Intrinsic Size Effect in Scaffolded Porous Calcium Silicate Particles

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Intrinsic size-effect in scaffolded porous calcium silicate particles and mechanical behavior of their self-assembled ensembles Sung Hoon Hwang, and Rouzbeh Shahsavari ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b15803 • Publication Date (Web): 14 Dec 2017 Downloaded from http://pubs.acs.org on December 15, 2017

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ACS Applied Materials & Interfaces

Intrinsic size-effect in scaffolded porous calcium silicate particles and mechanical behavior of their self-assembled ensembles Sung Hoon Hwang1, Rouzbeh Shahsavari1,2,3,* 1

Department of Material Science and Nano Engineering, Rice University, Houston, TX 77005

2

Department of Civil and Environmental Engineering, Rice University, Houston, TX 77005

3

The Smalley-Curl Institute, Rice University, Rice University, Houston, TX 77005

*Corresponding author email: [email protected] Abstract Scaffolded porous submicron particles with well-defined diameter, shape and pore size have profound impacts in drug delivery, bone-tissue replacement, catalysis, sensors, photonic crystals and self-healing materials. However, understanding the interplay between pore size, particle size, and mechanical properties of such ultrafine particles, specially at the level of individual particles and their ensemble states, is a challenge. Herein, we focus on porous calcium-silicate submicron particles with various diameters - as a model system - and perform an extensive 900+ nanoindentations to completely map out their mechanical properties at three distinct structural forms from individual submicron particles to self-assembled ensembles to pressure-induced assembled arrays. Our results demonstrate a notable “intrinsic size-effect” for individual porous submicron particles around ~200-500 nm, induced by the ratio of particle characteristic diameter to pore characteristic size distribution. Increasing this ratio results in a brittle-to-ductile transition where the toughness of the submicron particles increase by 120%. This size-effect becomes negligible as the porous particles form superstructures. Nevertheless, the self-assembled arrays collectively exhibit increasing elastic modulus as a function applied forces while pressureinduced compacted arrays exhibits no size-effect. This study will impact tuning properties of individual scaffolded porous particles, and can have implications on self-assembled superstructures exploiting porosity and particle size to impart new functionalities.

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Introduction The recent advance in nanofabrication and characterization techniques has enabled the synthesis and characterization of scaffolded nano- or sub-micron structures via numerous pathways.1-6 Among those distinct types of structures, porous particles with a uniform distribution of size, morphology and pore size offer a myriad of benefits compared to their non-porous counterparts in diverse industries. The most striking feature is the proven ability to encapsulate and release chemical species in a controlled manner and this has significantly enhanced the breadth of industrial applications of nano- or submicron particles with a narrow size distribution.7-10 For example, mesoporous particles offer additional advantages when used as building blocks of colloidal crystals, since the controlled trapping of external species enables the fine-tuning of refractive indexes over a wider range.11-12 This can further extend the applications of colloidal crystals from simple optics to gas sensors and lasers.13-14 In addition, porous silica particles can be readily functionalized with smart moieties and serve as stimuli-responsive nanocontainers for self-healing agents and corrosion inhibitors.15 Overall, over the last decades, research has confirmed the promising potential of porous particles for diverse industrial applications encompassing catalysis, chromatography and inorganic fillers.16-18 Mechanical properties is one of the critical yet often overlooked traits of the aforementioned porous particles, which is needed for the successful performance of their functions in industry. Whether the particles are employed as basic building blocks of colloidal crystals or as smart reinforcements encapsulating self-healing agents, they must be sufficiently strong and resilient to withstand constant mechanical stresses imposed on them. Mechanical rigidity is a critical feature even when it comes to therapeutic-delivery since high rigidity favors the cellular uptake of drug carriers.19 Consequently, in order to further boost the current scope of applications of porous particles, fine-tuning of their mechanical properties is one of the key strategies. In order to acquire the aforesaid control over the mechanics of individual particles, not only those with porous characteristics but of any type with nano- or submicron size, the accurate evaluation of standard parameters such as hardness and elastic modulus constitutes an imperative step. However, the process is challenging, since the experimental techniques to probe the mechanical behavior of single, individual particles are not as well-established when compared to bulk materials. Nevertheless, numerous studies have performed direct indentations on a single


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particle using a flat-punch indenter and calculated elastic modulus from the compression forcedisplacement data. He et al. directly compressed and obtained the rupture forces for acrylic copolymer and polystyrene particles with the diameter ranging from 2.6 to 5.1 um, two types of polymer particles applied in anisotropic conductive adhesives.20 Zhang et al. used atomic force microscopy (AFM) force-distance spectroscopy to investigate the effects of reaction parameters such as annealing temperature on the final mechanics of the resultant, individual silica microcapsules.21 Paul et al. also compressed a submicron sized spherical silica using a scanning electron microscopy (SEM) supported manipulation device and calculated its elastic modulus as 30.8±4 GPa.22 Despite the myriad of studies on compression of single particles, the types of particles used for such studies have largely been restricted to polymer, silica or metallic particles and the direct compression of single porous particle has not been witnessed. The study on mechanical properties of porous structures has been mostly focused on a larger, continuous network rather than discrete, individual particles.23-24 This scarcity of studies is likely due to the intuition that a porous particle alone does not possess sufficient mechanical strength to withstand the compressive force. Therefore, we hereby study the mechanical properties of calcium-silicate porous particles with the size ranging between 150-550 nm, recently synthesized in our group as universal building blocks for biomimetic self-healing applications.25 The particles exhibit narrow distributions in size (low standard deviation), morphology (spherical) and pore size (2-4 nm). In this study, we probe mechanical properties of those particles existing in three distinct structural forms: an isolated single particle, self-assembled arrays and a pressure-induced assembled sample. In the self-assembled arrays, the particles are closely packed and interact with each other weakly via capillary and Van der Waals forces. In a pressure-induced assembled sample, the particles are highly densified and interact with each other mainly via contact forces. By monitoring how the strength, stiffness and strain develop from the state of a single particle to different types of assembled states, the complete evaluation of mechanical properties of calcium silicate porous particles is provided for the first time. This work will open the door towards new opportunities for engineering mechanical properties of porous particles via fine-tuning of their porosities. Furthermore, calcium-silicate based materials are currently at the center of ongoing research interests for diverse industrial applications.26-35 Therefore, the mechanical evaluation presented in this report will provide a new insight into strength, toughness and stiffness


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development that occurs during the bottom-up fabrication of calcium-silicate based materials for bone-tissue replacement, drug delivery, self-healing, and refractory and cementitious materials.

Experimental section Structural and mechanical characterization The particles to be tested for micro-mechanical properties were synthesized based on our recent work.25 Altering the stirring rate during the hydrolysis and condensation stage, enables the sizecontrolled synthesis of particles within the range between 150 and 550 nm. BET was performed to confirm pore size and the total pore volume of the particles using a Quantachrome Autosorb3b BET Surface Analyzer. SEM analysis using FEI Quanta 400 ESEM FEG was performed to check the size and morphology of the particles and also, residual impressions left by the indentations. Samples for SEM analysis were coated with 4 to 5 nm layer of gold using Denton Desk V sputter system for enhanced quality of images. Particle size distribution was obtained by randomly selecting and examining between 100-150 particles on a SEM image using ImageJ software. All of the indentations in this study were performed using an Anton-Paar Nanoindentation Tester (NHT2) of the Laboratory of C-Crete Technologies LLC. The indenter approach speed and the approach distance were kept constant at 2000 nm/min and 3000 nm respectively. The retract speed was 2000 nm/min. The stiffness threshold, which corresponds to the zero point where the loading for each indentation starts was fixed at 300 µN/µm. For indentations on single particles and on self-assembled arrays, a cylindrical, flat-ended diamond tip with the crosssectional diameter of 20 µm was adopted. The surface of a flat-ended tip is a square-like, imperfect circle (Fig. S1). For indentations on a compacted sample, a three-sided, pyramidal Berkovich indenter (diamond) was used. The ramp and unloading time were fixed at 30 seconds and the hold time at the peak load was fixed at 5 seconds for indentations on self-assembled arrays and pressure-induced assembly sample. Indentation on a single particle Calcium silicate particles suspended in acetone with the concentration of 0.01wt% was sonicated for an hour and the particles were transferred to a glass substrate using drop-cast technique.36


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The solvent was evaporated at 60ºC for 2 hours prior to nanoindentation experiments. An optical microscope attached to the nanoindenter was used to identify an isolated particle distanced from other neighboring particles by at least 30 um in order to ensure that the indentation occurs on a single particle. The standard load-controlled mode with the rate of loading and unloading ranging between 1.0 and 1.5 mN/min was adopted. The stress and strain values were obtained by normalizing the force and displacement values over the size of the particle according to the following equations:

𝑆𝑡𝑟𝑒𝑠𝑠 =

𝐹 2 𝜋𝑅

(1)

𝑆𝑡𝑟𝑎𝑖𝑛 =

𝐷 (2) 2𝑅

In order to extract the elastic modulus of the single spherical particle, the Hertz theory was adopted to model the contact between the particle and the indenter tip. The theory is based on the key assumptions that the contact radius is much smaller in dimension relative to both the indenter and the radius of the particle and also, that the contact made by the particle with the indenter is frictionless.37 The aforementioned assumptions lead to the only normal stresses acting at the contact surface. The theory can be represented by the following equation, where the applied force, F, is proportional to the contact deformation, D, via. 𝐹=

! !

𝑅!/! 𝐸! 𝐷!/!

(3)

In the equation above, Er is the reduced elastic modulus and R is the initial radius of the particle. Er, the reduced elastic modulus can also be represented by the summation of the elastic modulus, E, the Poisson’s ratio, ν, of the particle (p) and the indenter (i) as: ! !!

=

!!!! ! !!

+

!!!! ! !!

(4)

Since the elastic modulus of a single calcium-silicate particle is negligible compared to the elastic modulus of the diamond indenter (1047 GPa), the equation above can be simplified further to the following form: ! !!

≈

!!!! ! !!


(5)

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After plotting F against D1.5 based on our experimental force-displacement data, the reduced !

elastic modulus, Er, can be calculated by extracting the slope ( 𝑅!/! 𝐸! ) of the linear fit. Since it !

is widely accepted that the Hertz relation is valid only for the initial deformation of the particle, the linear fit was constructed for the initial strain range up to ε=0.08.37-38 This fitting process was performed only for the indentations, where the steady progression of the loading curve and the clear failure stress could be observed. Indentation on self-assembled arrays and on Pressure-induced compacted samples For nanoindentation on self-assembled arrays, the particles were assembled on a glass substrate using an acetone suspension of the particles with the concentration of 0.5wt%, based on the evaporation-induced self-assembly (vertical deposition technique).39-40 The response of the thin and the thick region of the self-assembled arrays to nanoindentation with a flat-ended tip was analyzed using various indentation forces For nanoindentation on a pressure-induced assembly sample, the pre-weighed calcium-silicate particles were compacted inside a cylindrical pressing die composed of stainless steel base, with the cross-sectional diameter of 13 mm, an anvil, a plunger and a pellet extractor. After placing the cylindrical body on the top of the stainless steel base, the first anvil was inserted inside the hole of the cylindrical body to sit on the top of the base. The particles were subsequently placed onto the first anvil. After insertion of the second anvil to sandwich the powder particles, the plunger was placed on the top of the second anvil and the external pressure was applied on the entire assembly using a hydraulic pressing machine. During this cold pressing process, the pressure was slowly increased to 5 US tons, corresponding to ~335 MPa, and held for five minutes to produce a thin, cylindrical pellet with the diameter of 13 mm, akin to our previous study.41 Elastic modulus for the self-assembled arrays and that for the compacted pellet were obtained using the Oliver-Pharr approach.42 The contact stiffness, S, was obtained by taking the slope of the tangent to the initial portion of the unloading curve from the load-displacement data. The reduced elastic modulus, Er, for the self-assembled arrays and a compacted pellet was obtained using: 𝐸! =

𝜋 𝑆 2 √𝐴

(6) 𝑃


6

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For nanoindentation on a compacted sample using a Berkovich tip, hardness was also obtained in addition to elastic modulus, based on the following equation 𝐻=

𝑃𝑚𝑎𝑥 𝐴𝑃

(7)

where Pmax is the maximum indentation force and AP is the projected contact area, which is a function of the contact depth.

Results and Discussion Mechanical properties of an individual porous particle For nanoindentation on three different structural forms, a flat-ended tip with the cross-sectional diameter of 20 µm was employed for single particles and self-assembled arrays, while a pyramidal Berkovich tip was used for a compacted sample (Fig 1a-c). In this work, we performed an extensive 900+ nanoindentation to obtain reliable results and average. The representative nitrogen adsorption/desorption isotherms confirm the porous structure as indicated by the clear capillary condensation step occurring at the relative pressure between 0.3 and 0.4 and the total pore volume is around 0.43 cm/g2 (Fig. S2a). The typical pore size distribution acquired for our calcium-silicate porous particles using the method developed by Barrett, Joyner and Halenda (BJH) coupled with the TEM image of the typical single calcium silicate particle (Fig. S2b-c) confirm the narrow distribution of pore size from 2 to 4 nm.25, 43 Different sizes of the particles were acquired by controlling only the stirring rate during the synthesis and keeping all the other experimental conditions strictly the same. Prior to nanoindentation, the size and morphology of the particles were confirmed using SEM. The as-synthesized particles exhibit narrow distribution in both size and spherical morphology although there exists larger doublet or triplet particles (Fig. 1d-i). The particles with different sizes were prepared, with all of them achieving standard deviation in size below 10% except for those with the mean size of 423.2 nm and 523.9 nm (Fig. 1h-i). They show slightly higher standard deviations of 17.2% and 22.1% respectively, arising from the higher proportion of larger twin particles compared to smaller sizes of particles, which could be easily identified on SEM. For single particle indentations, the particles with three distinct diameters, 292.7 nm, 423.2 nm and 532.9 nm were employed. We carefully identified and compressed several individual


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particles slowly between the glass substrate and a flat-punch indenter. Due to the large difference in mass and volume between the particle and the indenter, the first critical step was finding the appropriate loading/unloading rate that leads to an analyzable load-displacement (P-D) curve with a clear fracture point. This loading rate has been proven to exert a significant influence on both the crushing point and deformation behavior of an individual particle.44-45 In our case, the rate of loading/unloading was kept within the range of 1.0 -1.5 mN/min, which generated a useful force-displacement curve for analysis, with the clear indication of fracture points. However, even within this range, it was inevitable that the indenter often hit the glass substrate instead of the target particle, leading to a large proportion of unsuccessful tries. Consequently, out of hundreds of indentations, only the successful indentations showing steady progression of the load-displacement curve up to the evident fracture point were used for calculating the strength and elastic modulus. We were able to perform seven, nine and ten successful indentations for the size of 292.7 nm, 423.2 nm and 523.9 nm respectively. The fracture points are indicated by the sudden major change in slope, followed by a long plateau which continues until the indenter tip hit the glass substrate and triggers the rapid increase in stress (Fig. S3a-c). The compressed particle (523.9 nm) identified on the optical microscopic image was taken to SEM and further analyzed (Fig. 2a-b). The SEM analysis confirms that the porous particle does not undergo severe cracking or brittle fragmentation shown by some polymer particles from previous publications.44 The average strength of the particle, calculated from the stress values at the fracture point (Fig. 2c), was 539.6±175.4 MPa, 575.3±162.6 MPa and 631.4±253.6 MPa for the size of 292.7 nm, 423.2 nm and 523.9 nm respectively, showing a moderate increase in the strength of the particle as the particle size is enhanced. Furthermore, the average strain at failure was 0.10±0.02, 0.14±0.02 and 0.22±0.03 for the abovementioned order of the size, again showing an upward trend as a function of the particle size. This enhanced failure strain hints that just by increasing the particle size while keeping the range of major pore sizes constant (centered around ~3 nm), the fracture nature of the particles switches from brittle to ductile mode. This change, combined with the moderate increase in strength is likely to indicate that due to the higher degree of porous scaffold existing within a larger particle, it possesses higher toughness under compression than the smaller particle, hence an intrinsic size-effect phenomenon. This will be further discussed shortly.


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Having acquired the strength and the failure strain for all three sizes, three displacementcontrolled indentations were performed for the particle with the largest size (523.9 nm) with the maximum displacement set at 70 nm (Fig. S4a). This investigation was performed to confirm that the largest particle undergoes ductile mode of failure and to see if there is significant plastic deformation prior to the fracture point. The linear loading with the loading/unloading rate of 1.0-1.3 mN/min was applied and the designated strain value was reached between 3 and 4 seconds with the holding time of 2 seconds (Fig. S4b). Interestingly, significant deformation occurs during the holding time when the stress and strain values reached only around 50% of the strength and failure strain respectively. This indicates that the particle undergoes significant deformation from the early stage of the loading before the complete failure. Also, the elastic recovery, defined as the ratio of the difference between the maximum displacement and the residual displacement, to the maximum displacement stays only within the range between 8.2 and 14.9%. This corroborates that large permanent deformation has occurred prior to failure, again confirming the ductile nature of the single, porous particle. This resembles that of amorphous silica particle and cubic C-S-H particle from previous studies.22, 41, 46 We calculated the elastic modulus of the single particle by constructing linear regressions to F vs D1.5 plots, which were acquired based on our load-displacement. The average elastic modulus was 13.2±5.3 GPa, 9.3±1.9 GPa and 6.0±4.9 GPa for the size of 292.7 nm, 423.2 nm and 523.9 nm respectively (Fig. 2d). It is interesting to note that while the strength and failure strain increased as a function of the particle size, the elastic modulus decreased. This manifests sizedependent mechanical properties for a single spherical porous calcium-silicate particle, akin to single polymer particles.47-48 These absolute values for elastic moduli might seem relatively low when compared with the spherical Stober silica particle (30.8±4.0 GPa, 500 nm) or silicon nanoparticles (40-140 nm, 600-180 GPa).49 This is in part because our particles are porous (to be discussed shortly) and in part due to the composition of our particles, which is different than the above systems. However, the elastic moduli of our particles are on the same order of magnitude to those of many sub-micron polymer particles such as polypropylene (1.79±0.38 GPa for 500 nm, 2.23±0.33 GPa for 370 nm) and polymethylmethacrylate (4.3 GPa for 350 nm).50-51 Note that all above comparisons are not direct and somewhat qualitative or semi-quantitative at best. This is because the experimental techniques previously adopted are diverse, ranging from AFM to nanoindentation methods, since there is no universal method for acquiring mechanical


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properties of individual particles. Nonetheless, the comparison provides a decent guide, confirming reasonably high elastic moduli of our mesoporous calcium-silicate particles. The presence of uniformly-sized pores throughout the particle integrity implies the decreased number of siloxane bonds compared to non-porous silica particle of the same size and thus, must serve as detrimental factors on the mechanical strength. However, the relatively large average elastic moduli of our porous particles indicate that despite their mesoporosity, they possess considerable intrinsic mechanical strength. In order to confirm the switch from brittle to ductile failure at the scale of single particles, toughness was calculated for each particle size. Note that here toughness is defined as the amount of energy a material absorbs before failure (representing the work-of-fracture), which is different from the classical “fracture toughness” with the unit of Pa 𝑚. The work-of-fracture is the area under the stress–strain curve, which is deeply affected by gradual, graceful fracture, whereas the “fracture toughness” does not incorporate this entire process.52-59 Furthermore, in this work the “porous” particle is not meant as a core-shell type model, but a scaffolded porosity within the particle. The average toughness acquired from the stress-strain curves was 27.7±12.6 MJ/m3 , 40.3±15.9 MJ/m3 and 61.2±21.0 MJ/m3 for the size of 292.7 nm, 423.2 and 523.9 nm respectively (Fig. 2d). This 120.9% increase in toughness from the size of 292.7 nm to 523.9 nm, coupled with 54.5% decrease in elastic modulus confirms that increasing the particle size while keeping the pore size distribution within the same range significantly enhances the toughness of individual particles. In other words, by keeping the distribution of scaffolded pore size within the same narrow range while increasing the particle diameter, there is a brittle to ductile transition. The size-effect observed for our amorphous calcium silicate particles differs in nature to that observed for metallic particles, such as a gold microparticle, where the yielding process is governed by dislocation nucleation on specific crystallographic planes.60 He et al found the similar trend in mechanical properties for individual micron-sized polymer particles.20 The authors ascribed the size-effect to the variable thermal effect induced by the energy imposed on the particle during the indentations. In our case, the size-effect could be due to the different degree of connectivity existing within an individual scaffolded porousparticle, which changes as a function of particle size. This can in turn directly influence the mechanical stiffness.24 Flat-punch indentation on self-assembled arrays


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The single porous particles were now self-assembled to form large, periodic arrays using evaporation-induced vertical deposition technique (Fig. 3a-c).39-40, 52 The purpose here was to investigate if the particles closely-packed within a large ensemble exhibit the similar strength or size-effect under flat-punch compression. The arrays exhibit some large defects in the form of voids or cracks between the particles, probably due to the high drying rate at 60°C, which induces high drying stress and also, due to the relatively large size of our submicron particles.61 The particles are closely-packed with each other (Fig. 3d). Also, they exhibit a varying thickness along the growth direction (Fig. 3e-f). The thick region comprising more than ten layers of the particles was at the lower-end of the substrate that had been in proximity to the surface of the container during the deposition process and the thinner region, comprising only two to three layers, was located higher up the substrate. The thickness (i.e. the number of layers of the particles) of the particular region for indentation was checked by examining the void defect during the SEM analysis. For the rest of this paper, we label “thin” and “thick” regions to those regions composed of up to three layers and more than ten layers of particles, respectively. To investigate the deformation behavior of the self-assembled film to high compressive forces, first we performed indentations with the applied force of 120 mN. The residual impression on the thin region of the self-assembled film induced by the applied force of 120 mN confirms the significant pile-up phenomenon around the edges of the impression (Fig. 3g). Pile-up is the upward extrusion of the material around the edge of the indenter, often observed during the indentation of metal due to the work-hardening effect.62-63 Here, the pile-up phenomenon is probably because the shear force created by the compression induces the upward movement of the particles near the edge of the indenter tip. Furthermore, the SEM analysis of compressed particles confirms that although the indentation process has induced the high densification of the particles, the deformation of the individual particles is minimal (Fig. 3h). This in turn illustrates that even at the compressive force as high as 120 mN, the resultant stress is successfully distributed between the particles. The SEM analysis of the residual impression on the thick region shows more interesting features. The applied force of 120 mN induces severe, radial cracks propagating from the edges of the impression (Fig. 3i), which can be explained as follows. The shape of the cross-sectional surface of the flat punch indenter is not a perfect circle but a somewhat square-like surface with four obtuse corners, implying that these four sites have high stress concentration during the


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indentation process, leading to symmetrical radial cracks around the indentation imprint, which branch further to relieve stress. The different deformation behavior between the thin and thick regions of self-assembled film upon flat-punch indentation can be elucidated using different mechanisms of energy dissipation. At the peak load of the indentation, where the indenter tip is held at five seconds, there is a greater number of layers of particles underneath the base surface of the indenter tip for the thick region than the thin region. Consequently, for the thin region, where the indenter tip is in proximity with the substrate, the majority of the plastic energy stored by the particles during the compression is dissipated to the glass substrate. On the other hand, for the thick region, the stored energy during compression is released in lateral dimensions through the sea of the particles. This radial cracking is facilitated by the weak, physical interactions existing between the particles. In order to comprehensively quantify the mechanical response of the self-assembled arrays, a series of indentations with various applied forces, ranging from 1 mN up to 120 mN was carried out. The thin region exhibits notable elasticity as verified by the considerable elastic recovery at low indentation forces of 1-3 mN (Fig. 4a). When the applied force reaches ~ 5 mN, significant permanent deformation starts to occur (Fig. 4b). The thick region behaves as a soft, elasto-plastic material with large permanent deformation even from low indentation forces (Fig. 4c). This is further verified by the notably low percentages of elastic recovery on the thick region, which are 0.21±0.08%, 0.13±0.02% and 0.15±0.06% for the indentation force of 1 mN, 3 mN and 5 mN respectively. This lower trend of elastic recovery of the thick region is repeated at higher applied forces, 5 mN, 10 mN and 20 mN as well (Fig. 4d). The aforementioned change in mechanical behavior of the thin region as a function of applied force is further confirmed by the rapid increase in the elastic modulus as a function of applied forces (Fig. 4e). It is imperative to note that the observed increase in elastic modulus beyond the indentation force of 5 mN originate largely from the substrate effect. The elastic modulus of pure glass under the applied force of 75 mN is 36.9 GPa, close to the values acquired herein at the applied force above 80 mN. For low applied indentation forces (1-3 mN), the elastic modulus of the thin region ranges between 2 and 5 GPa, which is close to the values acquired from the indentation of a single particle. This implies that under the compression with small forces up to 3 mN, the mechanical response of the thin region originates largely from the intrinsic mechanics of the single, individual particles. However, as the indentation force is


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increased from 3 mN to 5 mN, the elastic modulus undergoes about three-fold leap and beyond 5 mN, the elastic modulus exhibits a sharp increase as a function of the applied force, finally reaching a plateau between 34.3 and 43.5 GPa (Fig 4e). After indenting self-assembled ensembles composed of four different particle sizes, we found that the particle sizes had a lower impact at the scale of self-assembled arrays, as compared to single particle indentations. Although the elastic modulus acquired at higher indentation forces above 5 mN on the thin region is convoluted by the substrate effect, it can be safely concluded that the elastic modulus increases as a function of applied indentation forces. This is because as the maximum force used for compression is increased, it leads to a greater densification of the particles under the influence of compression. By the time the peak load is reached and held for five seconds, the particles are densely packed and start behaving collectively as a single film. This can elucidate the enhanced stiffness at higher indentation forces. The above conclusion acquired from the thin region is further supported by the similar indentations on the thick region. Indentations with the applied force ranging between 1 mN and 20 mN were performed for the thick region of the self-assembled arrays, which consist of particles with the size of 358.3 nm. The elastic modulus of the thick region acquired using low applied force of 1 mN is 2.2±0.4 GPa, almost identical to the value extracted from the thin region of the self-assembled arrays, 2.4±0.4 GPa (Fig. 4f). Overall, we can conclude that the selfassembled ensembles of porous submicron particles with narrow distribution of size and pore size exhibit “variable” stiffness, which increases as a function of the applied forces under flatpunch compression. Similar phenomenon on calcium silicate hydrate nanostructure has been recently studied by Tao et al via molecular dynamics simulation.64 Berkovich indentation on a compacted tablet Having investigated the mechanical response of the self-assembled arrays at various applied forces under flat-punch compression, the particles were now compacted to a pelletized form by applying an external pressure of ~335 MPa (Fig 5a). A compacted pellet is a common form used for measuring mechanical properties of powdery materials, such as synthetic calcium-silicatehydrate (C-S-H) or pharmaceutical products.65-67 For such semi-infinite stiff media, a pyramidal Berkovich tip, which induces high concentrated force is more appropriate for mechanical testing.68 The indentations were performed on 6 separate pellets, composed of the particles with


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numerous diameters, 172.2 nm, 172.8 nm, 220.nm, 287.2 nm, 423.2 nm and 523.9 nm. The samples were indented using four different maximum forces, 80, 160, 240 and 320 mN. The SEM image of the residual imprints induced by the force of 320 mN confirms that even with the notably high applied force, there is no sign of any brittle fracture or radial cracks (Fig 5b). This attribute, coupled with the large permanent deformation at each of the applied forces, confirms that the compacted sample is also elasto-plastic (Fig S5a-b). From the applied force of 80 to 320 mN, no significant relationship can be found between the applied force and elastic modulus or hardness (Fig 5c-d). The average hardness calculated from the four separate applied forces range from 367.8±46.7 to 515.1±26.3 MPa across different particle sizes and the elastic moduli ranges from 7.5±0.64 to 14.1±1.1 GPa. The Spearman’s rank correlation coefficient calculated for elastic modulus was -0.26, -0.20, -0.03 and -0.03 at the applied force of 80, 160, 240 and 360 mN respectively, all confirming the insignificant correlation with the individual particle size at a significant level of 0.1. Furthermore, the coefficient calculated for hardness was -0.77, -0.14, 0.2 and -0.71 for the aforesaid applied forces in the same order, again showing statistical independence at a significant level of 0.05. The degree of correlation may seem slightly higher for hardness but the large negative correlation was only achieved at the two extreme ends of the range (-0.77 at 80 mN and -0.71 at 360 mN) with the total number of data points being only six at each applied force. Consequently, it can be safely concluded from the current results that there exists no specific correlation between the micromechanical properties and the sizes of the constituent particles, likely due to the high compaction force, which makes the particle sizeeffect immaterial. The finding complies with the green body densities, 2.16 g/cm3, 2.02 g/cm3 and 2.13 g/cm3 obtained for the size of 172.8 nm, 220.1 nm and 423.1 nm, showing minimal change and little correlation as a function of individual particle size. Furthermore, the values are on the same order of magnitude as the elastic modulus for the single particles, indicating that the conversion of the structural state from a single particle to the pressure-induced assembly sample has not induced significant changes in mechanical properties. This in turn suggests that the sizeeffect observed for the individual particles becomes negligible when they are assembled to a larger superstructure. Moreover, the results further confirm that calcium silicate porous particles can be consolidated into a compacted form which exhibits notable micromechanical properties without the aid of an external agent. The interfacial bond strength between the particles is a critical factor in determining overall mechanical properties of compacted superstructure (i.e.


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strength and toughness), since cracks propagate along the boundaries between the particles. Our recent work has verified that the particles loaded with organic sealants, when used as building blocks of a compacted sample, can significantly enhance the interfacial bonding.25 Future studies on the propagation of cracks69 along the self-assembled particles or nanoindentation on pressureinduced assembled samples using lower forces should provide more insight on the collective mechanical behavior of such particulate materials.

Conclusion By performing 900+ nanoindentations, we provided a comprehensive picture uncovering the interrelationship of the particle size, pore size and mechanical properties of scaffolded calciumsilicate porous particles synthesized in different structural forms. At the level of individual porous particles, while the elastic modulus decreases by increasing the particle size from ~300 to ~500 nm, the fracture strain and strength increase, improving toughness by ~120%. This is a clear evidence of an “intrinsic size-effect” where increasing the ratio of particle characteristic diameter to pore characteristic size distribution (2~4 nm) increases toughness. In other words, by keeping the distribution of scaffolded pore size within the same narrow range while increasing the particle diameter, there is a brittle to ductile transition. However, this size effect becomes negligible as the porous particles form superstructures. However, this size-effect becomes negligible as the porous particles form superstructures. Nevertheless, the self-assembled arrays collectively exhibit variable elastic modulus, which increases as a function of applied forces while a pressure-induced compacted arrays exhibits no size-effect. Furthermore, we found that the elastic moduli of the single particles are on the same order of magnitude to those of the compacted sample, indicating no significant changes in mechanical properties as the particle state switches from single to the pressure-induced assembled states. These results will shed light on tuning properties of individual porous calcium silicate building blocks, and can also have implications to accurately evaluate mechanical properties of nano- or submicron porous materials existing in diverse structural forms, potentially impacting porous (nano)materials used in bone tissue replacement, drug delivery, and self-healing materials.


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Acknowledgment. We acknowledge support from National Science Foundation (NSF) Grant Number CMMI1538312. We also thank C-Crete Technologies LLC for providing the lab facilities and equipment for performance of this project.


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Fig. 1 Schematic illustrating the indentation process on three distinct structural forms and different size of particles. a) Indentation on an isolated, single particle using a flat-ended tip. b) Indentation on self-assembled arrays using a flat-ended tip. c) Indentation on a compacted sample using a pyramidal Berkovich indenter. d-i) porous particles with diameter of 172.8±15.9 nm (d), 220.1±16.9 nm (e), 292.7±18.0 nm (f), 358.3±29.6 nm (g), 423.2±93.4 nm (h), and 523.9 nm (i). Scale bar indicates 1 µm.


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Fig. 2 Mechanical properties of single particles. (a-b) Optical microscopic image of the particle before and after flat-punch indentation. Scale bar indicates 2 µm. The inset shows the SEM image of the corresponding indented particle (523.9 nm) with the scale bar indicating 500 nm. (c) Stress-strain curves acquired up to the failure point. (d) Average elastic modulus and toughness for individual particles with three distinct sizes.


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Fig. 3 SEM analysis of self-assembly process and residual impressions. a) Colloidal suspension (0.5wt%) of calcium-silicate porous particles. b) Schematic illustrating the selfassembly process performed based on vertical deposition technique. c) Picture of the selfassembled film on a glass substrate. d) SEM image of the self-assembled arrays. Inset shows the closely packed particles. SEM image of e) thin and f) thick region of the self-assembled arrays. SEM image of (g) residual impression induced by the applied force of 120 mN on the thin region and (h) the particles within the region of the impression. (i) SEM image of residual impression on the thick region induced by the applied force of 120 mN.


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Fig. 4 Mechanical properties of self-assembled arrays. Force-displacement curves with the maximum force set at 1 mN, 3 mN and 5 mN for a) the thin region and b) the thick region of the self-assembled arrays. Force-displacement curves with the maximum force set at 5 mN, 10 mN and 20 mN on c) the thin region and d) the thick region. e) The plot illustrating the increase in elastic modulus as a function of indentation force on the thin region for four different size of particles. f) The plot showing the difference in elastic modulus between the thin and the thick region at different applied forces. a)-d) and f) were obtained from the particles with the size of 358.3 nm.


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Fig. 5 Mechanical properties of a pressure-induced, compacted sample. SEM image of the surface of the tablet (a) before and (b) after indentation. Scale bar indicates 20 µm. The inset is a picture of the pressure-induced compacted sample. (c) Hardness and (d) elastic modulus acquired for particles with six different sizes using four different applied forces.


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Intrinsic Size Effect in Scaffolded Porous Calcium Silicate Particles

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