a new potential for the fine adjustment of the strength of interactions between metal nanoparticles towards the rational design of localized surface plasmonic materials.


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ACKNOWLEDGEMENT M.T. thanks W. Abuillan for helpful discussions, and thanks the INTERREG V Upper Rhine Program (NANOTRANSMED), the German Science Foundation (DFG Ta253/12), and Nakatani Foundation for supports. S.M. (Masuda) is thankful to Advanced Graduate Course on Molecular Systems for Devices (Leading Graduate Schools) and S.M. (Mielke) to Konrad Adenauer Foundation for the fellowships.

Supporting Information. Pressure-area isotherms of nanoparticle monolayers are presented in Figure S1.


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Highly Uniform, Mesoscopic, Self-Assembled Domains of Fluorocarbon-Hydrocarbon Diblocks at the Air/Water Interface: A GISAXS Study. ChemPhysChem 2017, 18, 2791−2798. (40) Abuillan, W.; Vorobiev, A.; Hartel, A.; Jones, N. G.; Engstler, M.; Tanaka, M. Quantitative determination of the lateral density and intermolecular correlation between proteins anchored on the membrane surfaces using grazing incidence small-angle X-ray scattering and grazing incidence X-ray fluorescence. J. Chem. Phys. 2012, 137, 204907.


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TOC GRAPHIC


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TOC Graphic 82x44mm (254 x 254 DPI)


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Figure 1 129x149mm (150 x 150 DPI)


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Figure 2 125x102mm (150 x 150 DPI)


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Figure 3 125x121mm (150 x 150 DPI)


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Figure 4 132x111mm (150 x 150 DPI)


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Figure 5 123x103mm (150 x 150 DPI)


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Figure 6 121x103mm (150 x 150 DPI)


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Figure 7 124x110mm (150 x 150 DPI)


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Figure 8 (double column) 256x89mm (150 x 150 DPI)


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Figure 9 (double column) 254x113mm (150 x 150 DPI)


Nonlinear Viscoelasticity of Highly Ordered, Two-Dimensional

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