Colloid Coalescence with Focused X Rays

B.M. Weon,1,* J. T. Kim,1 J. H. Je,1,† J.M. Yi,2 S. Wang,3 and W.-K. Lee3

1X-ray Imaging Center, Department of Materials Science and Engineering, Pohang University of Science and Technology,Pohang, 790-784, Korea

2Samsung Advanced Institute of Technology, Yongin, Gyeonggi, 446-712, Korea3Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

(Received 23 November 2010; revised manuscript received 17 February 2011; published 1 July 2011)

We show direct evidence that focused x rays enable us to merge polymer colloidal particles at room

temperature. This phenomenon is ascribed to the photochemical scission of colloids with x rays, reducing

the molecular weight, glass transition temperature, surface tension, and viscosity of colloids. The

observation of the neck bridge growth with time shows that the x-ray-induced colloid coalescence is

analogous to viscoelastic coalescence. This finding suggests a feasible protocol of photonic nano-

fabrication by sintering or welding of polymers, without thermal damage, using x-ray photonics.

DOI: 10.1103/PhysRevLett.107.018301 PACS numbers: 82.70.Dd, 47.20.Gv, 81.20.Ev, 87.59.�e

Colloidal particles, one of the self-assembling buildingblocks, are widely studied in an emerging variety of studiesand applications [1]. Key examples of colloidal particlesare polystyrene (PS) spheres suspended in water and poly-methylmethacrylate (PMMA) particles dispersed in hydro-carbon liquids. Coalescence is a fundamental process formerging particles into a solid body [2,3], particularly fornovel architectures such as colloidosomes [4] and photoniccrystals [5]. The reduction of surface free energy is thedriving force for material transport [2,3]. The mechanismof material transport can be elucidated by a direct obser-vation of neck bridge growth between particles [3].Conventional sintering using heat and/or pressure is oftenunsuitable to nanoscale colloids due to thermal damage orthe difficulty in temperature control [6]. Local rapid heat-ing like laser sintering is an alternative [7]. Laser sintering,however, has the risk of thermal damage despite improve-ments in beam quality, focusing ability, and stability inbeam power and position [7].

In this Letter, we present a feasible protocol to mergecolloidal particles using x-ray photonics at room tempera-ture. Contrary to laser sintering, x-ray photons can inducephotochemical scission without thermal damage [8].PMMA is a well-known material showing a high yield ofchain scission under x-ray irradiation [9]. The scission ismostly due to the loss of ester group (�CO2CH3) ofPMMA [10]. From the studies on various soft mattersystems in the past few years [11], we developed a non-thermal ablation technique with x-ray photons via rapidchain scission of polymers [12]. Despite basic knowledgeabout photochemical scissions of polymers under x-rayirradiation [9,10], a possibility of x-ray-induced coales-cence of polymer colloids has been little explored. Here,we present an x-ray-induced coalescence phenomenon ofPMMA spheres. The photochemical scission reduces themolecular weight and equivalently the glass transitiontemperature. The transition temperature varies with x-ray

dose [9]. The reduction of the transition temperature de-creases the surface tension and the viscosity, which con-sequently induces the coalescence process. For both x-rayirradiation and simultaneous imaging, we apply the full-field x-ray transmission microscopy (TXM) at a photonenergy of 8 keV on the 32-ID imaging beam line of theAdvanced Photon Source at the Argonne NationalLaboratory [13], as illustrated in Fig. 1. This approach isuseful not only to directly monitor the coalescence processof colloidal particles in real time, but also to concentratex-ray photons to induce the coalescence process.As a model system, we used hard-sphere PMMA col-

loids with radii of R ¼ 100, 550, 1000, and 1800 nm(polydispersity less than 5%), which were taken from

CapillaryCondenser

(a)

X rays

Zone PlateObjective

CCDCCD

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NeckingFocusedColloids(b)

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FIG. 1 (color online). Schematic illustration of the x-ray-induced coalescence of polymer colloids. (a) Full-field x-raytransmission microscopy (TXM) setup: X-ray photons are fo-cused on the sample via the capillary condenser lens andgathered through the zone plate objective on the CCD camera.(b) The coalescence process (necking) between colloids is in-duced by the focused x rays.

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dilute colloidal suspensions of PMMA spheres in decalin[14,15]. The PMMA colloids used here are the spheres(synthesized by Schofield [16]) that have a poly(hydrox-ystearic acid) (PHSA) sterically stabilizing layer 10 nm inthickness. They have been widely used as a model hard-sphere system [1]. The PMMA particles were deposited byevaporation on a clean Kapton tape (Kapton is transparentto x rays) and directly illuminated with the focused x raysin a normal direction to the incident x-ray beam. Real-time(Zernike-type) phase-contrast x-ray imaging with a phasering was performed using the TXM with spatial and tem-poral resolutions of 40 nm and 50 ms, respectively [13].The flux of the focused x-ray beam by the condenser lenswas f ¼ 2� 1011 photons s�1 at 8 keV [13]. The doseratio (k) could be estimated as k¼832photons�m�2Gy�1

at 8 keV from the empirical formula [17] of k ¼ 2000 ��2

(where thewavelength is � ¼ 1:55 �A at 8 keV). The focusedbeam size at the sample plane was 15� 15 �m2 in FWHM.Because �95:4% of the incident beam intensity (I) wasilluminated to the focal area A ¼ 25:5� 25:5 �m2 andthe condenser efficiency was " � 90%, we estimated thedose rate of the focused x rays as � ¼ 317 kGy s�1

(¼ 0:954 f"I=kA [17]) on the illuminated sample area.The high dose rate is expected to enhance the x-ray-inducedchain scission of PMMA colloids.

Direct visualization of coalescing colloids at the nano-scale is a challenging task [18]. The coalescence processarises from various kinds of mass transports [3] such asevaporation and deposition, surface diffusion, and viscousflow of matter. In the case of a polymer, coalescence isknown to occur via ‘‘viscous flow’’ [19,20] or ‘‘viscoelasticdeformation’’ [21–23]. The classical Frenkel-Eshelby the-ory [19,20], equating the rate of work done by surfacetension (�) to the rate of energy dissipation due to viscousflow, predicts that contact radius (r) between two spheres

increases with time (t) as ðr=RÞ � ð�t=�RÞ1=2, where R isthe radius of coalescing spheres and � is the fluid viscosity.On the other hand, the Johnson-Kendall-Roberts theory [21]predicts ‘‘zero slope’’ for elastic coalescence at early stage

and also the viscoelastic coalescence of r� t1=7 under zeroapplied load at late stage [22,23]. Neck bridge measure-ments, usually observed using optical microscopy with a hotstage, typically show the viscous coalescence for large PSand PMMA spheres (R ¼ 250–300 �m) and the viscoelas-tic coalescence for small spheres (e.g., R� 120 �m) [22].Considering material properties of polymer melts, it hasbeen suggested that colloidal particles from R ¼ 40 nm toR ¼ 2 �m sinter by viscoelastic deformation without anycontribution of viscous flow [22]. The most direct approachto verify the coalescencemechanism of colloidal particles atthe nanoscale is to simultaneously image the neck growth inreal time as the radiation dose is delivered to the sample.Our high-resolution TXM approach can directly visualizethe coalescence dynamics of PMMA colloids.

We present direct experimental evidence for the x-ray-induced coalescence of PMMA colloids with R¼1000nm

at room temperature (20 �C) in the atmosphere [Fig. 2(a)].The right area, where PMMA particles are irradiated for150.1 s by focused x-ray photons, is completely changedinto a merged film after the irradiation, clearly showing thex-ray-induced coalescence. Meanwhile the left area irradi-ated only for 2.6 s (for photography) shows no coalescence.This picture demonstrates the positional selectivity of thecoalescence process by locally focusing x-ray photons onthe sample. Additional examples for different sizedPMMA particles [Fig. 2(b)] show that the coalescencekinetics is likely to become fast as the particle size de-creases; as the colloid size decreases from R ¼ 1800 to100 nm, the complete coalescence time reduces from 198.5to 77.3 s. This is attributed to the increase in the surfaceenergy per unit volume with the decrease in the size. Thelocal heating by focused x rays is negligible, estimated as�5� 10�4 K for PMMA [8] under similar irradiationconditions. What causes the coalescence without heating?The answer is the significant reduction of the glass tran-sition temperature of PMMA via photochemical scissionby high-flux x-ray bombardment, as is well known [9]. Thex-ray dose rate in our case is high as � ¼ 317 kGy s�1 atthe focal plane of the sample surface. Such high flux of x-ray irradiation on a cluster of colloids in contact wouldpossibly reduce the glass transition temperature to roomtemperature, resulting in x-ray-induced coalescence with-out heating.To illustrate the coalescence dynamics in detail, we take

sequential images for PMMA particles with R ¼ 1800 nm[Fig. 3] during the continuous irradiation of x-ray photons.The colloidal particles are gradually merged into a filmwith the irradiation time. This again confirms that thex-ray irradiation induces the coalescence process ofPMMA colloids at room temperature in the atmosphere.

FIG. 2 (color online). (a) Evidence of coalescence for PMMAcolloids (R ¼ 1000 nm) with the focused x rays (8 keV). Thisimage was taken using the TXM during x-ray irradiation. Thelong-irradiated area (right), which was fully merged for 150.1 s,shows the x-ray-induced coalescence, while the short-irradiatedarea (left) for 2.6 s (for photography) shows no coalescence.(b) Additional examples for different sized PMMA particles. Thecoalescence kinetics becomes fast as the particle size decreases.

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The contact radii (r) between colloids are clearly visible, asillustrated in the photographic image of r� 230 nm at theirradiation time of 36.1 s.

We consider possible changes of material properties forthe x-ray-irradiated PMMA colloids in terms of glasstransition temperature, surface tension, and viscosity, be-cause the photochemical scission reduces the molecularweight. It is well known that the glass transition tempera-ture of PMMA is a function of x-ray dose (�t) as TgðtÞ ¼T0 � 0:082� 9:52�t [9] (the coefficient of the last term[9] was adjusted for PMMA), where T0 is the glass tran-sition temperature of nonirradiated PMMA (¼ 118:0 �C[9]),� is the dose rate (Gy s�1), and t is the irradiation time(s). Here the TgðtÞ of PMMA is not affected by the size for

the colloids larger than 100 nm [24,25]. As the x-ray doseincreases, the glass transition temperature linearly de-creases. We plot �T ¼ T0 � TgðtÞ as a function of the

irradiation time [Fig. 4(a)]. After the initial incubationperiod (� 30 s), �T linearly increases up to 80 K at 60 s.Thus, the glass transition temperature could be reduced toroom temperature at 60 s. This explains the room tempera-ture sintering of PMMA colloidal particles by x-rayirradiation.

The reduction of the glass transition temperature woulddecrease the surface tension and the viscosity of PMMAcolloids. The surface tension of PMMA at 20 �C is4:11� 10�2 Nm�1 and the temperature dependenceis d�=dT ¼ �7:6� 10�5 Nm�1 K�1 [26]. From �T ¼0:082þ 9:52�t, the surface tension is therefore�ðtÞ ¼ 4:11� 10�2 � 7:6� 10�5 (0:082þ 9:52�t). Theestimated surface tension [Fig. 4(b)] slightly decreases from33 Nm�1 at 32 s to 27 Nm�1 at 60 s.With the same reason,the viscosity of PMMA particles changes with the glasstransition temperature accordingly. To estimate the depen-dence of the viscosity on �T (or the irradiation time), theWilliam-Landel-Ferry equation for PMMA [27] is used as�ðtÞ ¼ �i expf�C1ðT � TiÞ=½C2 þ ðT � TiÞ�g, where�i is

the viscosity at a reference temperature Ti. Here C1 and C2

are constants that depend on the reference temperature. Wechoose the parameters C1 ¼ 20:9 and C2 ¼ 58 for T <160 �C [27]. Taking the glass temperature as the referencetemperature, T � Ti ¼ ð�T þ 118Þ � Ti, we get �0 ¼7:8� 1010 Pa s at Ti ¼ 105 �C for a molecular weightðMWÞ ¼ 105 (assuming ��MW3:4) [27]. Based on theseparameters, the time-dependent viscosity [Fig. 4(c)] shows asignificant decrease of � from �1010 Pa s at 32 s to�105 Pa s at 60 s. Such a remarkable decrease of theviscosity implies that the coalescence takes place by visco-elastic deformation [21–23]. The underlying mechanism ofthe x-ray-induced coalescencewould be analogous to that ofthermal sintering in terms of the decrease in the viscosityduring the coalescence process.To clarify the dominant mechanism of the x-ray-induced

coalescence, the contact radius growth (the normalizedneck radius r=R) is evaluated as a function of the normal-ized time (t=�) as ðr=RÞ � ðt=�Þ�, where � is the viscous

time � ¼ ð4�=3Þ1=3½�ðtÞRðtÞ=�ðtÞ� [22]. In the log-log plotof (r=R) versus (t=�), the slope � informs possible coales-cence mechanisms [3,22,23]. Our measurement from 7particles [Fig. 3] shows a significant slope transition aftert=� > 0:04 and indeed gives the slope � around 1=6[between 1=5 and 1=7, if we include the error bars (1 stan-dard deviation)] [Fig. 4(d)]. The 1=7 or 1=5 scaling isconsistent with the theoretical prediction based on theviscoelastic coalescence [23]. We conclude that the earlybehavior comes from the elastic contact behavior (theslope �0) [23] and the late behavior from the viscoelasticcoalescence (the slope �1=6), as expected for typicalpolymer sintering [22,23].

FIG. 3 (color online). Monitoring of a single coalescence eventfor PMMA colloids (R ¼ 1800 nm) with the focused x rays(8 keV). Sequential images taken using the TXM show that thecolloidal particles are gradually merged into a film with irradia-tion time. Schematic (bottom left) shows the x-ray-inducedcoalescence process. The contact radii between colloids (bottomright) are visible as r� 230 nm at 36.1 s.

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FIG. 4 (color online). Changes of material properties ofPMMA with x rays. (a) The change of the glass transitiontemperature is described as �T ¼ T0 � TgðtÞ for T0 ½TgðtÞ�without [with] irradiation. After initial incubation time(� 30 s), �T linearly increases with irradiation time, implyinga significant reduction of TgðtÞ to room temperature at 60 s.

(b) Surface tension (�) slightly decreases with irradiation time.(c) Viscosity (�) significantly decreases with irradiation time.(d) Normalized contact radius (r=R) versus normalized coales-cence time (t=�) demonstrates that the 1=6 slope (solid line)emerges at late stage, implying the viscoelastic coalescence.

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In principle, van der Waals and Young-Laplace forcescan contribute to polymer coalescence [23] in three suc-cessive steps: (i) elastic adhesive contact, (ii) ‘‘zipping’’contact growth driven by adhesive forces and accommo-dated by viscoelastic deformation, and (iii) ‘‘stretching’’contact growth driven by the surface tension and accom-modated by viscous flow. Recent simulation results [22]showed that the traditional viscous coalescence model (bycapillary forces) holds for large particle size (> 10 �m)and a significant deviation must exist for small colloidalparticles (< 10 �m) of identical materials. They predictedthat the effect of van der Waals forces would becomedominant for small sizes [22]. Our result shows evidence

that the t1=5 or t1=7 scaling indeed appears in the coales-cence kinetics of colloidal dimensions, suggesting thedominance of van der Waals forces.

Is there another possible mechanism for the colloidalparticle coalescence? One possibility is the surface diffu-

sion, typically observed with a scaling (r� t1=7) in thecoalescence of heated metal particles [28]. However, this isnot probable since the surface diffusion rate of colloidalparticles would be too slow to induce coalescence; e.g., itwould take 1 yr for a surface molecule to diffuse to theother side of a 10 �m particle, because the time is propor-tional to the mean-square diffusion distance [29]. Our

observation of neck growth of t1=6 suggests that colloidcoalescence by x-ray irradiation is analogous to viscoelas-

tic coalescence (t1=5 or t1=7) [21–23] instead of viscous

(r� t1=2) [19,20] or diffusive coalescence (r� t1=7) [28].Importantly, colloid coalescence differs from liquidcoalescence in terms of capillary speed (�=�) [30,31]:�=� < 10�7 m s�1 for colloids [Fig. 4] is much smallerthan that for ordinary liquids (e.g., �70 m s�1 for water).Viscoelastic deformation controls colloid coalescence,whereas capillary speed controls liquid coalescence.

In conclusion, we present a direct observation of an x-ray-induced coalescence in polymer colloids. We observenanoscale coalescence phenomena of colloids in real timewith the full-field TXM. The key mechanism of the non-thermal sintering is the x-ray-induced photochemical scis-sion reducing the molecular weight, which effectivelydiminishes the glass temperature, the surface tension, andthe viscosity of PMMA particles. High-resolution imagingfrom the TXM offers direct evidence that contact neckgrows with time initially by zero slope and in turn by1=6 power-law scaling. This result agrees well with atypical transition of polymer sintering from elastic coales-cence at early stage to viscoelastic coalescence at latestage. Conventional sintering using heat and/or pressurewould be unsuitable to nanoscale colloids because ofthermal damage. X-ray photons can effectively inducecoalescence via photochemical scission without thermaldamage in nanoscale spatial resolution. Our findings canopen opportunities of sintering or welding technology for

polymers by modifying their structures and propertiesusing x-ray photonics, which can be applied either atlaboratory sources or at synchrotron radiation sources.The x-ray-induced coalescence meanwhile may be a verycritical problem in probing colloidal or nanoparticlesamples by high-brilliance x-ray sources.This work was supported by the Creative Research

Initiatives (Functional X-ray Imaging) by MEST/NRF.Use of the Advanced Photon Source at Argonne NationalLaboratory was supported by the U.S. Department ofEnergy, Office of Science, Office of Basic EnergySciences, under Contract No. DE-AC02-06CH11357.

*bmweon@hotmail.com†jhje@postech.ac.kr

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