Xiaolai Li1,2, Yuliang Wang2,2, Mikhail E Zaytsev1,1, Guillaume Lajoinie1,1, Hai Le The1,1, Johan G Bomer1, Jan C T Eijkel1, Harold J W Zandvliet1, Xuehua Zhang1,3, Detlef Lohse1,4. 1. Physics of Fluids, Max Planck Center Twente for Complex Fluid Dynamics and J.M. Burgers Centre for Fluid Mechanics, MESA+ Institute, Physics of Interfaces and Nanomaterials, MESA+ Institute, TechMed Centre, and BIOS Lab-on-a-Chip, MESA+ Institute, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands. 2. Robotics Institute, School of Mechanical Engineering and Automation and Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, P.R. China. 3. Department of Chemical and Materials Engineering, Donadeo Innovation Centre for Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada. 4. Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, 37077 Göttingen, Germany.
Abstract
Under continuous laser irradiation, noble metal nanoparticles immersed in water can quickly heat up, leading to the nucleation of so-called plasmonic bubbles. In this work, we want to further understand the bubble nucleation and growth mechanism. In particular, we quantitatively study the effect of the amount of dissolved air on the bubble nucleation and growth dynamics, both for the initial giant bubble, which forms shortly after switching on the laser and is mainly composed of vapor, and for the final life phase of the bubble, during which it mainly contains air expelled from water. We found that the bubble nucleation temperature depends on the gas concentration: the higher the gas concentration, the lower the bubble nucleation temperature. Also, the long-term diffusion-dominated bubble growth is governed by the gas concentration. The radius of the bubbles grows as R(t) ∝ t 1/3 for air-equilibrated and air-oversaturated water. In contrast, in partially degassed water, the growth is much slower since, even for the highest temperature we achieve, the water remains undersaturated.
Under continuous laser irradiation, noble metal nanoparticles immersed in water can quickly heat up, leading to the nucleation of so-called plasmonic bubbles. In this work, we want to further understand the bubble nucleation and growth mechanism. In particular, we quantitatively study the effect of the amount of dissolved air on the bubble nucleation and growth dynamics, both for the initial giant bubble, which forms shortly after switching on the laser and is mainly composed of vapor, and for the final life phase of the bubble, during which it mainly contains air expelled from water. We found that the bubble nucleation temperature depends on the gas concentration: the higher the gas concentration, the lower the bubble nucleation temperature. Also, the long-term diffusion-dominated bubble growth is governed by the gas concentration. The radius of the bubbles grows as R(t) ∝ t 1/3 for air-equilibrated and air-oversaturated water. In contrast, in partially degassed water, the growth is much slower since, even for the highest temperature we achieve, the water remains undersaturated.
When noble nanoparticles immersed in water
are irradiated by a
continuous wave laser at their resonance frequency, a huge amount
of heat is explosively produced. This leads to a rapid temperature
increase and hence to the vaporization of the surrounding water, resulting
in the formation of microsized bubbles. These bubbles are referred
to as plasmonic bubbles.[1−3] The plasmonic bubbles are relevant
to various applications, such as biomedical diagnosis and cancer therapy,[4−6] solar energy harvesting,[2,7−9] micromanipulation of nano-objects,[10−13] and locally enhanced chemical
reactions.[1,14] To exploit their potential applications,
it is of key importance to understand the nucleation mechanism and
explore the growth dynamics of these bubbles.The formation
of plasmonic bubbles involves complex physical processes,
including optothermal conversion, heat transfer, phase transitions,
gas diffusion, and many others.[2,3,15−18] In these processes, many factors are relevant, such as particle
arrangement,[13] laser power,[19] liquid type,[20] and
gas concentration.[3,15] Among these factors, gas concentration
plays a crucial role in the formation and growth of plasmonic bubbles,
like in the formation of other types of micro/nanoscale surface bubbles.[21−23] This has been addressed in several studies[3,15,24] but ignored by many others.[25−27] By investigating the shrinkage dynamics of plasmonic bubbles, Baffou
and co-workers found that the plasmonic bubbles could survive for
several hundreds of seconds after the irradiation laser was switched
off.[15] This is due to the fact that the
bubbles are actually not vapor bubbles but mainly contain gas that
was originally dissolved in the liquid.[17] Later, Liu et al. generated microbubbles at highly ordered plasmonic
nanopillar arrays and observed a larger growth rate in air-equilibrated
water than that in partially degassed water, which underlines the
important role that the dissolved gas plays in the bubble formation.[3]Recently, we conducted a systematic study
of the plasmonic bubble
nucleation mechanism[18] and growth dynamics.[17] We found that plasmonic microbubble nucleation
and evolution in water can be divided into four phases: an initial
giant vapor bubble (phase 1), oscillating bubbles (phase 2), a vaporization-dominated
growth phase (phase 3), and finally, a gas diffusion-dominated growth
phase (phase 4).[17,18] Dissolved gas governs the bubble
dynamics, especially for phases 1 and 4. In phase 1, water surrounding
the laser-irradiated gold nanoparticles becomes superheated, that
is, reaching a temperature that substantially exceeds the boiling
temperature.[15,16,28−31] Consequently, vapor bubbles nucleate, grow, and then become microsized
bubbles. In partially degassed water, the lower gas concentration
leads to less nuclei and thus to suppression of the nucleation of
bubbles. As a result, the superheat temperature in partially degassed
water is higher than in air-equilibrated water, and it requires a
longer illumination time in partially degassed water before the nucleation
of the bubbles sets in. In phase 4, bubbles enter the long-term growth
regime. This phase is dominated by the influx of dissolved gas from
the surrounding water. Experimental results show that the bubble radius
roughly scales as R(t) ∝ t1/3 in air-equilibrated water, which is distinctly
different from the scaling in partially degassed water,[17] where the bubbles in the long-term hardly grow
at all. For both kinds of behavior, R(t) ∝ t1/3 for the gaseous case
and R(t) ≈ const for the
strongly degassed case, a theoretical explanation was given.[18]Despite the above-mentioned studies of
the dissolved gas effect
on bubble nucleation and growth dynamics, a quantitative understanding
and investigation for systematically varying gas saturation are still
lacking. In this work, such a systematic investigation is performed
at six different relative concentrations c∞/cs of dissolved gas, ranging from highly
degassed to oversaturated water. Here, c∞ is the actual gas concentration, and cs is the saturation concentration. This allows us to establish the
detailed dependence of the dynamic parameters of bubble formation
on the gas concentration. The understanding from this work facilitates
the control of plasmonic bubble formation in related applications.
Methods
Sample
Preparation
A fused-silica surface patterned
with an array of gold nanoparticles was used to produce plasmonic
bubbles. A gold layer of ∼45 nm was first deposited on an amorphous
fused-silica wafer by using an ion-beam sputtering system (home-built
T′COathy machine, MESA+ NanoLab, Twente University). A bottom
antireflection coating (BARC) layer (∼186 nm) and a photoresist
(PR) layer (∼200 nm) were subsequently coated on the wafer.
Periodic nanocolumns with diameters of ∼110 nm were patterned
in the PR layer using displacement Talbot lithography (PhableR 100C,
EULITHA).[32] These periodic PR nanocolumns
were subsequently transferred at the wafer level to the underlying
BARC layer, forming 110 nm BARC nanocolumns by using nitrogen plasma
etching (home-built TEtske machine, NanoLab) at 10 mTorr and 25 W
for 8 min. Using these BARC nanocolumns as a mask, the Au layer was
subsequently etched by ion beam etching (Oxford i300, Oxford Instruments,
U.K.) with 5 sccm Ar and 50–55 mA at an inclined angle of 5°.
The etching for 9 min resulted in periodic Au nanodots supported on
cone-shaped fused-silica features. The remaining BARC was stripped
using oxygen plasma for 10 min (TePla 300E, PVA TePla AG, Germany).
The fabricated array of Au nanodots was heated to 1100 °C in
90 min and subsequently cooled passively to room temperature. During
the annealing process, these Au nanodots reformed into spherical-shaped
Au nanoparticles. Figure a shows the schematic of a gold nanoparticle sitting on a
SiO2 island on a fused silica. The energy-selective backscatter
(ESB) and scanning electron microscopy (SEM) images of the patterned
gold nanoparticle sample surface are shown in Figure b, left and right, respectively.
Figure 1
(a) Schematic
of a gold nanoparticle sitting on a SiO2 island on a fused-silica
substrate, (b) energy-selective backscatter
(left) and scanning electron microscopy (right) image of the patterned
gold nanoparticle sample surface, and (c) schematic diagram of the
optical setup for plasmonic microbubble imaging.
(a) Schematic
of a gold nanoparticle sitting on a SiO2 island on a fused-silica
substrate, (b) energy-selective backscatter
(left) and scanning electron microscopy (right) image of the patterned
gold nanoparticle sample surface, and (c) schematic diagram of the
optical setup for plasmonic microbubble imaging.
Gas Concentration Control
During experiments, the nanoparticle-decorated
sample surface was immersed in deionized (DI) water (Milli-Q Advantage
A10 System, Germany). Experiments were separately executed to explore
the effect of gas concentration both on the nucleation dynamics of
the initial giant bubbles and on the long-term diffusive growth dynamics
of the plasmonic bubbles. For the latter, six different gas concentration
levels of c∞/cs = 0.55, 0.65, 0.75, 0.85, 0.96, and 1.20 were used.
For the initial giant bubbles, the nucleation dynamics only depends
weakly on the gas concentration, and therefore, we have only considered
three different gas concentrations of c∞/cs = 0.10, 0.80, and 1.20. All experiments
were conducted at 25 °C and 1 atm.The oversaturated water
was prepared by keeping the water at 4 °C for 12 h and then warming
up to the room temperature of 25 °C. After that, the measured
gas concentration c∞/cs was 1.2 (by an oxygen meter, Fibox 3 Trace, PreSens).
For the air-equilibrated water, a sample bottle containing DI water
was kept open in air for 10 h, and the measured gas concentration
is 1.0. Similarly, the nearly air-equilibrated water with c∞/cs = 0.96
was obtained by keeping the water in air for 8 h. To prepare partially
degassed water with different gas concentration values, the water
was first degassed for 30 min in a vacuum chamber, and then the concentration
of 0.1 was obtained. Subsequently, we kept the bottle of the highly
degassed water open in air, with the probe of the oxygen meter immersed
in the water. The gas concentration in the water was adjusted by varying
the air exposure time.
Setup Description
The experimental
setup for plasmonic
microbubble imaging is shown in Figure c. The gold nanoparticle-decorated sample was placed
in a quartz glass cuvette and filled with water. A continuous-wave
laser (Cobolt Samba) of 532 nm wavelength with a maximum power of
300 mW was used for sample irradiation. An acousto-optic modulator
(Opto-Electronic, AOTFncVIS) was used as a shutter to control the
laser irradiation on the sample surface. A pulse/delay generator (BNC
model 565) was used to generate two different laser pulses of 400
μs and 4 s to study the short-term and long-term dynamics of
microbubbles, respectively. The laser power was controlled by using
a half-wave plate and a polarizer and measured by a photodiode power
sensor (S130C, ThorLabs). Two high-speed cameras were installed in
the setup. One (Photron SA7) was equipped with a 5× long working
distance objective (LMPLFLN, Olympus), and the other (Photron SA1)
was equipped with various long working distance objectives [10×
(LMPLFLN, Olympus) and 20× (SLMPLN, Olympus)] and operated at
various frame rates from 5 kfps up to 540 kfps. The first camera was
used for top-view imaging, and the second one was for side-view imaging.
Two light sources, Olympus ILP-1 and Schott ACE I, were applied to
provide illumination for the two high-speed cameras. The optical images
are processed with a home-designed image segmentation algorithm for
the optimized extraction of the bubble radius in MATLAB.[33−35]
Results and Discussion
Giant Bubble Nucleation
The influence
of gas concentration
on the nucleation of plasmonic bubbles was investigated with a high-speed
camera at a frame rate of 540 kfps. Figure shows the nucleation and evolution of giant
bubbles for three different gas concentration levels of c∞/cs = 0.1, 0.8, and
1.2, respectively, at the same laser power Pl = 130 mW. The moment that the laser is switched on is taken
as the origin of time, that is, t = 0 s. One can
see that, upon laser irradiation, the vapor microbubbles nucleate
after a delay time τd. Subsequently, the bubbles
rapidly grow and reach a maximum size in several microseconds (∼5
μs after nucleation), followed by a sudden collapse. As can
be seen in Figure , the maximum volume Vmax of the plasmonic
bubbles counterintuitively decreases with increasing c∞/cs, as discussed
in ref (18). This can
be explained by the increase in delay time τd.[18] A longer delay time results in a larger amount
of energy dumped into the system (before nucleation) and thus to a
larger initial giant bubble.
Figure 2
Initial giant bubble nucleation at different
gas concentration
levels of (a) c∞/cs = 0.1, (b) c∞/cs = 0.8, and (c) c∞/c = 1.2 at the same laser power Pl = 130 mW. The giant bubbles nucleate after
a delay (τd), which decreases with the increasing
gas concentration, namely, τd(c∞/cs = 1.2)
< τd(c∞/cs = 0.8) < τd(c∞/cs = 0.1), while the maximum bubble sizes are smaller at
higher gas concentrations.
Initial giant bubble nucleation at different
gas concentration
levels of (a) c∞/cs = 0.1, (b) c∞/cs = 0.8, and (c) c∞/c = 1.2 at the same laser power Pl = 130 mW. The giant bubbles nucleate after
a delay (τd), which decreases with the increasing
gas concentration, namely, τd(c∞/cs = 1.2)
< τd(c∞/cs = 0.8) < τd(c∞/cs = 0.1), while the maximum bubble sizes are smaller at
higher gas concentrations.The dependence of the delay time τd on the laser
power Pl at each gas concentration was
also investigated, as shown in Figure a. Due to the limited spatial resolution (∼1
μm) of the optical imaging system and the limited temporal resolution
(frame rate, 540 kfps) of the high-speed camera, the estimated error
in the determination of the delay time is ∼2 μs. Since
the delay time is in the order of a few hundreds of microseconds,
the relative error is less than 1%. It is clear that, at each gas
concentration c∞/cs, the delay time decreases with increasing laser power Pl. For a given laser power value, the delay
time decreases with an increasing gas concentration in water.
Figure 3
Dependence
of the delay time τd on gas concentration
for giant bubble nucleation. (a) Measured delay time τd as a function of laser power Pl at different
gas concentrations. At a given laser power, the higher the gas concentration,
the shorter the delay time. (b) Double-logarithmic plot of τd versus Pl. The measured τd is fitted using a heat diffusion model, whose results are
displayed with solid lines. The three curves are all located in between
the boiling temperature curve and the spinodal curve. (c) Obtained
nucleation temperature T by fitting τd for gas concentration c∞/cs = 0.1, 0.8, and 1.2. The higher gas
concentration results in a lower nucleation temperature, which indicates
that the dissolved gas facilitates the bubble nucleation.
Dependence
of the delay time τd on gas concentration
for giant bubble nucleation. (a) Measured delay time τd as a function of laser power Pl at different
gas concentrations. At a given laser power, the higher the gas concentration,
the shorter the delay time. (b) Double-logarithmic plot of τd versus Pl. The measured τd is fitted using a heat diffusion model, whose results are
displayed with solid lines. The three curves are all located in between
the boiling temperature curve and the spinodal curve. (c) Obtained
nucleation temperature T by fitting τd for gas concentration c∞/cs = 0.1, 0.8, and 1.2. The higher gas
concentration results in a lower nucleation temperature, which indicates
that the dissolved gas facilitates the bubble nucleation.To determine the nucleation temperature for each combination
of
laser power Pl and gas concentration c∞/cs, we
have solved a simple heat diffusion model (see ref (18)). By assuming a spherical
geometry and constant thermal properties, from that model, the temperature
evolution around a nanoparticle can be computed by solving the thermal
diffusion equation through a Fourier transformation. The thermal field
generated by the nanoparticle array is estimated through a linear
superposition of the temperature field generated by the individual
nanoparticles within the Gaussian laser beam.[18] The numerical results from this approach were used to fit the measured
delay time τd with a root-mean-square minimization
method. The fitted curves for the three concentration cases are shown
in the double-logarithmic plot of Figure b. In Figure b, the liquid–vapor line (i.e., Tb=100 °C for the boiling temperature) and spinodal
line (Ts = 305 °C for an ambient
pressure of 1 atm) were determined by numerically calculating how
long it takes to heat the liquid up to 100 and 305 °C, respectively,
for given laser power Pl. The estimated
nucleation temperatures from the fitting process are T1 = 190 °C (c∞/cs = 0.1), T2 = 212 °C (c∞/cs = 0.8), and T3 = 245 °C
(c∞/cs = 1.2). Figure c
shows the decreasing nucleation temperature with increasing gas concentration
level of c∞/cs from 0.1 to 1.2. This quantifies how the gas dissolved in
water facilitates the bubble nucleation.The dependence of the
vapor bubble nucleation on dissolved gas
has been pointed out in several other studies. Indeed, the presence
of tiny cracks, cavities or pits filled with gas, and impurities or
aggregations of gas molecules can act as nuclei for bubble nucleation.[15,16,28−31] These impurities in water reduce
the nucleation temperature T to a value
substantially lower than the liquid spinodal temperature[36−38] and thus enhance the nucleation of bubbles. When the gas concentration
is lower, the probability of forming gas nuclei is statistically reduced,[39] resulting in a higher T. Accordingly, the delay time τd will increase with
decreasing gas concentration, as demonstrated in Figure .In Figure , the
maximum bubble size Vmax is plotted versus
the total dumped energy E = Plτd, which is defined as
the accumulated laser energy in the illumination spot on the substrate
from the moment the laser is switched on until the moment of bubble
nucleation. Here, the laser energy input during the period of bubble
growth to its maximum volume is neglected. The reason that this can
be done is that, once a giant bubble is formed on the substrate, it
isolates the water from the gold nanoparticles, resulting in a strongly
suppressed energy transfer to the water. Moreover, it normally only
takes ∼5 μs for the initial giant bubble to grow to its
maximum value right after it appears. This period of time (5 μs)
is much smaller compared to the bubble nucleation delay time τd of a few hundreds of microseconds to milliseconds. As a result,
the contribution of the energy transfer after bubble nucleation is
very small and can safely be ignored.
Figure 4
Maximum bubble volume Vmax versus deposited
energy E = Plτd at different gas concentration levels.
For all gas concentrations, the same linear relation between Vmax and E is found, regardless
of the actual value of τd and Pl.
Maximum bubble volume Vmax versus deposited
energy E = Plτd at different gas concentration levels.
For all gas concentrations, the same linear relation between Vmax and E is found, regardless
of the actual value of τd and Pl.We find an universal linear relation
between Vmax and E for
all gas concentrations.
This universal linear relation Vmax = kE reflects that the energy stored in the vicinity of the
nuclei determines how many water molecules can be vaporized. The maximum
volume of the giant bubble only depends on the amount of energy dumped
into the system before nucleation and not on the relative gas concentration.
The latter confirms that the giant bubbles mainly consist of vapor.
Long-Term Growth Dynamics
From the above analysis,
we have obtained a better understanding of the gas dependence of the
bubble nucleation dynamics. After the initial giant bubble collapses,
it sequentially enters phase 2 (oscillating bubble phase) and phase
3 (vaporization-dominated growth phase), followed by the diffusive
growth in phase 4.[18] Normally, the final
phase begins at t > 0.5 s. We now focus on this
long-term
growth dynamics of the bubbles to investigate the role of the dissolved
gas also on this terminal growth phase, again by varying the gas concentration
levels from undersaturation to oversaturation (now c∞/cs = 0.55–1.2).Figure shows the
long-term growth dynamics of plasmonic bubbles at six concentration
levels of c∞/cs = 1.2, 0.95, 0.85, 0.75, 0.65, and 0.55. For the oversaturated
water (c∞/cs = 1.2), the bubble volume V as a function
of time is shown for several laser powers in Figure a. The bubble volume V increases
linearly with time t for all laser powers. The corresponding
bubble radius R(t) ∝ V(t)1/3 is shown in Figure b but now as a double-logarithmic
plot. After ∼0.5 s, R roughly follows an effective R(t) ≈ t1/3 scaling law. Figure c,d shows the corresponding results in a nearly gas-equilibrated
case with c∞/cs = 0.95. The bubble growth has a similar behavior with
that in the oversaturated water. The linear relationship of bubble
volume versus time (Figure c) and the 1/3 effective power scaling law of R(t) (Figure d) are both observed again.
Figure 5
Long-term bubble growth dynamics at different
gas concentrations
and laser powers. (a, b) c∞/cs = 1.2, (c, d) c∞/cs = 0.95, (e, f) c∞/cs = 0.85, (g, h) c∞/cs = 0.75,
(i, j) c∞/cs = 0.65, and (k, l) c∞/cs = 0.55. Linear plots of bubble volume V (a, c, e, g, i, and k) and double-logarithmic plots of
bubble radius R (b, d, f, h, j, and l) as functions
of time t for gas concentrations c∞/cs = 1.2, 0.95, 0.85,
0.75, 0.65, and 0.55, respectively. At c∞/cs = 1.2 (oversaturated water), 0.95
(nearly air-equilibrated water), and 0.85 (partially degassed water), V linearly increases with time for different laser powers.
Accordingly, R(t) follows the t1/3 scaling law. At lower gas concentrations,
the volume no longer linearly increases with t but
exhibits a reduced power law dependence of R(t) ∝ tα with α
= 0.27, 0.22, and 0.07 for c∞/cs = 0.75, 0.65, and 0.55, respectively, as shown
in (h), (j), and (l).
Long-term bubble growth dynamics at different
gas concentrations
and laser powers. (a, b) c∞/cs = 1.2, (c, d) c∞/cs = 0.95, (e, f) c∞/cs = 0.85, (g, h) c∞/cs = 0.75,
(i, j) c∞/cs = 0.65, and (k, l) c∞/cs = 0.55. Linear plots of bubble volume V (a, c, e, g, i, and k) and double-logarithmic plots of
bubble radius R (b, d, f, h, j, and l) as functions
of time t for gas concentrations c∞/cs = 1.2, 0.95, 0.85,
0.75, 0.65, and 0.55, respectively. At c∞/cs = 1.2 (oversaturated water), 0.95
(nearly air-equilibrated water), and 0.85 (partially degassed water), V linearly increases with time for different laser powers.
Accordingly, R(t) follows the t1/3 scaling law. At lower gas concentrations,
the volume no longer linearly increases with t but
exhibits a reduced power law dependence of R(t) ∝ tα with α
= 0.27, 0.22, and 0.07 for c∞/cs = 0.75, 0.65, and 0.55, respectively, as shown
in (h), (j), and (l).The results for partially
degassed water are displayed in Figure e–l. In the
partially degassed water with c∞/cs = 0.85 (Figure e,f), we again observe a similar bubble growth
dynamics as in the overstaturated water and air-equilibrated water,
that is, a linear relationship of bubble volume versus time (Figure e) and an effective
1/3 power scaling law of R(t) (Figure f). However, when
the gas concentration in partially degassed water is even lower, the
growth dynamics is distinctly different. Figure g shows the bubble volume versus time in
water with c∞/cs = 0.75. In this case, the volume no longer linearly
increases with t. The radius scales as R(t) ∝ tα, with an effective exponent α ≈ 0.27 (Figure h). For even lower gas concentrations,
namely, c∞/cs = 0.65 and 0.55, α reduces to 0.22 and 0.07, respectively.In plasmonic bubble-related applications, the maximal bubble size
(volume) is an important parameter. Figure a,c,e indicates that, besides laser power,
the growth rate of the bubble volume κ = dV/dt is related to the gas concentration. Figure shows the growth
rate κ as a function of the laser power Pl for the three different gas concentrations (c∞/cs = 1.2, 0.95, and
0.85). Since V is not proportional to t when c∞/cs is lower than 0.75, we only extracted κ for these three cases. We can see that κ increases
roughly linearly with the laser power for all gas concentrations, κ = k · Pl. We find that,
for higher gas concentrations, the slope k increases, as seen in the inset of Figure .
Figure 6
Bubble volume growth
rates κ in the relation V = κt as a function of laser power Pl for different gas concentrations (from c∞/cs = 0.85
to 1.2). κ linearly increases with increasing
laser powers κ = k · Pl. The prefactor k is found to linearly increase with gas concentration levels c∞/cs, k ∝ c∞/cs, as
shown in the inset figure.
Bubble volume growth
rates κ in the relation V = κt as a function of laser power Pl for different gas concentrations (from c∞/cs = 0.85
to 1.2). κ linearly increases with increasing
laser powers κ = k · Pl. The prefactor k is found to linearly increase with gas concentration levels c∞/cs, k ∝ c∞/cs, as
shown in the inset figure.The above results quantitatively demonstrate the importance of
the dissolved gas on bubble growth. Previously, it was shown that,
for gas saturation c∞/cs ≈ 1, the long-term bubble growth (phase 4) is
dominated by the influx of gas, which is locally produced around the
plasmonic nanoparticles due to heating[17] as the solubility cs decreases with
increasing temperature. All the expelled gas by oversaturation is
taken up by the bubble. For such a production-limited growth process,
the growth rate is constant, dV/dt = κ, and consequently, V(t) ∝ t or R(t) ∝ t1/3. Considering
the heating transfer originated from gold nanoparticles and mass influx,
the bubble volume growth rate κ is given by[17]where Mg is the
molecular mass of the gas, Rg is the gas
constant, P∞ is the ambient pressure, σ is the surface tension, ρw is the water density, Cw is the specific heat capacity of water, and dT is
the increase in water temperature. Equation shows that, for large R ≫
2σ/P∞, κ is proportional to both the relative gas concentration c∞/cs and
laser power Pl. Again, these linear dependences
(κ ∝ Pl and k ∝ c∞/cs) are
consistent with the results shown in Figure .The effective power law exponent α in the
time dependence R(t) ∝ tα of the bubble radius R(t) is used to further investigate the role of the
dissolved gas in the bubble growth dynamics (Figure ). As shown in Figure a, the effective exponent α is ∼1/3
for all laser powers if c∞/cs exceeds 0.85. For lower gas concentrations, c∞/cs = 0.55–0.75,
the effective exponents are smaller than 1/3 and slightly increase
with increasing laser power Pl. These
results are consistent with our previous findings, where R(t) ∝ t1/3 and R(t) ∝ t0.07 for experiments in air-equilibrated water and degassed water, respectively.[17]Figure b shows the effective exponent as a function of c∞/cs. As seen before,
for a given laser power, the exponent increases with increasing gas
concentration. The dependence of α on both c∞/cs and Pl is summarized in the three-dimensional plot in Figure c.
Figure 7
Effective power law exponent
α in R(t) ∝ tα as a function
of laser power Pl and gas concentration c∞/cs. (a)
Effective exponent α as a function of laser power for six different
gas concentrations c∞/cs. (b) Effective exponent α as a function of gas
concentration for different laser powers Pl. (c) 3D plot of α as a function of c∞/cs and Pl. Approximately, α monotonously increases with
both Pl and c∞/cs.
Effective power law exponent
α in R(t) ∝ tα as a function
of laser power Pl and gas concentration c∞/cs. (a)
Effective exponent α as a function of laser power for six different
gas concentrations c∞/cs. (b) Effective exponent α as a function of gas
concentration for different laser powers Pl. (c) 3D plot of α as a function of c∞/cs and Pl. Approximately, α monotonously increases with
both Pl and c∞/cs.The above results reveal how the dissolved gas controls the long-term
bubble growth dynamics. For large gas concentrations, there is a constant
influx of gas into the bubble, leading to a linear growth of bubble
volume. The transfer of heat per unit area to the bubble/water interface
becomes so small that there is insufficient energy available to overcome
the large latent heat of the vaporization barrier. As a result, gradually,
the bubble is thermally decoupled from the nanoparticles. The amount
of vapor molecules inside the bubble stabilizes. Thus, the bubble
growth will be dominated by expelled gas due to the local gas oversaturation.For large enough initial gas concentration c∞/cs ≥ 0.85, the
effective exponent α in the dependence R(t) ∝ tα saturates
at an exponent of 1/3, which is the limit of value for the diffusive
growth. In addition, for strongly undersaturated water, the exponent
is smaller than 1/3. The latter can easily be understood since the
solubility of gas in water decreases with increasing temperature.
This means that the water first has to be heated up to a temperature
where it becomes supersaturated. Once the water has reached this supersaturated
regime, the bubble grows by gas that is expelled from the supersaturated
water. With increasing bubble size, the thermal energy transferred
per unit area of the bubble/water interface will rapidly decrease.
As a result, the amount of oversaturated gas per unit volume near
the bubble/water interface will decrease also. At some point, the
energy transferred to the bubble/water interface becomes so low that
no further gas is expelled and the bubble growth terminates.Notably, at higher laser powers, the effective scaling exponent
α for c∞/cs = 0.65 and 0.75 in Figure a becomes approximately equal. The reason
is that the relative oversaturation of gas, which dominates the long-term
growth of plasmonic bubble, depends on the original amount of dissolved
gas (at room temperature) as well as on the temperature (and thus,
the laser power). If the laser power is larger, then the water will
be heated up to higher temperatures, leading to a larger gas oversaturation
(the solubility of air in water decreases with increasing temperature).
As a result, the effect of the initial gas concentration will become
weaker at higher laser power. We found a similar behavior for c∞/cs = 0.85,
0.96, and 1.2. The effective scaling exponent α for these three
different but relatively large gas concentrations is very comparable
at higher laser powers.
Conclusions
In summary, the effect
of the dissolved gas on the dynamics of
plasmonic bubble nucleation in the early phase and in the long-term
growth regime has been systematically studied. In the early phase,
lower gas concentrations lead to a longer delay time τd, larger maximum volume, and higher nucleation temperature, which
indicate that the dissolved gas facilitates bubble nucleation. We
have found a linear relation between the bubble volume and the total
energy. The prefactor of this linear relation is the same for all
gas concentrations, reflecting that the bubbles that form in the first
stage of the irradiation process are vapor bubbles. Regarding the
long-term growth dynamics, we have shown that the growth rate κ
of the bubble volume monotonically increases with gas concentration c∞/cs and
laser power Pl. Moreover, the experimental
results show a linear dependence of κ = kP, where k linearly increases with c∞/cs. The radius R(t) of the plasmonic bubbles follows the
power law dependence R(t) ∝ tα. For all laser powers, the effective
exponent α for all laser powers is ∼1/3 when c∞/cs is larger
than 0.85. However, for lower c∞/cs values, the effective exponent is
smaller than 1/3 and monotonously decreases with decreasing Pl and c∞/cs. For strongly degassed water, the exponent
α is smaller than 1/3 because the water first has to be heated
up to a temperature where it becomes supersaturated and gas can be
expelled.
Authors: Yuliang Wang; Mikhail E Zaytsev; Guillaume Lajoinie; Hai Le The; Jan C T Eijkel; Albert van den Berg; Michel Versluis; Bert M Weckhuysen; Xuehua Zhang; Harold J W Zandvliet; Detlef Lohse Journal: Proc Natl Acad Sci U S A Date: 2018-07-11 Impact factor: 11.205
Authors: Hadi Ghasemi; George Ni; Amy Marie Marconnet; James Loomis; Selcuk Yerci; Nenad Miljkovic; Gang Chen Journal: Nat Commun Date: 2014-07-21 Impact factor: 14.919
Authors: Ekaterina Lukianova-Hleb; Ying Hu; Loredana Latterini; Luigi Tarpani; Seunghyun Lee; Rebekah A Drezek; Jason H Hafner; Dmitri O Lapotko Journal: ACS Nano Date: 2010-04-27 Impact factor: 15.881
Authors: Oara Neumann; Alexander S Urban; Jared Day; Surbhi Lal; Peter Nordlander; Naomi J Halas Journal: ACS Nano Date: 2012-11-28 Impact factor: 15.881
Authors: Steven Jones; Daniel Andrén; Tomasz J Antosiewicz; Alexander Stilgoe; Halina Rubinsztein-Dunlop; Mikael Käll Journal: ACS Nano Date: 2020-12-08 Impact factor: 15.881