Pattern formation often reveals constituent nonlinear mechanisms of a complex system. Here, we study self-synchronizing, light-induced thermal cycles in plasmonically absorbing nanofluids, whose anomalous thermal, optomechanical, electrochemical, and hydrodynamic responses are not yet well understood. We show that the oscillatory behavior—caused by light grazing the nanofluid meniscus—exhibits a strong dependence on hydrogen bonding in the solvent environment and that there are low-intensity optical thresholds in alcohol–water binary-solvent nanofluids. Moreover, these thermal cycles occur with a periodic, vertically discharging heat-dissipation mechanism, which could be facilitated by nanobubbles or thermophoresis. We show that an incoherent white-light source, such as sunlight, will also induce self-synchronizing thermal cycles; in this demonstration, we illustrate new methods of energy storage, transfer, and harvesting that will not alter the natural carbon cycle of life.
© 2015 Optical Society of America
Metal nanofluids, i.e., liquid mixtures containing plasmonically absorbing nanoparticles, are appealing for their potential uses in numerous light harvesting applications [1,2]; however, control of the associated light-driven dynamics remain a challenge. Nanofluids exhibit complex behavior, with thermal conductivities far greater than those of the solvent alone [3 –7]. Local heating effects increase the mean free velocity of both surface and solvent charges that shift the chemical, electrical, and hydrodynamic equilibrium, particularly in the presence of heat or light [5,8 –12]. Correspondingly, nanoparticles associate with the solvent environment in a manner similar to molecules during solvation processes . Control of the light-driven nanofluid dynamics is further complicated by the temperature-dependent refractive indices, photoinduced pressure gradients, thermal or chemical diffusion processes, and changing reaction affinities with the nanoparticles [3,5,9,14]. The recently observed memory of nanofluids that occurs as a result of the applied DC magnetic fields [15,16] remains unexplained by conventional Mie scattering or light diffusion dynamics and may be a result of longer-lived changes in the solvent environment of the nanoparticle .
This investigation is centered on the oscillations or thermal cycles that spontaneously commence when light grazes the meniscus of the nanofluid [18 –20]. The spatiotemporal oscillations are previously established and point to a class of instabilities that occur via the asymmetric dissipation of heat near a “free interface,” i.e., the meniscus (see Ref.  for a review). A generic description of the periodic heat cycles follows: light illuminates a fluid, is strongly absorbed and converted to heat; the heat is transferred to the surrounding liquid; subsequently, the heated liquid expands and its refractive index is lowered; due to gravity, the hotter fluid rises, resulting in a higher refractive index below the light beam; light refracts toward the cooler fluid, providing an instability or a Marangoni flow that dissipates heat via the meniscus and the neighboring liquid; the liquid immediately above the beam cools; and the light Poynting vector is returned to its starting direction. This periodic behavior is broadly modeled by a “dripping faucet” or continuously charging/threshold-discharging capacitor , where limit cycles exhibit bifurcations and hysteresis. Figure 1 illustrates the cycle in four separate processes of the oscillations (light absorption, heat dissipation, light refraction, and convection) even though the processes occur with varying degrees, simultaneously.
Further complexity arises in our study of various polar organic-aqueous nanofluid mixtures (water with methanol, ethanol, isopropanol, acetone, or acetonitrile). In fact, alcohol–water binary mixtures exhibit numerous intriguing physical properties that may manifest in novel nonlinear effects in nanofluids. Partial molar volume, adiabatic compressibility, deviations in the expected heat capacity and viscosity, variable boiling point and light scattering, and ultrasonic speeds [22,23] are some anomalous behaviors of binary mixtures that have been documented for decades. Enhanced Marangoni convective flows with binary mixtures may play a role in the low-threshold illumination intensities necessary to produce the oscillatory modes . Our investigation highlights the solvent-dependent mechanical, chemical, thermal, and optical coupling of energy in alcohol–water nanofluids that are of broad interest and warrant further study.
We provide the first study of the thermal cycles in plasmonically absorbing nanofluids, which are produced at low illumination intensities in a stable, collimated-light geometry with alcohol–water nanofluid mixtures. Significantly higher intensities or focused-light geometries are necessary to produce the periodic cycles when instead pure aqueous solvents are chosen or when absorbing nanoparticles are not present. In the first part of our report, we show that the intermolecular hydrogen bonding in alcohol–water mixtures correlates with the reliable low-threshold production of the oscillations, which are subsequently controllable via the choice of polar organic-aqueous solvent. In the second part of this report, we provide numerical calculations of the temperature profiles, from which we extrapolate different heat-discharging mechanisms and associate the driving dynamics of the thermal cycles with alcohol–water binary fluids. In the final section of this report, we demonstrate that it is possible to drive the spontaneous thermal cycles with an incoherent white-light source in an isopropanol–water nanofluid.
The stock aqueous nanofluids [polyvinylpyrrolidone (PVP)-coated 80 nm gold, 0.05 mg/ml, Nanocomposix] compose one-fifth of each of the samples by volume. The remaining four-fifths are a mixture of either a protic (methanol, ethanol, or isopropanol) or an aprotic (acetone or acetonitrile) organic solvent and deionized water as the base solvent. Figure 2 shows the general experimental setup with a laser light source and further illustrates the periodic behavior that is the focus of this study. Light is polarized horizontally, with 2 ps pulse duration (), 300 mW average power, 1 MHz repetition rate, and a 0.9 mm beam diameter, and propagates through a 1 cm quartz cuvette containing the nanofluid. In contrast to prior work where light is focused onto or into a liquid sample, here light is collimated when it enters the plasmonically absorbing sample. The collimated-light setup reduces the likelihood of nanofluid degradation  and may provide more reliable oscillations.
In this system, light simultaneously drives and provides a signature of the nonlinear dynamics: the transmitted far-field beam exhibits power-dependent ring-like interference fringe patterns (Figs. 1 and 2, insets), which provide information about the energy transfer in the nanofluids. The transmitted beam interference patterns are clearly visible on a white screen placed 80 cm from the sample and the projected beam diameter is reduced or enlarged as a function of time. We image and record the far-field beam pattern at 30 frames per second with a CCD camera and quantify oscillations via the intensity-integrated unsaturated CCD images or by the beam power measured by a silicon photodetector in place of the screen (not shown). A motorized translation stage (MTS) translates the sample vertically. The characteristic frequency of the oscillations decreases as a function of depth from the meniscus [Fig. 2(e)].
The generated far-field pattern is stable when the beam depth is greater than 5 mm measured from the nanofluid–air interface; instabilities are observed when the beam grazes the meniscus above this depth. The subsequent oscillations vary with light-entrance depth and with solvent mixture, and in general, the periodic oscillations are not purely sinusoidal. We plot the Fourier decomposition of the integrated CCD images as a function of depth in each nanofluid mixture in Fig. 3. From left to right, the organic solvent contribution for each nanofluid increases from 1 part solvent/3 parts deionized water/1 part aqueous stock nanofluid solution () to 3 parts solvent/1 part deionized water/1 part aqueous stock nanofluid solution (). Figure 3 shows acetone, acetonitrile, methanol, ethanol, and isopropanol mixtures from top to bottom, arranged in order of increasing proticity.
Distinct differences between polar protic (alcohols) and aprotic (acetone and acetonitrile) organic–aqueous nanofluids are evident in the Fourier decomposition of the transmitted light patterns (Fig. 3). The light-induced oscillations are limited or negligible with polar aprotic organic–aqueous mixtures. In the alcohol–water mixtures, the oscillations vary with mixture and appear strongest when samples have a net composition ratio of of water to alcohol. This approximate ratio between water and alcohol corresponds to a change in sign of the Soret thermophoretic coefficient  and enhanced Marangoni flows , which may increase the thermal dissipation. Here, we show that the thermal cycles depend strongly on the hydrogen bonding of the alcohols in the nanofluid and correlate with the proticity of the solvent in the mixture. Therefore, the choice of binary mixture yields control of the nanofluid thermal dynamics.
The amplitudes of the oscillations are largest when light enters the nanofluid at an intermediate distance from the meniscus [Fig. 2(e)]. At this intermediate light-entrance depth, the Fourier decomposition shows the presence of additional harmonic oscillatory frequencies, or a sharp difference in the characteristic times for heat charging (absorption and storage) or discharging (thermal dissipation). Analysis of the heat equation indicates that the maximal oscillations are related to higher temperatures: if we assume negligible heat dissipation at the meniscus–air interface, then the highest steady-state temperature is produced when a light beam enters at a depth of approximately one beam diameter below the liquid–air interface. The characteristic oscillatory frequencies decrease as the entrance depth increases and could be a result of lower nanofluid temperatures and reduced heat dissipation rates. Figure 3 indicates that the energy storage and transfer in the thermal cycles are tunable with solvent, yet the underlying physical mechanisms remain unclear—particularly in relation to the properties of the binary mixture.
In an effort to understand the dynamics of the binary mixture, we scrutinize the concentration-dependent transmission and focus solely on aprotic acetone and protic isopropanol, each in a mixture with water alone, without the plasmonically absorbing 80 nm gold nanoparticles. Figure 4 shows the optical transmissions of aqueous-acetone and aqueous-isopropanol mixtures in 1 cm quartz cuvettes, which are measured at varying volume ratios with 532 nm, 2 ps, 150 nJ laser pulses. Prior to measuring, samples were stirred and visually inspected to ensure homogeneity, and each transmission measurement is averaged over 50 s. In contrast to the measured linear transmissions of acetone–water mixtures associated with a Maxwell–Garnett effective-medium approximation, alcohol–water binary mixtures exhibit a 10% dip in transmission when the volume ratio of alcohol to water is . The sharp absorption coincides with strong hydrogen bonding with the reported presence of alcohol–water nanocage structures, and with an anomalous and increased thermal conductivity [13,25 –30], as discussed further in Section 4. We experimentally observe that ethanol and methanol aqueous mixtures exhibit similar but less-pronounced transmission dips. The transmission dips are also less pronounced at higher illumination powers. An analysis of the potential heat dissipation mechanisms, as extrapolated from the transmitted optical behavior, follows in the next section.
We analyze the interference fringes, which are produced by shifts in the nanofluid refractive index as a result of variations in temperature or high light intensity; the intensity of the far-field fringe patterns are approximated by Fraunhofer diffraction:1) assumes light propagation in short optical-path-length samples and averages dynamics in the direction of light propagation.
Temperature-dependent changes in refractive index dominate the outlines of the far-field interference patterns; the effects of self-focusing and diffraction are present but are reduced in the presence of plasmonically absorbing nanoparticles. In fact, temperature-dependent phase shifts are more than an order of magnitude larger than Kerr effects. The temperature-dependent phase shift is
The heat and light that are absorbed depend on the distribution of nanoparticles, whose dynamics are challenging to model. Our quasi-steady-state thermal “snapshots” of the nanofluid assume that the absorption parameter varies over the nanofluid thermal cycle, but not spatially as a function of or . Here, we approximate that the nanoparticle density is uniform in the nanofluid, although we expect that several effects lead to the contrary. Gradient and scattering forces are not expected to significantly influence the nanoparticle density in our experimental setup, which employs a low-duty-cycle laser in a collimated geometry; gradient forces are several orders of magnitude smaller than scattering forces [31,32], which are of the same order as Brownian forces , or for average illumination intensities. In contrast, it remains an open question as to whether thermophoretic effects are significant. We expect that variations in the nanoparticle density would influence the optical absorption and the thermal profiles calculated here (see Section 4). In fact, experimentally, we observe that the gold nanoparticles move toward the laser beam profile; however, the thermophoretic coefficients for nanofluids are nonlinear and even change sign with mixed-solvent mixtures .
We calculate the average temperature profile from the far-field interferometric patterns and allow asymmetric thermal diffusion with the assumption of slow thermal changes governed by transverse diffusion and light absorption:
The larger far-field beam size and flat-topped asymmetry are produced by higher absorption and an appreciable vertical heat diffusion (a large with respect to ), as shown in Fig. 5. As increases and heat is increasingly dissipated in the vertical direction, the thermal gradient for is reduced. Subsequently, the far-field diffraction is also truncated as increases, leading to a flattened far-field intensity profile, , as illustrated in Figs. 5(b)–5(c). Moreover, the wider far-field patterns correspond with sharper heat gradients and higher light absorption. Marangoni and Rayleigh–Bénard convective flows partially explain how heat is dissipated in the vertical direction due to the rise of heated solvent toward the meniscus. A question remains as to the physical mechanism that leads to the extreme changes in absorption and heat dissipation in the vertical direction. There is evidence that as gold nanoparticles are illuminated, the surrounding solution can undergo a phase transition to a superheated metastable liquid state as an alternative to direct vaporization, which, upon cooling, collapses into mixed states of higher and lower density; this could account for the vertical motion of the nanoparticles . The dynamics of the water–solute interactions at this stage must both enhance and play a critical role in the low-light threshold heat oscillations. We also observe a cyclic nanoparticle flow in the vertical plane of the light via side-camera images that would be facilitated by nanobubbles, thermal blooming, and thermophoresis [10,11,32 –35].
From the numerical calculations and the far-field patterns, we extrapolate that varies by three orders of magnitude over the duration of one thermal cycle. The large and sudden changes in suggest a threshold heat-discharging mechanism that sharply accelerates the Marangoni flows, which could be explained by the finite heat of vaporization required to produce the nanobubbles. The formation of nanobubbles or vapor enclosures around hot nanoparticles would produce buoyant lifting forces and accelerate the removal of heat from the nanofluid center. Moreover, the simultaneous removal of plasmonically absorbing particles from the light path would also rapidly decrease the light that is absorbed. The presence of nanobubbles agrees experimentally with the time-dependent changes in the far-field patterns, where the diffraction pattern simultaneously shrinks as it gains the flat-topped asymmetry (insets in Figs. 1 and 2).
Knowledge of the thermal profiles and the presence of the heat dissipation alone does not adequately explain why the thermal cycles commence with organic protic-aqueous nanofluids (i.e., isopropanol) and not organic aprotic-aqueous nanofluids (i.e., acetone): acetone and isopropanol have similar viscosities and volatilities; in fact, acetone has a lower heat of vaporization than isopropanol, from which one would extrapolate a lower threshold for heat dissipation if facilitated by the presence of nanobubbles. We turn our attention to the nature of solute–solvent interactions, which directly influence the physical behavior of liquids [17,31,36] and account for the existence of water–alcohol clusters [13,27]. By contrasting the behavior of nanoparticles in aqueous solutions of acetone versus isopropyl alcohol, we note that acetone, unable to function as a proton donor either to other acetone molecules or to its solvent environment, is fully miscible in water with a correspondingly low entropy of mixing .
We claim that the concentration-dependent drop in the transmission of alcohol–water mixtures (Fig. 4) reflects an essential component of the low-intensity thermal cycles of the alcohol–water nanofluids studied here. With the addition of nanoparticles under laser illumination, these variations in concentration would manifest as noticeable changes in the optical properties. We suggest that the dynamic changes in sample transmission and conductivity occur via concentration variations in the local mixture, which toggle the heat storage and dissipation mechanisms: during the discharge or heat-dissipation process, alcohol is preferentially vaporized and ejected with hot nanoparticles from the beam center. The discharge mechanism would decrease the ratio of alcohol to water as the temperature drops; subsequently during the reset process, close to the critical threshold of alcohol:water, the generation of nanobubbles is clamped, the transmission of the matrix decreases significantly; more heat is absorbed and dissipated by the solvent and less heat is absorbed by the nanoparticles; and the charging or heat storage cycle recommences.
Isopropyl alcohol and water show inhomogeneities in mixing and show evidence for supermolecular structure formation at the critical threshold of alcohol:water. Although there is not yet consensus on the exact nature of these structures, it has been shown that these structures are long-lived, i.e., stable beyond the time scales of experiments [13,27,38]. Alcohol–water mixtures are often considered to be miscible, but are in fact anisotropic; cluster radii are theoretically calculated and experimentally verified to be as large as 2.6 Å [39,40]. Through Kirkwood–Buff integration theory, the critical volume fraction of 0.32 isopropanol:water maximizes the intermolecular self-interaction energies  that provide a cluster volume surrounding the isopropanol molecules.
Our report marks the beginning of understanding how alcohol–water binary mixtures may be exploited for optical applications. The interplay of alcohol–alcohol, alcohol–water, and water–water hydrogen bonding leads to unusual optical characteristics that are underexplored. Further investigations with threshold-generated nanobubbles and azeotropic mixtures may yield new control over complex nanofluid dynamics associated with the excess entropy that arises from the incomplete mixing at the molecular level . The robust thermal cycles studied here would be useful for characterizing the solvent mixture and thermal diffusivity of binary liquids. The heat cycles may characterize optically induced modes for heat and energy transfer and may provide a mechanism by which the anomalous properties of liquids and mixtures may be further explored. The optical transmission spectra of alcohol–water mixtures indicate strong intermolecular interactions that might be exploited or utilized to more effectively absorb and convert the energy in broadband low-intensity light sources such as sunlight, which we further demonstrate experimentally.
Oscillations are produced when a low-average-power, 1.3 W, continuous incoherent xenon-lamp source (collimated to a 1.4 mm beam) grazes the meniscus of a silver nanofluid. The silver nanofluid contains 20% aqueous stock (equal parts of PVP-coated 60 nm nanospheres, 650 nm resonant nanoplatelets, and 750 nm resonant nanoplatelets, 0.05 mg/ml, Nanocomposix) with 40% isopropanol and 40% deionized water. The transmission spectrum of the silver nanofluid is shown in Fig. 6(a). With a setup similar to that in Fig. 1 (replacing the laser with a collimated lamp source), we measure the transmitted power as a function of time and show the depth-dependent decrease of the characteristic frequency. The fluctuations of the transmitted power are plotted at different depths in Fig. 6(b), where the peak-to-peak amplitudes vary between 1% and 3%. The Fourier transform of the measured transmission is plotted as a function of depth in Fig. 6(c); from this plot, we extrapolate that the broadband light excitation provides a comparable effect to that achieved using a pulsed coherent-source laser even though the time-varying diffraction patterns are not observable. The data presented in Fig. 6 establish detectable oscillations that arise when the fluid is pumped with low-power, incoherent white light. The white-light-induced thermal cycles would be stronger by increasing the broadband nanoparticle absorption, tightening the collimation of the input beam, as well as by tuning the solvent mixture ratios.
In conclusion, we have shown that low-intensity light-pumped oscillations in nanofluids are enabled with the presence of alcohol as the polar organic solvent in deionized water mixtures. We propose that the preferential vaporization of alcohol in nanobubbles, in combination with the anomalous optical transmission and thermal behavior of alcohol–water binary mixtures, enables the thermal cycles to be produced at low light intensity thresholds. The corresponding thermal cycling, which characterizes a complex nonlinear system, provides a mechanism that can identify intermolecular hydrogen bonding associated with organic-aqueous binary mixtures, where small amounts of alcohol added to a nanofluid sample lead to the onset of the low-power-threshold heat oscillations. There exists further demand for investigations of the transmitted optical behavior with the thermal response of nanofluids and for determining the ideal environment that induces the instabilities in the nanofluids, i.e., investigating the contribution of gravity-induced concentration gradients , thermodiffusion, and Soret coefficients in water–solvent mixtures. Our understanding of the hydrogen bonding in alcohol-aqueous solutions may be relevant to the future designs of ion switches, optical pulse shaping techniques , engineered microfluidic flows [43,44], biomimetics , or ionic gradients [46 –50] for osmotic energy harvesting.
Division of Materials Research (DMR) (1151783).
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