highly birefringent vaterite microspheres: production, characterization and applications for optical...

Highly birefringent vateritemicrospheres: production,

characterization and applications foroptical micromanipulation

Simon J. Parkin, Robert Vogel, Martin Persson, Maren Funk,Vincent L. Y. Loke, Timo A. Nieminen, Norman R. Heckenberg

and Halina Rubinsztein-DunlopThe University of Queensland, Quantum Science Laboratory, School of Mathematics and

Physics, QLD 4072, Australia

[email protected]

Abstract: This paper reports on a simple synthesis and characterizationof highly birefringent vaterite microspheres, which are composed of20–30 nm sized nanocrystalls. Scanning electron microscopy shows a quitedisordered assembly of nanocrystals within the microspheres. However,using optical tweezers, the effective birefringence of the microsphereswas measured to be Δn = 0.06, which compares to Δn = 0.1 of vateritesingle crystals. This suggests a very high orientation of the nanocrystalswithin the microspheres. A hyperbolic model of the direction of the opticalaxis throughout the vaterite spherulite best fits the experimental data. Re-sults from polarized light microscopy further confirm the hyperbolic model.

© 2009 Optical Society of America

OCIS codes: (140.7010) Laser trapping; (160.1190) Anisotropic optical materials; (260.1180)Crystal optics; (260.1440) Birefringence; (350.4855) Optical tweezers or optical manipulation.

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1. Introduction

Since the first demonstration of optical tweezers [1], there has been little advance in the particlesused for trapping. The polystyrene and silica microspheres used in initial experiments turnedout to be very suitable for making precise force measurements [2, 3]. In fact, similar particlesare still used in more recent experiments concerned with studies of the force–velocity relation-ship of a biological motor and for adhesion and bonding strength [4, 5]. Yet there is room forfurther development, such as choosing a particle that allows for increased trap strength. Cre-ating a probe particle with an antireflection coating will increase the trap strength as a highercore refractive index can be used [6]. Another improvement is to introduce an extra degree ofcontrol of the particle. This can be achieved by selecting a highly birefringent particle so thatspin angular momentum from a circularly polarized light beam can be transferred to it [7].

There are many interesting and potentially useful applications of the rotation of vaterite par-ticles in optical traps. Their high birefringence results in large torques acting to spin or alignthe particles, and the torque can be measured optically [8]. This immediately opens the pathto many possible applications, such as torque spectroscopy of single molecules [9, 10, 11] ormolecular motors [12, 13]. Since rotation of a particle in a fluid results in flow of the fluidaround the particle, vaterite particles can be used as micropumps [14], or, when combined withtorque measurement, as sensors to measure the properties of the surrounding fluid [15, 16, 17].Such particles can also be used as “handles” for the manipulation of microscopic objects suchas cells which can be difficult to rotate or align directly [18]. They are also a suitable basis forthe development of improved methods for the application of controlled torques [19, 20].

Vaterite is a natural occurring calcium carbonate crystal [21]. Although it is rare in naturedue to its instability, it can be artificially synthesized, [22]. It is the least stable of three crys-talline polymorphs of calcium carbonate, the other two being calcite and aragonite. Vaterite hasa hexagonal crystal structure, with unit cell parameters a = 7.169 A and c = 16.98 A and Z = 12[23, 24]. Vaterite crystals typically form polycrystalline spherical particles that are microns indiameter, often referred to as spherulites. It is currently unclear whether the process of forma-tion of these vaterite spherulites is the result of nano-aggregation or classical spherulitic crystalgrowth [25, 26]. However it is known that the spherulites are comprised of single crystal sub-units that arrange with some degree of order that gives the spherulite an overall birefringence[27]. A “sheaf of wheat” structure within spherulites was proposed by Morse et al. [28]. Onecan imagine this structure as a bundle of fibers tied together at the center so that the ends fan outand as the number of fibers increases, and the fibers themselves grow, the ends close off to form


a sphere. The growth begins with a rod structure and progresses to a dumbbell shape, finallyclosing to form a sphere [29, 30, 31]. Although vaterite spherulites have been produced be-fore [25, 26, 24, 32], their birefringence hasn’t been quantified yet. Measurements that clearlydemonstrate a very strong birefringence of these particles, and a detailed discussion about theordered assembly of nanocrystals within the vaterite microspheres are presented in this paper.

Vaterite is generally synthesized through precipitation in a saturated aqueous solution con-taining calcium and carbonate ions. Various methods are used to favour the growth of vateriteover the other two calcium carbonate polymorphs, such as the presence of sulphate ions [22, 33]and temperature control [34]. Slow diffusion of ions tends to favour relatively large crystals[23], while vigorous agitation has been used to grow spherulites [25, 26, 35]. Various additiveshave been used to promote the growth of vaterite and affect its morphology, such as organicadditives for biomimetic growth, [36] double hydrophilic block copolymers for mesocrystalgrowth [37, 38], polyacrylic acid [39, 40] and polycarboxylic acid [41]. For our experimentswe have produced vaterite spheres via precipitation in a mixture of K2CO3 and CaCl2 solu-tions in a similar fashion to previously reported methods [22, 42, 43, 15]. However, we useda seeded growth method, resulting in higher yield and improved size uniformity compared tothe previous method developed in our lab [15]. The microspheres produced were typically 2to 5 μm in diameter [44]. The preference for vaterite formation is likely to be due to the ionicactivity product lying between the solubility product for amorphous calcium carbonate and thesolubility product for vaterite [25, 45].

2. Experimental section

2.1. Synthesis

Our production method can be broken down into two distinct parts; the first involving agitation,the second is a seeding technique. The first part is based on a previously published procedure[15]. In a typical synthesis aqueous solutions of CaCl2, K2CO3 and MgSO4 were prepared, allhaving a molarity of 0.1 M. 1.5 mL of CaCl2 was pipetted into a 5 mL plastic vial, followed by60 μL of MgSO4 and then 90 μL of K2CO3. The solution was agitated by vigorous pipetting ofthe solutions. To stabilise the products of the reaction, a few drops of Agepon (a wetting agentmade by Agfa) were added to the solution.

The second part involves the use of seeds to act as nucleation sites to promote crystal growth,which is a common technique and has previously been used for growth of vaterite spherulites[25, 39]. The method requires the same three solutions used in the first part of the method. 5 mLof CaCl2 is added to a 10 mL plastic vial, followed by 1.5 mL of MgSO4. After gentle mixingof the solution, 1 mL of K2CO3 is added, followed by a drop of seed solution. The solution isthen gently mixed and allowed to stand undisturbed for 5 minutes, after which Agepon is addedto halt the reaction and stabilize the crystal products.

The seed solution used is ideally one that contains monodisperse, spherical vaterite particlesonly. The product of this seeding tends to have a higher yield of the desired particles than theoriginal seed solution. This means that the product of seeding can then be used as a seed solutionitself to produce a new “generation” of vaterite products. With each new generation, the yield ofvaterite spheres increases. This method allows production of large enough quantities of vateritespherulites for experimentation and characterization.

X-ray diffraction (XRD) was used to determine the abundance of the different calcium car-bonate polymorphs in our samples and to estimate crystallite sizes. The diffraction patternswere measured using CuKα x-ray radiation in a Bruker Axs diffractometer.


2.2. Electron microscopy

Scanning Electron Microscopy (SEM) images of platinum coated samples were collected ona JEOL 6300. Crushed vaterite spherulites were prepared by grinding the ethanol suspensionwith a mortar and pestle before putting it on the sample holder. Bright field TEM images wererecorded on a JEOL 2010 using an operating voltage of 200 kV. Samples were prepared bycrushing vaterite microspheres and also by embedding microspheres in resin and then using amicrotome to produce a thin slice for viewing.

2.3. Laser tweezers

A laser beam was focussed to a diffraction-limited spot by high numerical aperture (NA =1.3) microscope objective. The free-space wavelength of the beam was 1064 nm, with 250 mWavailable at the focus.

Since the torque is due to spin angular momentum, it can be measured optically by deter-mining the Stokes parameters of the transmitted beam [46]. Since the beam is fully polarized,it is sufficient to measure the power of the left circularly polarized component, PL, and theright circularly polarized component, PR. Since the left circular component carries +h angu-lar momentum per photon, and the right component −h, the total angular momentum flux is(PL −PR)/ω , where ω is the optical angular frequency.

With a left circularly polarized trapping beam, and no particle in the trap, the angular mo-mentum flux will be P/ω , where P is the power of the beam at the focus. The change in theangular momentum flux due to the presence of a birefringent particle is the rate at which an-gular momentum is transferred to the particle, that is, the optical torque. The power of the leftand right circular components can be measured by using a λ/4 plate followed by a polarizingbeam splitter as a circular polarization beam splitter. A photodetector can be used to measurethe power in each of the outputs of the beamsplitter. Further details of the experimental setupand the technique have been described in [8, 16].

2.4. Modeling

The experimental data in Fig. 3(a) was fitted, using a finite difference frequency domain(FDFD) T-matrix method [47]. The distribution of the optical axis of vaterite (Fig. 3(b)) wasderived from a hyperbolic cylindrical coordinate system [48].

The Kohler illumination images in Fig. 4(b) were produced using a modeling method thatwe had developed for mesoscale microscopy. The method combines the T-matrix for the va-terite [47] (or any given particle) with the T-matrix for the imaging system, which is calculatedusing the far field point matching scheme from [49], incorporating methods to account for themicroscope objective and cross polarizer system. Since we want to simulate what is seen by theobjective, the fields outside the captured angles are treated as zero in the point matching scheme.The cross polarizer was simulated by applying the appropriate operator to the scattered field tofilter out one of the transverse electric field components.

3. Results and discussion

There are several techniques that can be used for the characterization of vaterite spherulites.These can be divided into those which help to understand the structure of the material andthose which give clear information on the optical properties.

X-ray diffraction (XRD) was used to examine the crystal structure. A typical pattern fromthe crystals is shown in Fig. 1. It displays strong peaks indicative of vaterite with an averagecrystal size of approximately 20–30 nm [50], which was calculated using the Debye–Scherrerformula [51]. The vaterite peaks are labeled with V, showing (004), (110), (112), (114), (211),


Fig. 1. X-ray diffraction spectrum of a typical sample, showing predominantly vaterite(diffraction peaks are indexed) and to a lesser degree calcite and aragonite polymorphs(unlabeled diffraction peaks).

(008), (300), (304) and (118) diffraction peaks from left to right. The XRD spectrum also showsthe presence of aragonite and calcite polymorphs (unlabeled peaks in Fig. 1). However, vateriteseems to be the dominant phase component in a typical sample.

Electron microscopy was conducted to investigate the surface and internal structure of thevaterite spherulites. Figure 2 shows scanning electron microscopy (SEM) and transmissionelectron microscopy (TEM) images of vaterite microspheres. It can be seen that the vateriteparticles are almost perfectly spherical and have quite a smooth surface with particle diametersranging from 1.5 to 2 μm (figures 2A,B). Closer inspection reveals a granular outer surface onthe particles, with a granule size of approximately 30 nm (Fig. 2(B)). An example of a vateriteparticle that has been cracked in half is shown in Fig. 2(C). A similar granular structure aspresent on the surface is observed in the interior of the vaterite particle. Another feature of theinterior is the presence of grooves that, in general, radiate from the centre of the particle givingthe appearance of a radial fibre-like structure.

Two TEM micrographs of vaterite particles that have been set in a resin and sliced intolayers thinner than 100 nm using a microtome, are shown in figures 2D,E. From these imagesit seems that either the vaterite particles are very porous, or that some of the material withinthe particle has fallen out of the resin during the slicing process. In fact, it seems likely thatboth have occurred, as the granular structure observed in the SEM images is consistent with


Fig. 2. SEM (A,B,C) and TEM (D,E,F) images of vaterite particles. Vaterite particles canbe grown almost perfectly spherical and with a smooth surface (A,B). A vaterite particlethat has been cracked in half is shown in C. TEM images of microtomed vaterite particlesat different magnifications are shown in D and E. A TEM micrograph of a fragment of avaterite particle is displayed in F. Moire patterns can be observed at various locations in thefragment.


porous particles. Both TEM images (figures 2D,E) also show that these vaterite spherulitesconsist of sub-units 20–30 nm in size, which agrees well with the SEM and XRD results. Weascertained that these sub-units are indeed crystalline by conducting TEM on a crushed sampleof vaterite particles, shown in Fig. 2(F). The crushed sample consisted of fragments of vateriteparticles that were thin enough at the edges to allow imaging with TEM. We observed Moirepatterns within the individual sub-units, which are characteristic of crystal planes in a crystallinestructure.

The vaterite spherulites have also been characterized by optical methods, which are of par-ticular interest, because the optical properties determine the behavior of a vaterite particle inan optical trap. In fact, the optical trap itself allows us to characterize the birefringence of in-dividual vaterite particles. The particles can be trapped and rotated using circularly polarizedlight and at the same time the applied torque can be measured optically. The details of the ex-perimental setup and the technique are briefly described in the method section and also in moredetail in [8, 16]. We measured the change in polarization caused by vaterite spherulites in thetrap, for particle diameters ranging from 2–11 μm. The results for this measurement are shownin Fig. 3. The data was fitted using the relation,

Δσs = 1− cos

(π

Dhalfd

)(1)

where Δσs is the change in circular polarization caused by the vaterite particle, Dhalf is thediameter of the vaterite particle that corresponds to a half wave plate and d is the vateriteparticle’s actual diameter. The degree of circular polarization is defined as σs = (PL −PR)/P,where PL and PR are the left and right circular powers, and P = PL −PR is the total power [8].Δσs is the difference between the circular polarization with and without a vaterite sphere in thetrap. For circularly polarized light, incident on a wave-plate, a quarter-wave retardation (i.e., aλ /4 plate) gives Δσs = 1, and half-wave retardation gives the maximum possible value Δσs = 2.Intermediate retardations give intermediate values of Δσs (Fig. 3).

From the fit, Dhalf = 11.3 μm, which can then be used to calculate the effective birefringenceof the vaterite particles,

Δn = 0.64λ/Dhalf = 0.06, (2)

where λ is the wavelength of the trapping laser. This compares to Δn = 0.1 for the vateritecrystal itself and to 0.087 for vaterite fibers [52, 27]. The result from equation 2 assumes thatthe vaterite spherulite has a uniform birefringence, or put another way, a unidirectional opticalaxis throughout the volume of the particle. From XRD and SEM results we can see that thesespherulites are composed of vaterite nanocrystals, which seem to have assembled in a rather dis-ordered manner. However, the high measured effective birefringence of these particles suggestsa very ordered arrangement of the crystalline subunits. In comparison a quartz single crystal isfar less birefringent (Δn = 0.009) than polycrystalline vaterite spheres. This allows more torqueto be applied to the vaterite microspheres in tweezer experiments.

We have addressed both the issues of non-uniform birefringence and the small size of theparticles by using a finite difference frequency domain (FDFD) T-matrix method to calculate thechange in circular polarization, a method which has previously been described in [47]. Figure3(a) shows the change in circular polarization due to vaterite particles of different diameters.The dashed curve is a fit to the data, which suggests that a vaterite with a diameter of 11.3 μmwill behave as a half wave plate. The dotted line shows the expected behaviour if the vateriteparticle had a birefringence of 0.1 and an optical axis that was uni-directional throughout itsvolume. The solid curve is the prediction by the FDFD T-matrix hybrid model, which assumesa hyperbolic distribution of the direction of the optical axis throughout the particle (Fig. 3(b)and best fits the experimental data.


A

B

�� )m

Fig. 3. The degree of spin generated in the optical trapping beam for varying particle di-ameters is shown in A. Results of various fitting models are also plotted. A hyperbolicdistribution of the optical axis (B) throughout the volume of the spherulites best fits theexperimental data.


Fig. 4. Vaterite particle, rotated to different angles in an optical trap, viewed betweencrossed polarizers. The diameter of the vaterite particle is approximately 10 μm (A). Bshows the calculated images of vaterite particle with a diameter of 6.6 λ .


A second optical technique that we have used to characterize the vaterite particles is polar-ization microscopy. By adding polarizers to our microscope we can view the optically trappedvaterite particle between crossed polarizers, which gives us an image of the birefringence of thevaterite particle as seen by the illumination light. Since vaterite is positive uniaxial, a trappedsphere will orient with its effective optic axis parallel to the electric field vector of the trap-ping beam. Using a half-wave plate in the trapping beam, the trapped vaterite particle can berotated to any angle about the beam-axis. Vaterite particles with 10 μm in diameter are shownin Fig. 4(a), rotated by 7.5 degree intervals through 180 degrees. Kohler illumination imagesfor a 6.6λ vaterite particle in Fig. 4(b) were produced using a modeling method that we haddeveloped for mesoscale microscopy. The method combines the T-matrix for the vaterite [47](or any particle) with the T-matrix for the imaging system. The sequence of patterns calculated(Fig. 4(b)), is in agreement with the experimental results, shown in Fig. 4(a). The Kohler il-lumination is further described in the method section. It should be noted that white light wasused in the cross polarization experiment whereas the calculation was based on monochromaticlight, with λ being the wavelength of the illumination light. The agreement of experiment andtheory strongly supports the hyperbolic model for the vaterite birefringence.

The value for the effective birefringence allows us to calculate the behavior of a vateriteparticle in a typical optical trap (optical power = 250 mW, wavelength = 1064 nm and the sur-rounding fluid is water). In particular we are interested in the effect of particle diameter onthe optical torque and the viscous drag torque, as shown in the top plot of Fig. 5. The dragtorque is for a sphere in water rotating at 50 Hz. The intersection of the two curves indicatesthat a vaterite sphere, 3.9 μm in diameter, will rotate at 50 Hz when trapped with 250 mW ofoptical power. The radius cubed dependence of the viscous drag means that vaterite particlesrotate much more slowly as the particle size increases (bottom plot in Fig. 5), despite the opticaltorque increasing with radius. It leads to the conclusion that if fast rotation rates are requiredfor an experiment, then small particles should be used. Note that these calculations use a geo-metric optics model that will not be very accurate for particles less than a couple of microns indiameter. The advantage of having a spherical particle is that the rotational viscous drag torquecan be easily calculated, as was done for Fig. 5.

4. Conclusion

In conclusion, we report here for the first time the production and characterization of extremelybirefringent vaterite microspheres. The effective birefringence of the microspheres was meas-ured to be Δn = 0.06, which is considerably higher than the birefringence of quartz single crys-tals. A hyperbolic model of the direction of the optical axis throughout the vaterite spherulitebest agrees with the experimental data. Based on their high birefringence these particles arebeing used in fields such as microrheology, microfluidics and the micromanipulation of singlebiological molecules.

Acknowledgements

We wish to acknowledge the help of the Centre for Microanalysis and Microscopy (CMM) atthe University of Queensland. This project was supported by the Australian Research Council.


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diameter (μm)

0

50

100

150

200

250

300to

rque

(pN

μm

)opticaldrag

Fig. 5. The top plot shows the dependence of the optical torque and the viscous drag torqueon the diameter of a vaterite particle. The optical torque is for a trapping beam with 250 mWof power at 1064 nm. The drag torque is for a sphere in water rotating at 50 Hz. The bottomplot shows the rotation rate of different sized vaterite particles in water with 250 mW oflaser power.


highly birefringent vaterite microspheres: production, characterization and applications for optical...

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