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Transition in Dynamics as Nanoparticles Jam at the Liquid/Liquid Interface Mengmeng Cui, Caroline Miesch, Irem Kosif, Huarong Nie, Paul Kim, Hyunki Kim, Todd Emrick, and Thomas P. Russell Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b03159 • Publication Date (Web): 19 Oct 2017 Downloaded from http://pubs.acs.org on October 19, 2017

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Transition in Dynamics as Nanoparticles Jam at the Liquid/Liquid Interface Mengmeng Cui, † Caroline Miesch, † Irem Kosif,† Huarong Nie,‡ Paul Y. Kim,† Hyunki Kim,† Todd Emrick,† and Thomas P. Russell*†§& †

Polymer Science and Engineering Department, University of Massachusetts Amherst, 120 Governors Drive, Amherst, MA, 01003

‡

Key Laboratory of Rubber-Plastics, College of Polymer Science and Engineering, Qingdao University of Science and Technology, Qingdao 266042, PR China §

Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cylcotron Road, Berkeley, CA 94720 &

Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical Technology, Beijing 100029, China Corresponding author: [email protected]

Keywords: dynamics, interfacial jamming, X-ray photon correlation spectroscopy, nanoparticle

ACS Paragon Plus Environment

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Abstract

Nanoparticles (NPs) segregated to the fluid/liquid interface form disordered or liquid-like assemblies that show diffusive motions in the plane of the interface. As the areal density of NPs at the interface increases, the available interfacial area decreases and the interfacial dynamics of the NP assemblies change when the NPs jam.

Dynamics associated with jamming was

investigated by x-ray photon correlation spectroscopy (XPCS). Water-in-toluene emulsions, formed by a self-emulsification at the liquid-liquid interface and stabilized by ligand-capped CdSe-ZnS NPs, provided a simple, yet powerful platform, to investigate NP dynamics.

In

contrast to a single planar interface, these emulsions increased the number of NPs in the incident beam and decreased the absorption of x-rays in comparison to the same path length in pure water. A transition from diffusive to confined dynamics was manifest by intermittent dynamics, indicating a transition from a liquid-like to a jammed state.


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Introduction Understanding the nature of the glass transition and jamming behavior are long-standing challenges in materials science. Jamming occurs for a wide range of systems and on many different length scales, from traffic jams experienced in daily life to the jamming of granular matter in sand piles or powder flows to colloidal and nanoscale particles.1-11 Jamming, as initially described by Liu and Nagel,1 reflects a transition from a liquid- to solid-like state as the packing density increases above a critical value and establishes a common framework connecting these disparate systems. At the jamming transition, percolated pathways of particles in close contact can bear load and prevent further reduction in volume. Aside from crystallization and vitrification, jamming provides a pathway by which liquids rigidify. Jamming can occur in the bulk (3D) or at interfaces (2D). The interfacial jamming of particles at a liquid/liquid interface begins with Pickering emulsions, where partially wettable solid particles self-assemble at the interface between two immiscible liquids to minimize the free energy of the system.12-13 In NP-stabilized emulsions the interactions between the NPs and the two liquids are energetically more favorable than the interactions between the two liquids. The energetic gain for placing the particles at the fluid-fluid interface scales with the square of the particle radius and, as such, as the particles become nanoscopic in size, the energetic gain is small, on the order of several kT. By using functionalized NPs in one fluid with complementary end-functionalized polymers in the second fluid, the NPs and polymers interact at the interface to form NP surfactants, leading to a significant increase in the energy holding each NP at the interface. In the plane of the interface, nanoparticle packing is disordered and liquid-like. By decreasing the interfacial area, the lateral packing of the NPs at the interface, i.e. the areal


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density, increases and, as with bulk systems, the particles can jam, preventing further reduction in the interfacial area, locking-in the shape of the liquid phases. NP jamming opens the possibility to manipulate liquids into highly non-equilibrium shapes, i.e. structuring the liquids or even producing bicontinuous liquidic structures. The jamming of particles at the interface indefinitely locks the shape of one liquid within the other.14-22 Clegg and Cates, used this concept with liquids undergoing spinodal phase separation where, in the presence of colloidal particles, segregation of particles to the interface locked-in a bicontinuous morphology to generate a “bijel”,14-15 or bicontinuous interfacially jammed emulsion gel. Mahadevan and Stone produced oblate ellipsoidal liquid domains by compressing a fluid droplet between two planar surfaces, using the interfacial jamming of colloidal particles to preserve the non-equilibrium shape.17 Recently, we introduced a simple route to manipulate the mesoscale structuring of liquids using an electric field to control the shape of one fluid domain in a second fluid, where the electric field acted on the dielectric constant difference between the two fluids.23, 24

The interfacial jamming of nanoparticles solidified the interface, enabling the generation of

stable bi-phasic systems.

The jamming of these interfacial assemblies was broken by the

application of an external field, which re-established fluidity to the system, and allowed a further reshaping of the liquid domains. Consequently, these nanoparticle-based fluid-fluid interfacial assemblies are both responsive and adaptive. There has also been significant interest in the dynamics of the jamming transition. The dynamics, internal structure, and mechanical properties are inter-related and, as such, understanding dynamics will deepen our insight into the jamming behavior and lead to utilization of jammed structures in materials applications. Studies about the jamming transition are focused on not only the simulated systems25 but also experiments across a wide range of systems, such as


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granular materials26, emulsions27, foams28,29, colloidal gels30 and 2D NP gels31-34. Most of these systems, if not all, exhibit the characteristic slowing-down of the dynamics, as well as dynamical heterogeneities as the jamming transition is approached. Among many studies on the dynamics, only a few have been extended to the 2D air/liquid interface successfully using XPCS31-33 and even less to the 2D liquid/liquid interface,34 where controlling the lateral packing of the nanoparticles and bringing the assemblies from a liquid state into a jammed or vitrified state is challenging. Therefore, the dynamics of interfacial jamming at liquid/liquid interface is not fully understood. Here, we studied the dynamic transition of nanoparticles at the liquid/liquid interface as the packing fraction increased and approached the jamming transition. The nanoparticles consist of an ~8 nm, hard-inorganic core and an organic soft shell, ~1 nm in thickness, which make the system different from previous systems investigated.

Results and Discussions We investigated NP dynamics during the jamming transition at a water/oil interface using Xray photon correlation spectroscopy (XPCS). CdSe-ZnS NPs capped with trioctylphosphine oxide (TOPO) ligands self-assembled at a water/toluene interface for the XPCS measurements.3536

The NPs jammed at the interface by their continuous adsorption and reduction of the

interfacial area, driving the system to a lower interfacial energy state.


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Scheme 1. Illustration of small-angle x-ray photon correlation spectroscopy measurements on NP-stabilized emulsions. A schematic of the experiment is shown in Scheme 1. Coherent X-rays impinge on an emulsion formed at the interface between two bulk liquid phases, i.e. water and toluene. CdSeZnS NPs dispersed initially in toluene segregate to the interface between water and toluene. Since the electron density difference between the NPs and liquids is much larger than that between water and toluene, scattering from the NPs dominates the scattering intensity. The contribution of the scattering arising from NPs dispersed in the toluene phase, relative to the total scattering is small, since the concentration of the dispersed NPs is small. Consequently, the observed scattering arises from interferences characteristic of the NP center-to-center distances at the interface and from the emulsion droplets coated with a layer of NPs. Since the NP assembly at the interface is liquid-like, only a diffuse scattering peak is observed with a maximum characteristic of the average NP center-to-center distance.37 At any instant of time, the scattering profile consists of a collection of points of scattering or speckles, where each speckle


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corresponds to two NPs of a given size, separation distance and orientation, corresponding to the to the qx and qy where the scattering is observed. Here, q = (2π/λ)sin(ε/2), where ε is the scattering angle, λ is the wavelength of the x-rays, and the subscripts

x and y indicate

orthogonal directions in the scattering plane. As the NPs diffuse in the interfacial plane, the positions of the speckles change with time from which an autocorrelation function in time can be calculated that has characteristic decay times corresponding to the NP motion. To increase the number of scatterers intercepted by the incident X-ray beam, we took advantage of a selfemulsification that occurred at the water-toluene interface. Experimentally, a layer of toluene was placed on top of a layer of water in a thin-walled capillary tube. The toluene phase contains the ligand-stabilized CdSe-ZnS NPs and the salt. The presence of the salt drives a spontaneous emulsification at the interface, where aqueous droplets form at the interface that are covered with NPs. The droplets initially coarsened, then remained stable for extended periods of time, and were concentrated at the toluene-water interface. By translating the capillary vertically in the incident x-ray beam, an abrupt change in the scattering intensity marked the interface due to a reduction in the x-ray absorption (changing from water to toluene) and the presence of the emulsion droplets. The emulsions formed a ~ 300-mm thick “froth-like” layer at the interface allowing the 20 µm x 20 µm beam to be positioned near the interface (Fig. S1). By increasing the NP concentration, the NPs could be jammed at the interface.


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Figure 1. (A)-(C) Optical micrographs of emulsions at the water/toluene interface. (A) two water droplets immersed in 30 mg/ml nanoparticle solution for 30 mins and 10 s; (B) pendant drop of water in a toluene dispersion of NPs; (C) higher-magnification image pendant drop showing heterogeneous distribution of dark regions at interface; (D) optical micrograph of the emulsions at the water/oil interface; (E) solid-like, wrinkled nanoparticle thin film formed at the water/toluene interface after washing with toluene; (F) TEM micrograph of CdSe-ZnS nanoparticles dried on a copper grid with carbon film. The self-emulsification experiments were inspired by an observation that a water droplet changes from transparent (droplet indicated after 10 s) to cloudy after immersion in a TOPOfunctionalized CdSe-ZnS solution (droplet indicated after 30 mins) (Fig. 1A). A pendant drop appears dark after 30 mins (Fig. 1B) and high-magnification images (Fig. 1C) show many dark regions at the interface which, by optical microscopy on a water/oil system (Fig. 1D), arose from small droplets formed at the interface. After washing the water droplet with toluene, the small secondary droplets were removed and a solid-like, wrinkled film (Fig. 1E) was left behind. This


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thin film consisted of NPs that assembled at the water/oil interface achieving a jammed state after 30 mins. The wrinkling of the jammed NP assembly was induced by the reduction

Figure 2. Time dependence of the interfacial tension at the toluene/water interface for different CdSe-ZnS NP concentrations (expressed as mg/ml). in the droplet surface area when water evaporated. A TEM image (Fig. 1F) of CdSe NPs shows that the size is ~8 nm. The evolution of the droplets is shown in Figure S2. Fig. S3 shows optical images of the system with salts in both the water and oil phases. In the Fig. S3, the osmotic pressure difference between the water in the salt aggregates and in the continuous aqueous phase causes the emulsification. By adding salt to the continuous aqueous phases, the osmotic pressure difference can be decreased and the self- emulsification process arrested.


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The areal density of NPs at the toluene/water interface is reflected in dynamic interfacial tension measurements. As shown in Fig. 2, a rapid decrease in interfacial tension was observed initially, followed by a gradual leveling off. This indicates a two-stage interfacial adsorption of NPs to the interface, which agrees well with previous work,38 where NP adsorption leads to a potential barrier, ∆Ep, that slows further adsorption. There are several different contributions to ∆Ep. The first is physical, meaning that there is less surface area available for adsorption and NPs already adsorbed to the interface must undergo in-plane diffusion to accommodate additional NPs. A second contribution is NP desorption from the interface due to thermal fluctuations, since desorption hinders NP diffusion from the bulk to the interface.

A third factor is inter-NP

repulsion, since CdSe-ZnS NPs are known to possess a surface charge even when functionalized with ligands.39, 40 The equilibrium interfacial tension, as approximated by the dashed line in Fig 2, decreased from 24 to 13 mN/m with increasing NP concentration, indicating the impact of NP coverage at the interface. Fig 3 shows the small angle X-ray scattering profiles of the emulsions as a function of q, arising from the incoherent addition of the scattering from the emulsion droplets and from the NPs at the droplet interface. The observed scattering is given by:

At very small q (~ 10-3 nm-1), the scattering intensity is dominated by diameters of the droplets and their separation, both being micrometers in size. For q > 2π/R, where R is the droplet radius, the scattering intensity from droplets decays according to Porod’s law, i.e., I(q)~q-4, for infinitely sharp interfaces; the intensity decays more rapidly if the interface is rough or diffuse. At higher q, interferences arising from spatial correlations of the NPs assembled at the fluid-fluid interface dominate the scattering. If the NPs form a percolated cluster on the


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Figure 3. Small angle X-ray scattering profiles of polydisperse NP-stabilized emulsions at different NP concentrations (from 0.5 to 30 mg/ml). droplet surface, a power law exponent of 2.5 would be expected. 41 For the range of q examined, as shown in Fig. 3, the scattering profiles follow a power law decay of the form I (q) ~q-x, where x ranges from 2.57 to 3.32. A similar power law decay has been reported by Schmitt, et al. for micrometer-sized crosslinked gels comprised of nanoscopic particles.42 XPCS experiments afford the intensity autocorrelation function g2 (q, t): 37


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Here, I (q, t) is the intensity measured at time t and wave vector q. If the system does not have time-related density fluctuations, i.e., where I (q, t) = I (q, t+∆t), then g2 (q, t) =1. If the system is diffusive (Brownian motion), then g2 (q, t) will be:

Here, D (q) is the diffusion coefficient. The microscopic dynamics of a system near the jamming transition often follows the Kohlrausch-Williams-Watts (KWW) relaxation function,4346

where b is a correction factor that depends on the experimental setup and β is a stretching exponent that characterizes the curve shape. In comparison with a simple exponential decay (i.e. β=1), the curve shape is stretched for β1. τ is a structural relaxation time that depends on D and q:

The exponent γ indicates the type of motions, such as Brownian motion (γ~2) or hyper (or ballistic) diffusion (γ~1). The dynamic transition is derived from g2 (q, t). Fig. 4 shows g2 (q, t) at q = 0.022 nm-1 for different concentrations. Due to the similarities between jamming and glass transitions, the classic Mode Coupling theory has been widely used to analyze g2 (q, t) at the jamming transition.47-51 The characteristic decay pattern with a two-step relaxation separated by a plateau is expected from Mode Coupling theory.49 Due to the limitation of the detector frame rate and scattering intensity, the first decay was not observed. The red solid lines in Fig. 4 are the fits based on the KWW expression, while the blue lines fit to the data using the corresponding


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expression for Brownian motion. Through line fitting with the KWW expression, β and τ were calculated for

Figure 4. The corresponding intensity autocorrelation function g2(q, t) at wave vector q=0.022 nm-1 for varied concentrations.

each concentration. From the value of the plateau, the dynamics of the first decay was assessed. For concentrations higher than 5 mg/mL, both the plateau and the second decay were observed, while the plateau was not measurable for concentrations lower than 5 mg/ml. Characteristic relaxation times as a function of concentration at a wave vector 0.022 nm-1 are shown in Fig. 5A. τ increases by two-orders of magnitude, from 0.2 to 12 s, with increasing concentration. The dynamic structure factor f (q, t) can be calculated from the intensity autocorrelation function g2 (t) using the Siegert relation:


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In the above equations, fq is the short-time plateau amplitude and b0 is the Siegert factor defined by the experimental geometry (b0~0.30). Ideally, the amplitude fq = 1 as t approaches 0. The value of fq is smaller than 1 in Fig. 5B, indicating a partial relaxation at very short times

Figure 5. (A) Concentration dependence of the relaxation time at wave vector q=0.022 nm-1. (B) Concentration dependence of the short-time plateau amplitude of 0.01 s at wave vector q=0.022 nm-1.

(not accessible in these studies), followed by a second observable relaxation. Similar behavior has been observed in other disordered systems, such as emulsions and colloidal suspensions.37-41 The relaxation results from the formation of cages for each particle by its neighbors. The first step of the relaxation corresponds to a fast local motion of particles inside the restricted cages, while the second step of the relaxation corresponds to particle escape from the cages with cooperative motion from its neighbors. Due to the limitations in the frame rate of the CCD camera, the first-step of the relaxation was not observed. The short-time plateau arose from the relaxation of cages. The relaxation observed arises from particles trying to escape the cages formed by the NP assemblies. The dependence of fq on q implies local motions within cages at larger wave vectors, corresponding to smaller length scales.


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The dependence of fq on concentration was only observed for concentrations greater than 5 mg/ml. For lower NP concentrations, the plateau appeared at times scales less than observable experimentally. Comparing f(q) at 5 and 30 mg/ml, one can see that fq decreases with concentration, indicating that more free collisions occured at lower concentrations.

Figure 6. (A) Wave vector q dependence of exponent β at different concentrations. (B) Logarithmic presentation of characteristic relaxation time as a function of a wave vector q for concentrations ranging from 0.5 to 30 mg/ml.

The variation in β suggests a change in the shape of the autocorrelation function. As shown in Fig. 6, at lower NP concentrations (0.5, 1 and 2mg/ml), the faster relaxation can be explained by a stretched exponent, where β is ~ 0.7. In most cases, β is ~1 for Brownian dynamics. Here, fitting to the incomplete autocorrelation function gives rise to β < 1. Since no cages are formed at low concentrations (1) deviates from Gaussian (i.e. β=1). However, this model does not predict the q-dependence of β observed in our experiment. An extended model developed by Duri and Cipelletti hypothesized that the correlation of the scattered intensity is driven by rare intermittent rearrangements.53 As shown in Scheme 2,


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interacting NPs form the backbone of a network. The intermittent motion happens when the NP positions rearrange due to the occasional rupturing of bonds in the network.

During the

intermittent motion, there is a sudden change in the NP correlations. In this model, β changes as q increases from 1.5 to 1, in agreement with the observations in our study. When assembled on a droplet, NP motion may arise from either diffusion at the fluid-fluid interface or from the motion of the droplets themselves. Since gravity concentrates the droplets at the oil/water interface, droplet motion is suppressed. Over the range of scattering vectors investigated, scattering from the droplets will be negligible. So, with the observed concentration dependence of the dynamics, NP motions observed must be dominated by diffusion at the droplet interface. Our finding of a dynamic transition from Brownian to intermittent motion shares similarities with previous investigations on the dynamics of liquid-solid transitions in different jamming systems, such as emulsions27, foams28,29, colloidal gels30, and 2D NP gels32. The dynamics for each of these systems is intermittent. Studies on emulsions and foams show that the intermittent dynamics is induced by coarsening of the system due to Ostwald ripening or applied stress. Our system differs from these, since an osmotic pressure was used to generate the emulsion droplets, the effect of Ostwald ripening was offset by the osmotic pressure, and no stress was applied. As the thickness of NP soft shell is much smaller than the one of hard core, the NPs behave more like a hard sphere here. But it points out a very interesting direction to study the jamming of soft particles at the liquid/liquid interface by using NPs with long ligands (such as the high Mw polymer chain), which will make the particles behave as the soft sphere.

Conclusions


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We overcame the difficulties of traditional methods on dynamic study of the liquid/liquid interface by implementing XPCS in a self-emulsification system. We investigated the trasnsition in dynamics during NP jamming, in which NPs self-assemble at the liquid/liquid interface and reach the jammed state when the NP concentration increases to a critical value. Selfemulsification compensates for scattering intensity losses due to X-ray adsorption in the liquid and eliminates the effects of emulsion droplet growth on dynamics. Interferences arising from spatial correlations of the NPs assembled at the fluid-fluid interface dominated the scattering. We successfully characterized a transition from diffusive to confined dynamics, intermittent dynamics, indicating a transition from a liquid-like state to a jammed state. Spatially heterogeneous and temporally intermittent dynamics were observed when the system becomes confined. The confined dynamics show scaling exponents that fit well with the mode-coupling approximation which normally is used to describe the glass transition. This suggests that jamming is a universal phenomenon related to glassy behavior, even though the control variables are different. Experimental Section Optical microscopy: The images of self-formed emulsions near the liquid/liquid interface were taken using a Zeiss Axiovert 200 inverted optical microscope with 10x objectives. Transmission electron microscopy: The morphology of NPs was studied with highresolution transmission electron microscopy (JEM-2000FX, JEOL, Japan). Dynamic interfacial tension by tensiometer: The tensiometer (Dataphysics, OCA15 plus) was used to measure the influence on the oil/water interfacial tension of CdSe-ZnS NPs. The interfacial tension was obtained by fitting the shape of a pendant droplet to the Young-Laplace equation.


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X-ray Photon Correlation Spectroscopy: The samples were prepared by placing water into a capillary tube with a 1-mm diameter, and then adding CdSe-ZnS NP solutions in toluene. Because of salt aggregates inside the NP solution in toluene, osmotic pressure drives formation of emulsions. The samples were aged for 10 hours to reach an equilibrium state. Experiments were conducted at sector 8-ID at the Advanced Photon Source at the Argonne National Laboratory. The X-rays, with an energy of 7.35 keV, were incident on the water/oil interface of the sealed capillary tube. The temperature was always kept at 20 °C during the experiment. The scattering vector range from 0.02 nm-1~0.1 nm-1 corresponds to size scale from 60 nm to 300nm. The quantity characterizing the dynamics is obtained by averaging the measured intensity autocorrelation function over a duration that is usually much longer than the relaxation time of system. A multi-element detector was used, so the intensity was averaged over both time and different speckles from different detector elements. The typical exposure time of scattering images is 0.5 s and the duration time is about 20 min. Nanoparticle synthesis: please find it in the supporting information.

ASSOCIATED CONTENT Corresponding Author *To whom correspondence should be addressed: [email protected] Notes The authors declare no competing financial interest. Supporting Information Available


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Supporting information includes x-ray scattering intensity across the interface, optical micrographs of the evolution of the emulsion at the interface, optical micrographs of the systems with salts in both water and oil phase, the corresponding intensity autocorrelation function g2 (q, t) at different wave vectors and the method of nanoparticle synthesis. Acknowledgements This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC0205-CH11231 within the Adaptive Interfacial Assemblies Towards Structuring Liquids program (KCTR16). MC was initially supported by U.S. Department of Energy Office of Basic Energy Science through contract DE-FG02-04ER46126. The synthesis of the NPs was performed by CM, IB, HK and TE who were supported under NSF-CHE-1506839. PK and HN characterized the NPs used in these studies. The XPCS experiments were carried out at beamline 8-ID-I of Advanced Photon Source, Argonne National Lab. We thank Dr. Suresh Narayanan and Dr. Alec Sandy for assistance with the XPCS experiments. References 1. Liu, A. J.; Nagel, S. R.; Nature, 1998, 396, 21. 2. Bi, D.; Zhang, J.; Chakraborty, B.; Behringer, R.P.; Nature, 2001, 480 (7377), 355–358. 3. Clusel, M.; Corwin, E. I.; Siemens, A.O.N.; Brujić, J.; Nature, 2009, 460 (July), 611–615. 4. Pusey, P.N.; Megen, W. van; Nature, 1986, 320 (6060), 340–342. 5. Torquato S., Stillinger, F.H.; Rev. Mod. Phys., 2010, 82 (3), 2633–2672.


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Table of Contents Figure


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