Thermal fiber drawing has emerged as a novel process for the continuous manufacturing of semiconductor and polymer nanoparticles. Yet a scalable production of metal nanoparticles by thermal drawing is not reported due to the low viscosity and high surface tension of molten metals. Here, we present a generic method for the scalable nanomanufacturing of metal nanoparticles via thermal drawing based on droplet break-up emulsification of immiscible polymer/metal systems. We experimentally show the scalable manufacturing of metal Sn nanoparticles (<100 nm) in polyethersulfone (PES) fibers as a model system. The underlying mechanism for the particle formation is revealed, and a strategy for the particle diameter control is proposed. This process opens a new pathway for scalable manufacturing of metal nanoparticles from liquid state facilitated solely by the hydrodynamic forces, which may find exciting photonic, electrical, or energy applications.

## Introduction

Metal nanoparticles possess unique mechanical, physical, and chemical properties that are of great significance to both technologies and fundamental science. The making of such nanoscale entities has been an active research field for the last two decades. While bottom–up [1] and top–down [2] methods for metal nanoparticle manufacturing exist, there is always a need to produce them inexpensively at high volume.

## Materials and Methods

In this proposed method, the metal nanoparticles are formed at liquid state, as a result of the break-up of an initially slender droplet surrounded by a viscous elongational flow created by the drawing process. The material selection criteria is as follows:

1. (1)

Controllable cladding viscosity (102.5–106 Pa ·s)

2. (2)

Metal is molten at the processing temperature

3. (3)

Metal does not react with the cladding

Polyethersulfone (PES) and crystalline metal Tin (Sn) were chosen for the experimental validation of the proposed method. The glass transition temperature of the PES is 225 °C, and the melting point of Sn is 232 °C, which are close enough for the metal to be molten during the drawing process. While most metals require high glass transition point glasses such as Pyrex glass and fused silica as cladding, the selection of a thermoplastic material allows for a relatively low temperature processing.

### Preform Fabrication.

Extruded polyethersulfone (PES, BASF Ultrason E3010) rods (extruded and distributed by Port Plastics, Inc., Los Angeles, CA) with an outer diameter (OD) of 19.05 mm and length of 10 cm were first dried at 150 °C for 5 days under vacuum (2 Torr) to remove moisture. A through hole was then drilled to allow insertion of a Sn metal wire (SRA Soldering Products, Walpole, MA). The PES preform was then consolidated in a vertical tube furnace at 250 °C for 30 mins under a vacuum of 40 mTorr before the first cycle of thermal fiber drawing. The consolidation has to be conducted at a temperature higher than the melting point of the metal but lower than the softening point of the polymer to ensure seamless contact between the metal core and the cladding.

### Iterative Thermal Fiber Drawing.

During a typical fiber drawing process, as shown in Fig. 1, the metal-embedded preform is slowly lowered into a furnace, where temperature is carefully controlled and stabilized at a designated value. After the heated preform in the furnace necks down under its own weight, the bottom portion of the preform is cut away, and the fiber is pulled at a constant speed while the preform continues to be fed into the furnace. The diameter of the fiber $Df$ is controlled by varying the fiber pulling speed $vf$. The draw-down ratio $Dr$ is defined as the ratio between the fiber pulling speed and preform feeding speed $vp$. At steady-state, the law of mass conservation requires $Dr≡(vf/vp)=(Dp/Df)2$, where $Dp$ is the preform diameter, and $vp$ is the preform feeding speed.

The fibers obtained from the first-drawing cycle are cut into equal lengths and bundled, as shown in Fig. 2, to serve as the core for a new preform, which is again thermally drawn to thin fibers. All the drawings were done in a furnace with a graphite liner resistively heated. The liner has inner diameter of 36 mm and length 35 mm. The temperature of the furnace is measured with a K-type thermocouple inserted horizontally into furnace with the tip of the thermocouple aligned with the inner wall of the graphite. Table 1 lists the preform/fiber dimensions and the process parameters for each drawing cycle. The fibers achieved in one cycle (iteration) are bundled and inserted into the inner hole of a new preform for the next drawing cycle (iteration).

### Particle Formation Mechanism and Size Control.

The nanoparticles are formed at liquid state as a result of the break-up and deformation of the initially slender metal wires under the physical forces of interfacial tension and viscous stress.

Long microwires are first produced after the first and second iterations, which then start to break in the third iteration.

Various break-up events then follow. The formation of the smallest particles may be attributed to the satellites drops or a phenomenon known as tip-streaming, during which the droplet becomes slender with a pointed end, where the extremely small droplets may eject, first documented by Taylor [7]. Recent theoretical studies suggest that, at nanoscale, thermal fluctuation may dominate [8].

The largest particles are those that survive the flow without further break up after sufficient times of iterations. A theoretical estimation of the size of the largest particle is given in the discussion.

### Particle Production Rate.

The upper bound of the volume production rate of the nanoparticles can be estimated as , where $d0$ is the initial metal wire diameter in the perform, and $vp$ is the preform feeding speed, assuming the metal wire being completely converted to nanoparticles after enough number of iterations. Plugging in the preform inner diameter (ID) and feeding speed of iteration 1 from Table 1 yields a theoretical volume production rate of 0.064 mm3/s. The actual production rate is much lower than this value considering the material loss during the production and collection.

### Sample Preparation and Characterization Methods.

Samples for characterization by scanning electron microscope (SEM) are prepared by laying down multiple fibers on a silicon wafer submerged in dimethylacetamide (DMA; Sigma–Aldrich, St. Louis, MO) at room temperature for 4 h until all the polymer claddings are dissolved. Samples for characterization by transmission electron microscope (TEM) are obtained by dissolving the fibers in DMA followed by centrifuging. The sediments are dispersed in ethanol from which one drop is cast onto the TEM grid.

## Results and Discussion

Slender and long metal microwires were achieved after two drawing cycles as shown in Fig. 3. The measured diameter is close to the thinnest continuous metal wires reported that was drawn in a polymer cladding [9].

Nanoparticles were successfully produced, as shown in Fig. 4, with diameters ranging randomly from 100 nm to 500 nm. TEM image (Fig. 5) with selected area electron diffraction (SAED) patterns (Table 2) further show that the Sn nanoparticles smaller than 20 nm could be achieved. While it is confirmed that the Sn nanoparticles can be produced as shown in Fig. 5, it is possible that the particles shown in Fig. 4 are still encapsulated in polymers that are not fully dissolved away.

To the best of the author's knowledge, there is no published model yet that can satisfactorily describe the dynamics of the metal core during thermal drawing process from a preform. In an attempt to fill this gap, we start with a heuristic way and recognize that in addition to the breakup of a cylindrical thread or layers of concentric cylindrical shells with various ratios of the material properties for which a wealth of literature exist [10,11], attentions must also be brought to the deformation of the metal droplets inside an elongational flow which we believe is the main cause of the formation of the nanoparticles.

During a typical run of thermal drawing, as the preform is slowly fed into the furnace at a constant speed and uniform fibers being pulled from below, a steady-state in Eulerian frame is soon reached such that the temperature and velocity profile in the preform remains constant with time, if viewed from a fixed laboratory position. We assume the flow is one-dimensional recognizing that the length of the preform is much larger than its diameter. The molten metals embedded in different locations in the preform thus experience an almost identical flow history as they melt, deform and solidify under the influence of the energy and momentum input from the surrounding viscous cladding under thermal drawing.

A complete mathematical description of the dynamics of the shape evolution from a cylindrical metal rod to the final nanoparticle products is a formidable task, which involves multiple length scales spanning from millimeters to nanometers, and requires taking into account all the relevant physical forces from interfacial tension, viscous stresses, inertia, and gravity. Fortunately, since we focus on small droplet sizes at micro/nanoscale, gravity and inertia effects are negligible due to small Reynolds number and body force. This greatly simplifies the problem by allowing us to consider only the surface forces that are the interfacial tension, and viscous stresses in the cladding, neglecting the viscous stress of the molten metal because the viscosity ratio $(λ)$ between molten crystalline metal and the viscous cladding is close to zero (typically <10−7). The ratio of these two forces defines the dimensionless capillary number $Ca=(τa/γ)$, where $τ$ is the first normal stress difference in the cladding flow [12], $a$ is the radius of the droplet retracted to a perfect sphere, and $γ$ is the interfacial energy between the viscous cladding and the droplet. $τ$ measures the external viscous stress and ($γ/a$) scales with the interfacial-tension pressure. A low capillary number ($Ca≪1$) indicates that the dynamics of the droplet deformation is governed by the interfacial tension alone while a high capillary number ($Ca≫1$) suggests the viscous force is dominating.

Under steady-state drawing, the $τ$ increases in the direction of pulling and scales with the inverse of the area of the circular cross sections because the fiber tension (T) is the same everywhere along the axis. The corresponding capillary number increases from $Camin=(Ta/A0γ)$ to $Camax=(Ta/ALγ)$, where $A0$ is the area of the cladding on the cross section of the preform, and $AL$ the area of the cladding on the cross section of the fiber.

In the low capillary number limit, when $Camin≪1$, corresponding to the case of a small pulling force or when the metal wires or droplets just enters the heating zone and are just melted, its dynamics is governed solely by interfacial tension.

Two modes of break-up may result in this case, namely capillary break-up and end pinching. An unconstrained slender molten metal thread is inherently unstable. It flows spontaneously to minimize its surface energy by reducing its surface area. An unperturbed slender thread would shrink and eventually become one single sphere. In the presence of any disturbances from the surrounding, which is always the case, the disturbances can be decoupled into superposition of sinusoidal perturbations along its three axes as shown in Fig. 6.

Since the volume of the thread keeps constant, sinusoidal undulation of centerline does not change its surface area, the fluid thread would not break under such perturbations alone. Azimuthal modulation increases its surface area, and therefore, the thread will not grow in this direction either. However, when the radius of the thread is perturbed along its symmetric axis as shown in Fig. 6(c), one can calculate and see that its surface area is reduced if the wavelength of the perturbation is larger than a critical value [8], meaning the perturbed state has lower surface energy and thus is more stable than the unperturbed state. It is for this reason that the initial small perturbation grow spontaneously and quickly leads to breakage of the fluid thread into droplets along its centerline. In the case of end pinching, droplet break-up does not happen simultaneously but sequentially from the two ends of the slender thread as it retracts to the spherical shape to minimize its surface energy [8], which typically happens when the viscosity of the droplet is much lower than its surrounding as in the molten metal/viscous cladding case. Studies show that there exists a critical aspect ratio (ARcr) above which either end pinching or capillary break-up may happen. Experiments and numerical simulations indicate that the moderately stretched droplets with an aspect ratio can retract back to the spherical shape without fragmentation [13], and the critical aspect ratio is a function of viscosity ratio. Here, we again utilize the fact that $λ$ is close to zero, therefore, assuming that ARcr is a constant not sensitive to the viscosity changes of the metal and polymer arising from the spatial temperature and velocity profile.

As the capillary number increases along the fiber axis, the metal droplets or wires experiences stronger flow. Studies show that there exists a critical capillary number Cacr above which the droplet may disintegrate due to the viscous shearing as well, and the break-up may assume more than one mechanism, namely, center pinching, indefinite elongation, or tip streaming [14], among which indefinite elongation and tip streaming are believed to be able to produce nanoscale droplets which we do observe in this study.

With the knowledge of the possible break-up mechanisms, it is now possible to estimate the size of the largest droplet that can survive the fiber drawing flow without further break-up after multiple iterations of bundle-and-draw.

We argue that, in order for a droplet with radius $a$ to survive the fiber drawing flow without breaking up, it may neither break due to interfacial tension, nor viscous shearing. This essentially requires that the aspect ratio and the capillary number corresponding to the droplet exceeds neither the critical aspect ratio ARcr, nor the critical capillary number Cacr.

We further argue that the capillary number needed to stretch a droplet to its critical aspect ratio is always smaller than the critical capillary number that may give rise to its disintegration by shearing, which is self-evident as break-up can only happen when the shearing is too strong such that a stationary shape, which assumes a finite-aspect ratio, can no longer exist.

Now, we define a new critical capillary number $Cacrit(a)=(τa/γ)$, above which a droplet with initial radius $a$ will be stretched to an aspect ratio larger than ARcr. Equivalently, if the maximum stress $(τmax)$ in the flow is known, any droplets with radius larger than $amax=(γCacrit/τmax)$ is subject to break-up thus will not survive.

In the fiber drawing, the maximum axial stress in the flow $(τmax)$ is proportional to the fiber tension force ($T$) divided by the area of the fiber cross section ($AL$). We, therefore, reach the following expression:

The proposed functional relationship captures the key process parameters as well as the material properties that governs the metal particle size. The suggested mechanism has general implications for metal particle size design and control. The validity of this relationship should be experimentally tested in future.

Several assumptions are inherent in the above analysis which needs to be noted here:

1. (1)

The effect of temperature gradient on the interfacial tension is neglected, which can be justified when the Marangoni number is much smaller than one.

2. (2)

It is assumed that the droplets are small enough, so that the flow around it can be considered as linear, although the actual flow is nonlinear at larger length scale.

3. (3)

It is assumed that there is no interaction between droplets.

4. (4)

Continuum hypothesis is assumed to be valid, neglecting the molecular effects.

## Conclusions

In this study, a novel method for the scalable nanomanufacturing of metal nanoparticles is proposed and experimentally validated. It is proposed that the metal nanoparticles can be produced in a scalable manner by thermal fiber drawing utilizing the iterative size reduction method. Sn metal nanoparticles smaller than 100 nm were successfully produced by drawing inside a thermoplastic cladding (PES). The successful manufacturing of metal nanoparticles in liquid state from long and slender metal filaments is attributed to the physical forces of interfacial tension and viscous stress. The diameter of the particles produced is predicted to be a function of the maximum stress in the fiber and the interfacial tension between the molten metal and the viscous cladding. This proposed method is generic and can be readily extended to other material systems, following the material selection criteria given, to produce higher melting point metal nanoparticles for many exciting photonic, electrical, or energy applications.

## Acknowledgment

This work is supported by National Science Foundation.

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