NANO LETTERS
Single Nanoparticle Tracking Reveals Influence of Chemical Functionality of Nanoparticles on Local Ordering of Liquid Crystals and Nanoparticle Diffusion Coefficients
2009 Vol. 9, No. 7 2794-2801
Gary M. Koenig, Jr., Rizal Ong, Angel D. Cortes, J. Antonio Moreno-Razo, Juan J. de Pablo, and Nicholas L. Abbott* Department of Chemical and Biological Engineering, UniVersity of Wisconsin-Madison, 1415 Engineering DriVe, Madison, Wisconsin 53706 Received May 11, 2009
ABSTRACT This letter reports that darkfield microscopy can be used to track the trajectories of chemically functionalized gold nanoparticles in nematic liquid crystals (LCs), thus leading to measurements of the diffusion coefficients of the nanoparticles in the LCs. These measurements reveal that the diffusion coefficients of the nanoparticles dispersed in the LC are strongly dependent on the surface chemistry of the nanoparticles. Because the changes in surface chemistry are measured to have negligible influence on the diffusion coefficients of the same nanoparticles dispersed in isotropic solvents, we conclude that surface chemistry-induced changes in the local order of LCs underlie the behavior of the diffusion coefficients of the nanoparticles in the LC. Surface chemistry-dependent ordering of the LCs near the surfaces of the nanoparticles was also found to influence diffusion coefficients measured when the LC was heated above the bulk nematic-to-isotropic transition temperature. These experimental measurements are placed into the context of past theoretical predictions regarding the impact of local ordering of LCs on diffusion coefficients. The results that emerge from this study provide important insights into the mobility of nanoparticles in LCs and suggest new approaches based on measurements of nanoparticle dynamics that can yield information on the ordering of LCs near nanoparticles.
Introduction. The assembly of colloids into ordered structures has fundamental and practical importance. Structured colloidal arrangements can exhibit optical,1-5 electronic,6-8 and mechanical9-14 properties that depend strongly on the symmetry of the assembly, and they have been used as model systems to provide insights into quantum15 and molecular16,17 phenomena. In recent years, a number of investigators have reported on the behaviors of colloids dispersed in nematic liquid crystalline (LC) solvents. The elastic energy stored in strained states of the LC solvent as well as defects generated locally in the LC can lead to LC-mediated interactions (with energies of ∼103 kBT) that possess symmetries that differ substantially from those typically encountered in colloidal systems in isotropic solvents.18-28 These LC-mediated interactions have been used to drive colloids into a range of different types of ordered assemblies.22-27 In addition to investigating the thermodynamics of colloidal interactions mediated by LCs, several past studies have reported on the mobilities of colloids in LCs.18-22 Experi* To whom correspondence should be addressed. Tel: 608-265-5278. Fax: 608-262-5434. Email:
[email protected]. 10.1021/nl901498d CCC: $40.75 Published on Web 05/21/2009
2009 American Chemical Society
mental studies have established that the translational diffusion coefficient of a micrometer-sized colloid in a LC depends on the direction of displacement of the colloid relative to the far-field director of the LC.18-20,29 Theoretical investigations have predicted that the diffusion coefficient should also depend on the nature of the anchoring of the LC on the colloid surface,30-34 although no experimental tests of these latter theoretical predictions have been reported to date. In this letter, we report experimental measurements that confirm the predicted influence of surface chemistry, and thus ordering of the LC, on the mobility of colloids in LCs. In addition, in contrast to past experimental studies of the mobility of micrometer-sized colloids,18-22,29 we demonstrate methods that permit measurements of diffusion coefficients of nanoparticles in LCs by using gold nanoparticles in combination with darkfield microscopy. We note that several past studies of nanoparticles in LCs have been reported in the literature.35-45 In particular, nanoparticles have been dispersed into LCs with the goal of exploiting the optoelectronic properties of both nanoparticles and LCs.35-41 For example, ferroelectric nanoparticles dis-
persed in LCs have been found to lower the threshold voltage required to induce a Fredericksz transition in a LC.35,36 Also, nanoparticles have been found to preferentially segregate into defects and other localized regions of polymer-dispersed LCs37 and cholesteric LCs.38 Whereas these past studies have focused on the influence of the nanoparticles on the bulk properties of the LC35,36,39,40 and on the segregation of clusters of nanoparticles,37,38 the effects of LCs on the mobilities of isolated nanoparticles have not been studied. Of relevance to the study reported herein, we note that investigations by us and others have revealed that the ordering of LCs can be controlled at the surfaces of gold nanoparticles in ways that lead to changes in the optical properties (localized surface plasmon resonances) of the nanoparticles.42-45 In addition, a number of past studies employing numerical simulations have reported on the local ordering of LCs (and associated defects formed in the LC) around nanoparticles.30-33,46-51 In this paper, we build from these prior reports to describe experimental measurements of the impact of the surface chemistry of gold nanoparticles (and thus the local ordering of LCs) on the mobility of nanoparticles in LCs. Results and Discussion. In this study, we used gold nanoparticles purchased with nominal diameters of 150 nm (Ted Pella, Inc.). A scanning electron micrograph (SEM) of the gold nanoparticles dried on a silicon wafer is presented in Figure 1a. The actual distribution of diameters of the nanoparticles was determined from SEMs to be 169 ( 16 nm (determined from an analysis of 62 nanoparticles). To control the ordering of the LC near the surfaces of the nanoparticles, self-assembled monolayers (SAMs) were formed on the surfaces of the nanoparticles using alkanethiols. The nanoparticles were functionalized with either a single-component SAM formed from decanethiol or a mixed SAM formed from an 8:2 mixture (as prepared in solution) of decanethiol:hexadecanethiol. Using gold films evaporated onto silicon wafers, we determined the ellipsometric thicknesses of SAMs formed from decanethiol or hexadecanethiol to be 1.5 and 2.3 nm,52 respectively. Therefore, we conclude that the thickness of these SAMs will have a negligible direct impact (within the experimental uncertainty) on the hydrodynamic sizes of the nanoparticles in isotropic solvents (confirmed below). The two types of SAMs described above were selected because past studies have demonstrated that they lead to different surface-induced ordering of nematic LCs.53-57 In particular, past studies have shown that SAMs formed from decanethiol cause nematic phases of 4-pentyl4′-cyanobiphenyl (5CB) to assume an orientation parallel to a gold surface.53,54 In contrast, mixed SAMs formed from decanethiol and hexadecanethiol (at the composition noted above) will cause perpendicular (homeotropic) anchoring of nematic 5CB.53-55 These conclusions regarding the impact of surface chemistry on the orientational anchoring of nematic 5CB are also supported by localized surface plasmon resonance measurements of gold nanoparticles immersed under 5CB in which the optical properties of the gold nanoparticles were characterized as a function of surface chemistry.44,45 To functionalize the gold nanoparticles in the experiments reported in this paper, we used the following Nano Lett., Vol. 9, No. 7, 2009
Figure 1. (a) SEM image of gold nanoparticles on a silicon wafer. Scale bar is 1 µm. (b) Experimental setup for using darkfield microscopy to track gold nanoparticles dispersed in LC. (c) Darkfield optical micrograph of gold nanoparticles functionalized with decanethiol and dispersed in nematic 5CB. Scale bar is 10 µm.
procedure. Ethanolic solutions (absolute ethanol, AAPER) containing either 4 mM decanethiol (Sigma-Aldrich) or an 8:2 mixture of decanethiol:hexadecanethiol (total thiol concentration of 4 mM) were prepared. The gold nanoparticles, which were purchased as dispersions in water, were added to the ethanolic thiol solutions to form a single phase comprising 80% by volume ethanol and 20% water. After several hours of incubation at ambient temperature, we observed the nanoparticles to sediment; an observation that is consistent with surface chemical functionalization of the nanoparticles (the hydrophobic surfaces of the nanoparticles drives their aggregation and subsequent sedimentation under gravity).58 After an overnight incubation (20 h), the nanoparticles were centrifuged and rinsed five times with 5 mL of ethanol, and then dried under vacuum for 1 h. 5CB, heated into its isotropic phase (or a viscous isotropic oil, see below), was added to the dried nanoparticles and mixed by vortexing, sonication, and stirring. The volume fraction of gold nanoparticles in the dispersion of 5CB was maintained well below 1%. Prior to performing experiments with the nanoparticles, we confirmed that the solutions used to functionalize the nanoparticles led to planar (for SAMs formed from decanethiol) and perpendicular (for SAMs formed from the mixture of decanethiol and hexadecanethiol) anchoring of 2795
Figure 2. Director profiles for nanoparticles dispersed in LCs (a) with strong perpendicular anchoring of the LC, resulting in a Saturn ring defect, (b) with planar anchoring of the LC, resulting in a bipolar configuration with two boojum defects, and (c) with very weak anchoring of the LC, resulting in uniform LC ordering. Relative orientations of the LC director and the shear that define the three Miesowicz viscosities (d) νc, (e) νa, and (f) νb.
nematic 5CB on gold films evaporated on glass microscope slides (data not shown). Measurements of the diffusion coefficients of the nanoparticles were performed in optical cells that were made by confining the LC between two glass surfaces functionalized with dimethyloctadecyl[3-(trimethoxysilyl)propyl]ammonium chloride (DMOAP, Acros). The spacing between the two glass slides was established by using a 12 µm thick film of Mylar. Past studies have determined that DMOAP-treated glass causes perpendicular ordering of 5CB at the glass surface.59 The functionalized nanoparticles dispersed in the isotropic 5CB were drawn between the DMOAP-treated glass slides by capillary action. The 5CB was then allowed to cool into the nematic phase. After cooling into the nematic phase, the optical cell was equilibrated for at least an hour to eliminate convection that results from the process of filling the optical cell with 5CB. The nanoparticles dispersed in the LC film were imaged using a darkfield oil condenser on an Olympus BX60 microscope in combination with a 100× oil immersion objective that contained an internal aperture. The focal plane in which the nanoparticles were imaged was located 5 µm above the bottom surface of the optical cell. The experimental system is shown in Figure 1b. When using the darkfield condenser, the angle of incidence of the light rays is such that in the absence of scattering of light by a nanoparticle the incident light is not collected by the objective and the sample appears dark. For strongly scattering colloids such as the gold nanoparticles used in this study, light scattered by the nanoparticles is collected by the objective and thus the nanoparticles appear as bright features on a dark background. Because the scattering cross-section of gold nanoparticles is much larger than their physical diameter,60,61 2796
individual nanoparticles can be readily imaged using an optical microscope in the darkfield mode.62-64 In our preliminary experiments, we imaged nanoparticles with diameters as small as 20 nm. However, they were relatively faint, and we found the larger nanoparticles described in this paper easier to track and analyze. In future studies, we will report on these small nanoparticles. A typical darkfield image of gold nanoparticles (diameter of 169 nm) functionalized with SAMs formed from decanethiol and subsequently dispersed in the 12 µm thick film of nematic 5CB is shown in Figure 1c. We note that we found it important to prepare well-aligned LC films, as defects within the LC film (in the absence of nanoparticles) can scatter light, thus making identification of the nanoparticles difficult. These defects can also interact with the nanoparticles and thus influence measurements of diffusion coefficients. As noted above, the nanoparticles used in our experiments were chemically functionalized so as to promote either perpendicular or planar anchoring of the LC near each nanoparticle surface. Previous studies of micrometer-sized particles have shown that a variety of defect structures are observed around microparticles dispersed in uniformly aligned LC films. The type of defect formed has been shown to be dependent on the nature of the anchoring of the LC at the microparticle surface, although the influence of surface anchoring on the mobility of microparticles has not been reported.20,22-24,28 Microparticles with surface chemistry that causes perpendicular ordering of LCs form either (dipolar) hyperbolic “hedgehog” defects24-27 or (quadrupolar) “Saturn ring” defects (Figure 2a).24,27,29,65,66 In particular, particles with diameters of ∼1 µm that cause perpendicular anchoring of LC have been observed in experiments to exhibit Saturn Nano Lett., Vol. 9, No. 7, 2009
ring defects,29 and it has been predicted that the Saturn ring defect will be stable with respect to the hyperbolic hedgehog defect for small particles.28,46 Specifically, for the case of strong perpendicular anchoring at the particle surface, the energy of a Saturn ring defect has been predicted to become energetically favorable below a diameter of 540 nm and was predicted to be stabilized by an energy of more than 500 kBT (compared to the dipolar hyperbolic defect) for a particle with a diameter of 360 nm.28 Complementing these predictions made by numerically minimizing the Frank free energy,28,67 Monte Carlo simulations48,49 and dynamic field theory47-49 applied to nanoparticles (with diameters as small as tens of nanometers) that cause perpendicular surface anchoring of LCs predict the formation of Saturn ring defects.47-49 These results, when combined, lead us to conclude that the nanoparticles used in our experiments (diameters of 169 nm) with surface chemistry designed to cause perpendicular surface anchoring of the LC will likely possess Saturn ring defects (Figure 2a). Because of the symmetry of the experimental system, the plane containing a Saturn ring will lie parallel to the confining DMOABtreated surfaces (i.e., perpendicular to the far-field director). In contrast to the case of perpendicular anchoring of the LC, microparticles that cause planar anchoring of the LC at the microparticle surface have been experimentally observed to result in a bipolar director profile comprising two “boojum” defects,23,24 as depicted in Figure 2b. This topological defect is predicted to be stable with decreasing particle size, and thus we predict a bipolar configuration consisting of two boojum defects (Figure 2b) located at the top and bottom of the nanoparticles used in our experiments that are functionalized with a single-component SAM formed from decanethiol. However, we note that due to the small size of the nanoparticles used in our experiments, it is not possible to directly image the defects around the nanoparticles. Because of the symmetry of the above-described defects, we predicted that the diffusion coefficients of the nanoparticles would be the same in the two directions contained in the plane parallel to the confining surfaces, a result that we confirm below. In this paper, we do not attempt to characterize the mobility of the nanoparticles in the direction that is perpendicular to the plane of the confining surfaces.18,20,29 The trajectories of the nanoparticles obtained from darkfield microscopy were stored and analyzed using methods described elsewhere.68 Typically, we recorded nanoparticle trajectories for approximately 180 s with an image acquisition rate of 30 ms/image. A typical trajectory of a nanoparticle functionalized to cause planar anchoring of the LC is shown in Figure 3a. The displacement of each nanoparticle between each frame was determined in both the x and y directions (arbitrarily defined in this geometry). These displacements were grouped into bins with widths of 10 nm, and a Gaussian function was then fit to this distribution of nanoparticle displacements to determine the diffusion coefficient. As discussed previously, the precision with which the nanoparticles can be located is better than 10 nm20,22,68 and the bin sizes used in our analyses are consistent with previous reports.69 Figure 3b shows the distribution of displacements Nano Lett., Vol. 9, No. 7, 2009
Figure 3. (a) Measured trajectory of a gold nanoparticle functionalized with a decanethiol SAM in nematic 5CB. (b) Distribution of particle displacements for a gold nanoparticle functionalized with a decanethiol SAM in nematic 5CB.
for a nanoparticle with surface chemistry that causes planar anchoring of 5CB. The Gaussian function fit to the data has the form P(δ,τ) ) Po × exp(-δ2/∆⊥2(τ)),29,68 where P is the probability that the nanoparticle will diffuse a distance δ in time τ with a normalization constant of the distribution of Po. The width of the distribution, 2∆⊥, was measured in the two orthogonal directions perpendicular to the bulk director. The diffusion coefficient perpendicular to the bulk director, D⊥, of the nanoparticle is related to ∆⊥ by D⊥)∆⊥2/ 2dτ,29,68 where d is the dimension of the trajectory (1, 2, or 3). Below, we interpret these diffusion coefficients using the Stokes-Einstein equation, D⊥) kBT/(6πνR),29,68 where kB is the Boltzmann constant, T is the absolute temperature, ν is the effective viscosity of the medium surrounding the nanoparticle, and R is the nanoparticle radius. Before measuring the diffusion coefficients of the nanoparticles in the LC, we verified that we could accurately measure the diffusion coefficients of the nanoparticles using isotropic solvents. First, we measured the diffusion coefficient of the gold nanoparticles in water (prior to chemical functionalization with SAMs) to be 272 ( 16 × 10-2 µm2/s (determined from measurements of 24 nanoparticles). We note that the standard deviation of the diffusion coefficient is influenced by the variation of nanoparticle sizes within the population of nanoparticles that were analyzed. For convenience, all diffusion coefficients reported in this paper 2797
Table 1. Diffusion Coefficients and Apparent Viscosities Measured for the Nanoparticles Used in This Study and Relevant Reference Viscosities viscosity (mPa·s)
diffusion coefficient (10-2 µm2/s)
nanoparticles functionalized with decanethiol; in isotropic oil 25.3 ( 3.2 nanoparticles functionalized with 8:2 decanethiol: 25.1 ( 2.5 hexadecanethiol; in isotropic oil viscosity of isotropic oil measured using capillary viscometer 25.7a nanoparticles functionalized with decanethiol; in nematic 5CB 39.2 ( 3.1 nanoparticles functionalized with 8:2 decanethiol: 58.9 ( 7.2 hexadecanethiol; in nematic 5CB calculated effective viscosity perpendicular to director for 85.3b particle with saturn ring defect Miesowicz viscosity parallel to director for 5CB (νb) 22.9b Miesowicz viscosity perpendicular to director for 5CB (νa) 37.4b Miesowicz viscosity perpendicular to uniform homeotropic 129.6b director for 5CB (νc) nanoparticles functionalized with decanethiol; in isotropic 5CB 19.2 ( 3.3 at 40 °C nanoparticles functionalized with 8:2 decanethiol: 25.3 ( 3.1 hexadecanethiol; in isotropic 5CB at 40 °C isotropic 5CB at 40 °C 22c nanoparticles, as purchased; in water 0.943 ( 0.056 a Isotropic oil was a mixture of hexadecane (30% vol) and mineral oil. b Taken from ref 34. c Taken from ref 70.
are compiled in Table 1. For comparison, the diffusion coefficient of a nanoparticle in water was calculated from the nanoparticle radius obtained from the electron micrographs (Figure 1a) and the Stokes-Einstein equation. The value was calculated to be 275 ( 26 × 10-2 µm2/s with the uncertainty due to the nanoparticle size distribution (the viscosity of water was assumed to be 0.933 mPa·s70). This value is in good agreement with the diffusion coefficient determined from the nanoparticle trajectories. We also measured the diffusion coefficient of the nanoparticles in an isotropic oil, after functionalization of the nanoparticles with the two types of SAMs described above. We sought to confirm that the SAMs did not measurably impact the diffusion coefficients of the nanoparticles measured in the isotropic oil (see comments above, regarding the thicknesses of the SAMs). The isotropic oil used in our measurement was a mixture of hexadecane and mineral oil (30 vol % hexadecane), which we determined to have a viscosity of 25.7 mPa·s using a capillary viscometer. We formulated this mixture because it has a viscosity that is similar to the apparent viscosity experienced by the nanoparticles in nematic 5CB (see below).34 Within this isotropic oil, we measured the diffusion coefficient of the decanethiolfunctionalized nanoparticles to be 10.2 ( 1.3 × 10-2 µm2/s (determined from measurements of 22 nanoparticles) and the diffusion coefficient of the mixed SAM-functionalized nanoparticles to be 10.3 ( 1.0 × 10-2 µm2/s (determined from measurements of 25 nanoparticles). These two values, which are in close agreement, are also very close to the diffusion coefficient calculated using the Stokes-Einstein equation for a nanoparticle with a diameter of 169 nm dispersed in an oil with a viscosity of 25.7 mPa·s (10.1 ( 1.0 × 10-2 µm2/ s). In conclusion, these measurements confirm that the presence of the two different SAMs on the nanoparticles did not have a measurable effect on the diffusion coefficients of the nanoparticles in the isotropic oil. The diffusion coefficients measured by particle tracking in isotropic solvents are also in good agreement with the diffusion coefficients calculated from the Stokes-Einstein equation. 2798
10.2 ( 1.3 10.3 ( 1.0 6.58 ( 0.52 4.38 ( 0.53
14.1 ( 2.3 10.7 ( 1.3 272 ( 16
Next, we sought to determine if the presence of the two different types of SAMs on the nanoparticles would result in changes in the diffusion coefficients of the nanoparticles in nematic 5CB. The first nanoparticles that we studied were functionalized with mixed SAMs that promoted perpendicular anchoring of the LC on the surfaces of the nanoparticles. We note that past studies have reported measurements of diffusion coefficients for micrometer-sized particles that promote perpendicular anchoring of the LC with a focus on determining the difference between the diffusion coefficients measured either parallel or perpendicular to the far-field orientation of the director of the LC.18,20,29 In those experiments, the influence of changes in the surface chemistry of the micrometer-sized particles (and thus surface-induced ordering of the LC) was not investigated. As mentioned above, in our experiments we have focused on quantifying the effects of surface chemistry-induced ordering of the LC on the diffusion coefficients measured in directions perpendicular to the far-field director (defined as x and y directions). For the nanoparticles functionalized with mixed SAMs, we measured the diffusion coefficient in the x direction to be 4.43 ( 0.48 × 10-2 µm2/s and in the y direction to be 4.33 ( 0.59 × 10-2 µm2/s (determined from measurements of 41 nanoparticles). Within experimental error, these two diffusion coefficients are indistinguishable, which is consistent with the presence of nanoparticles with Saturn ring defects contained within a plane that is parallel to the confining surfaces (Figure 2a). From the above measurements, we conclude that the average diffusion coefficient of the nanoparticles chemically functionalized to cause perpendicular anchoring of the LC is 4.38 ( 0.53 × 10-2 µm2/s. By using the average diameter of the nanoparticles (measured to be 169 nm) and the Stokes-Einstein equation, the effective viscosity experienced by these nanoparticles (translating in a direction perpendicular to the far-field director) was calculated to be 58.9 ( 7.2 mPa·s. To put this result into perspective, we note that for nematic 5CB, there exist three Miesowicz shear viscosities.34 The largest of these viscosities, νc (Figure 2d), is 129.6 mPa·s, Nano Lett., Vol. 9, No. 7, 2009
corresponding to a shear flow with the velocity perpendicular to the director. The intermediate viscosity, νa (Figure 2e), has a value of 37.4 mPa·s and is measured when the shear direction is perpendicular to a uniform director field. Shear flow along the director is characterized by the lowest of these three viscosities, νb (Figure 2f), and its value for 5CB is 22.9 mPa·s. The effective viscosity measured for a nanoparticle with a surface that causes perpendicular anchoring of the LC that is diffusing perpendicular to the far-field nematic director has been predicted to lie between νa and νc,34 consistent with the value of 58.9 mPa·s that we measured. That the effective viscosity lies between νa and νc can be understood by reference to the illustration of the nanoparticle with a Saturn ring defect shown in Figure 2a. Very near the nanoparticle surface (inside the Saturn ring), the director is oriented in the radial direction. When the nanoparticle translates in the plane of the Saturn ring, the shear flow will possess a local velocity perpendicular to the director (thus the apparent viscosity is bounded by νc (Figure 2d)). However, in regions beyond the Saturn ring there will be some volumes of the LC where the shear direction is perpendicular to the director, thus corresponding to an apparent viscosity of νa (Figure 2e). These considerations lead to the conclusion that the overall effective viscosity should lie between νa and νc (provided the director profile is not perturbed by the flow; see below). In ref 34, the effective viscosities experienced by particles with Saturn ring defects were calculated by solving the Ericksen-Leslie equations. These calculations lead to the prediction that the effective viscosity for a particle with a Saturn ring defect translating in a direction perpendicular to the far-field bulk director of nematic 5CB at 25 °C would be 85.3 mPa·s. We note that the calculation was performed in the limit of an Ericksen number much less than unity (the Ericksen number is defined as νv∞R/K, where ν is the viscosity of the fluid surrounding the particle, v∞ is the velocity of the fluid far from the particle, R is the particle radius, and K is the Frank elastic constant of the LC), corresponding to the physical situation where viscous forces do not influence the orientation of the director. In our experiments, we estimate the Ericksen number to be
