Evaporative deposition of polystyrene microparticles on PDMS surface
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Evaporative deposition of polystyrene microparticles on PDMS surface
Correction: Author Correction
OPEN Evaporation of water and ethanol/water droplets containing large polystyrene (PS) microparticles on polydimethylsiloxane (PDMS) surface was experimentally investigated. It is found that no matter with or without small addition of ethanol, a compact monolayer deposition is formed for lower microparticle concentration while mountain-like deposition for higher concentration. Since the more volatile compound (ethanol) evaporates more quickly than the less volatile compound (water), evaporation of ethanol/water mixture droplet exhibits different characteristics from pure water. When the concentration of microparticle is low, the contact radius of ethanol/water mixture droplet decreases throughout the whole process, while the contact angle increases at first to a maximum, then keeps almost constant, and finally decreases sharply. However, the evaporation of ethanol/water mixture droplet with higher concentration of microparticle behaviors more complex. The settling time of microparticles was estimated and its theoretical value agrees well with the experimental one. Moreover, a mechanism of self-pinning of microparticles was used to elucidate the deposition behavior of microparticles, indicating that as the contact line is depinning, the liquid film covering the outmost microparticle becomes thicker and thicker, and the microparticles have to move spontaneously with the depinning contact line under the action of capillary force.
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When a sessile suspension droplet containing micro/nano-particles evaporates on a solid substrate, these particles
will be left on the substrate after evaporation. Using this method, we can obtain desirable deposition pattern for
applications in fields such as electronics, optoelectronics, sensors, nanotechnology, and biotechnology, etc.1 However,
when the substrate is hydrophilic and the contact line is pinned, there will be a singular evaporation flux near the
contact line, resulting in a strong outward capillary compensation flow (it should be noted that there is no singularity
of the evaporation flux near the contact line for hydrophobic case and thus the outward capillary flow is very weak),
which will carry the particles (whose diameter is usually of the order of several micrometers or below) towards the
edge. Then a ring-like structure is formed at the perimeter, which is known as the coffee-ring effect2. Besides of the
contact line pinning, suppression of Marangoni flow is another necessary condition for the formation of the coffee
ring3. Shen et al.4 pointed out that there will be no coffee ring effect when the liquid evaporates much faster than
the movement of particle, and found that a coffee ring structure will be still formed until the droplet size decreases
to a critical value. Mar?n et al.5 showed that the singularity of the flow velocity at the end of an evaporating droplet
will bring about a sharp transition from ordered crystals to disordered packings in the coffee stain. The coffee-ring
phenomenon6?8 makes the deposition pattern nonuniform and thus hinders the application of droplet evaporation.
Moreover, using droplet evaporation, except for coffee ring structure, researchers obtained different deposition
patterns such as hexagon9,10, stripe10, hemispherical particle assemblies with ordered nanoporous structures11, highly
ordered monolayer12,13, concentric ring14, coffee eye15, inner deposit16 and nearly uniform deposition17,18.
To better understand the coffee-ring phenomenon and apply evaporation-induced deposition, researchers
have set up theoretical models19?24 for self-pinning of microparticles at the contact line. Using the scaling analysis,
Jung et al.19 estimated the role of various forces such as drag, electrostatic, van der Waals, and capillary on the
particle motion and found that i) the motion of a single particle suspended in liquid is mainly affected by drag force
in the pinned contact line stage, and ii) capillary force controls its motion in the depinning contact line stage.
Wong et al.20 elucidated the physics of particle separation during coffee-ring formation based on a particle-size
selection mechanism near the contact line of an evaporating droplet. Later, on the basis of Jung et al.19 and Wong
et al.20, Chhasatia and Sun21 proposed a self-pinning mechanism, however, the velocity of water in evaporating
drop 0.2 m/s was suspectable. In 2013, Weon and Je22 compared the spreading and drying behaviors of pure
and colloidal droplets and set up a mechanism for the self-pinning of particles at the contact line. Hurth et al.23
conducted evaporation of sessile droplet containing streptavidin- or biotin-coated fluorescent polystyrene (PS)
particles and found that both the biological binding force and the capillary force play significant roles in particle
deposition and that the viscous drag, van der Waals forces, and solid-solid friction forces are negligible. Recently,
using particle tracking velocimetry technique, Yu et al.24 studied the motion of fluorescent PS microparticles at
the depinning contact line and built up a self-pinning mechanism. Besides, Li et al.25 predicted three different
motions of a single nanoparticle at the contact line using molecular dynamics simulation.
Besides single-component droplet, mixture droplet has also been widely used in many fields. Because different
component of a mixture droplet usually has different evaporation rate and there is a diffusion of one component
into another, evaporation of a mixture droplet is more complex. For example, evaporation of water/1-propanol
mixture droplets at room temperature on polymethyl methacrylate (PMMA) exhibits two types of behavior
depending on the molar fraction of the mixture26. One is a long-time contact line pinning (scaled around two
thirds of the evaporation time) for the molar fracture greater than the azeotropic point (0.39 mol fraction of
1-propanol), and the other is an instable behaviour when its molar fraction is less than the point. Rusdi et al.27
found that the evaporation rate for water-ethylene glycol liquid mixture increases with increasing temperature,
and decreases with increasing mole fraction of ethylene glycol. Evaporation of ethanol/water mixture droplets has
been extensively studied on smooth planer surface28?31 and chemical micro-patterned surface32. And it is found
that the contact line recedes throughout the evaporation and the contact angle increases at first to a maximum
and decreases thereafter. Christy et al.31 found that there are three evaporating stages of ethanol/water droplet
on clean glass surface, viz., a multiple-vortices-dominated stage, a transition stage due to a remarkable spike in
outward flow, and a stage because of outward flow which is the same to that of pure water. Therefore, evaporation
of mixture droplet might be used to eliminate the coffee ring effect.
Due to good biocompatibility, nontoxicity, optical transparency and easy fabrication, polydimethylsiloxane
(PDMS) has been widely used in micro- and nano-systems. Recently, sessile droplet on PDMS surface has been
intensively studied and it is found that substrate deformation induced by sessile droplet significantly influences
the wetting and evaporation characteristics as well as the deposition pattern after evaporation33?38. Weon and
He39 reported that the coffee-ring effect can be suppressed for the case of sessile evaporating droplet containing
large microparticle under the action of capillary force. In this paper, evaporation of sessile water and ethanol/
water droplets containing PS microparticles with diameter of 20.33 ?m was experimentally investigated. When
the concentration of microparticle is low, the contact radius of ethanol/water mixture droplet decreases
throughout the whole process, while the contact angle increases at first to a maximum, then keeps almost constant, and
finally decreases sharply. However, the evaporation of ethanol/water mixture droplet with higher concentration of
microparticle behaviors more complex.?Settling time of microparticles inside evaporating droplet was estimated
and compared with the experimental data. Finally, deposition patterns were analyzed using a laser scanning
confocal microscope. It was found that i) at low particle concentration, a compact monolayer deposition was formed
while compact multilayer structures was formed for high concentration, ii) addition of ethanol has no significant
influence on deposition pattern, as illustrated in Fig.?1. Moreover, the formation of deposition patterns was
elucidated using a self-pinning mechanism of microparticles confined at the contact line24.
Evaporation of sessile droplet. Because the characteristic length of 0.6 ?L sessile droplet is obviously less
than its capillary length, the influence of gravity on its shape is negligible and the droplet has a spherical cap. Thus
the volume can be written as
?a3(1 + cos ?)2(2 ? cos ?)
where V , a and ? are the volume, contact radius and contact angle, respectively. Substituting the measured initial
contact angles into Eq. (
), the initial contact radii were obtained. Both the contact radius and the contact angle
have been averaged. Figure?2 shows the evolution of volume of pure water droplet and ethanol/water mixture
droplet containing 0.02 wt.% PS microparticles versus normalized time t/tf (tf is the total evaporation time) (the
curves for droplets containing 1.28 wt.% PS microparticles are not given because each of them is similar to that
for 0.02 wt.% case). When the concentration of ethanol is low (10%), the slope of the droplet volume differs
slightly from that of pure water. As the concentration of the volatile liquid increases to 20%, the curve deviates
from that of pure water. As compared with the slope for pure water, that for mixture droplet becomes larger at first
and less later when ethanol is introduced into the droplet.
Figure?3 shows the evolution of contact radius and contact angle versus time for pure water droplet and
ethanol/water mixture droplet containing 0.02 and 1.28 wt.% PS microparticles. For water droplet containing colloidal
particles, due to contact angle hysteresis, all experiments proceeded with constant contact radius (CCR) mode,
constant contact angle (CCA) mode and mixed mode. For ethanol/water mixture droplet, because the vapor
pressure of ethanol is about 7.0 kPa at 23 ?C, which is higher than that of water (~2.8 kPa at 23 ?C)29, ethanol will
evaporates faster and the surface tension of mixture is increased. Meanwhile, the diffusion coefficient of ethanol
into water is about 1.22 ? 10?9m2/s40, which is much smaller than that of ethanol into air (~1.2 ? 10?5m2/s41).
Thus the diffusion of inside the mixture droplet also controls the evaporation of ethanol from the droplet. As
more and more ethanol evaporates from the liquid-vapor interface, the evaporation of ethanol/water mixture
droplet behaviors as that of pure water droplet at the final stage. For mixture droplet containing 0.02 wt.% PS
microparticles, the contact radius decreases throughout the whole process, while the contact angle increases at
first to a maximum and decreases later. However, when the microparticle concentration of mixture suspension
droplet increases to 1.28 wt.%, the contact angle exhibits different behavior. For 10% ethanol, at first there is short
CCR stage and then both the contact radius and the contact angle decrease. After it, the contact angle keeps
almost constant and finally the droplet evaporates completely with mixed mode. For 20% ethanol concentration,
the contact radius decreases all over the whole process and the contact angle increases to a maximum at first. Then
it decreases to about 53? and keeps almost constant for about 35% of the whole evaporation time. Finally, the
evaporation completes with mixed mode.
Figure?4 shows the initial contact angles of sessile droplets with different concentrations of ethanol and
PS microparticles. On the one hand, at the same concentration of PS microparticles, the initial contact angle
decreases with increasing ethanol concentration, which can be explained using Young?s equation. As ethanol was
added into water, both the liquid-vapor and solid-liquid interfacial tensions decreased, thus the contact angle
has to decrease. On the other hand, at the same ethanol concentration, the initial contact angle decreases with
increasing concentration of PS microparticles for 0% ethanol and 10% ethanol while increases with increasing
concentration of PS microparticles for 20% ethanol. The reason is not clear, and it might be related to the
interactions between microparticles and water or ethanol, between water and ethanol, and between the mixture and
the substrate, etc.
Settling time of microparticles. The drag force acting on a microparticle by evaporating droplet can be
calculated from the Stokes equation42,43 and given as
Fd = 6?R?u
?(?P ? ?L)R3g
2 (?P ? ?L)R2g
where R is the radius of the microparticle, ? is the dynamic viscosity of water (~9 ? 10?4 Pa?s), u is the velocity of
the microparticle relative to the droplet in the vertical direction. Such a force is balanced by the net force between
the gravity of the microparticle and its buoyancy as
where ?P is the particle density (1050 kg/m3), ?L is the fluid density (1000 kg/m3), g is the gravitational acceleration
(9.8 m/s2). Thus we can get the resulting settling velocity as
The calculated settling velocity for the microparticles inside water droplets is 13.8 ?m/s. 0.60 ?L pure water
droplet with 0.02, 0.08, 0.32 and 1.28 wt.% PS microparticles on PDMS has, respectively, average initial droplet
heights of 1.099, 1.066, 1.027 and 0.828 mm. Thus the times for all particles to settle are 79.6, 77.2, 74.4 and 60.03s,
respectively. From the videos (see supplementary information) we observed the motion of some microparticles
inside pure water droplets containing PS microparticles. From (supplementary movies?1?4), we estimated the
settling time for pure droplet containing 0.02, 0.08, 0.32 and 1.28 wt.% PS microparticles are, respectively, about
120, 90, 130 and 66 s. As an example, Fig.?5 shows the location of microparticles inside evaporating droplet at
different time and it is found that there are more microparticles settling on the central zone of solid-liquid interface.
For ethanol/water mixture droplets, because ethanol is more volatile, there will a more intense internal flow inside
them than pure water droplet, which makes the settling of microparticles difficult. Under the action of such a flow,
the microparticles inside the droplet moves so quickly that we cannot track their motion at the speed of 0.5 fps.
Analysis of deposition patterns. Figure?6 shows the deposition patterns of evaporating droplets with
different microparticle concentration and ethanol concentration. To get a more detailed information on deposition
patterns for higher microparticle concentration, we choosed about 1/4 of the deposition patterns and measured
their topographical features (as shown in Fig.?7). It was found that 1) when the concentration of PS microparticles
is low, there will be a compact monolayer pattern while multi-layered or mountain-like deposition is formed for
higher microparticle concentration, 2) the addition of ethanol into the liquid droplet has an influence on the
shape of the deposition pattern.
Why is there a compact monolayer deposition for lower microparticle concentration and a compact
multi-layer structure for higher one? As Fig.?3 shows, no matter pure water droplet or ethanol/water mixture
droplet, the depinning contact line stage dominates the droplet evaporation. When all the microparticles settle on
PDMS surface, the outmost microparticles will experience van der Waals force, electrostatic force, drag force and
capillary force when the receding three-phase contact line (TPCL) approaches to them.
In our previous paper24, we established a mechanism for the self-pinning of microparticles located at the
contact line as (as shown in Fig.?8)
FS sin ? ? ???f (FS cos ? + nFwps + nFeps) + nFd??? = 0
where f is the friction coefficient between the microparticle and the substrate in water or ethanol/water mixture
(it should be noted that the coefficient is difficult to be determined up till now and it is assumed to be 0.1 or 0.2)
and n is the number of microparticles located at the contact line in the radial direction. Fwps and Feps are,
respectively, the van der Waals and electrostatic forces between a microparticle and the substrate. FS = 2?R?lv cos ? is
the capillary force acting on the outmost microparticle, where ? is an angle to be determined and (? ? 2?) is the
angle of the liquid layer covering the outmost microparticle, as shown in Fig.?9. Table?1 lists all the parameters for
calculation of all the interaction forces in eq. (
) and Table?2 lists the values of these forces. Using eq. (
critical angle ?C depending on the number n was calculated, as shown in Fig.?9. It is found that there is only a thin
liquid film acting on the outmost microparticle when it is self-pinned on the contact line.
For droplets with low microparticle concentration (the total number of microparticles inside the droplets is
small), when the receding contact line approaches to the outmost microparticles, the liquid layer acting on the
microparticles will become thicker and thicker, and there will be a very larger capillary force if the microparticles
is still stationary. Meanwhile, the values of all the other forces do not increase. Thus Eq. (
) cannot hold and the
microparticles have to move spontaneously together with the receding contact line under the action of capillary
force, resulting in a compact monolayer structure. For a high microparticle concentration, on the one hand, the
microparticles inside evaporating droplet is settling during the early stage, and there will be more microparticles
settling near the center of the solid-liquid interface, meanwhile, similar to the case of low microparticle
concentration, the outmost microparticles also move toward the center under the action of capillary force. Since there
are more microparticles settling on the central zone of solid-liquid interface for this case, it is more likely to form
a multi-layered compact structure. However, it should be noted that it is difficult to set up a self-pinning
mechanism?of multi-layered microparticles confined at the contact line.
We prepared PDMS membranes for studying evaporation of sessile droplets containing PS microparticles. PDMS
(Sylgard 184, Dow Corning, USA; mass ratios of base to curing agent = 10:1) was vacuumed for 30 minutes to
remove the trapped air-bubbles and then spin-coated on the surface of clean glass surface at the rate of ~2000
rpm. Finally the samples were cured for about 8 hours at 80 ?C. Particle suspensions were prepared by diluting
PS suspensions (PS07N, mean diameter of particles: 20.33 ? 0.614 ?m; Bangs Laboratories, Fisher, USA), from
initial concentration of 9.9 wt. % to 0.02, 0.08, 0.32 and 1.28 wt. % in deionized water or ethanol/water mixture.
The volume by volume concentration of ethanol in ethanol/water mixture was 0%, 10% and 20%.
0.60 ? 0.05 ?L suspension droplet was deposited on the PDMS substrates using a micropipette. Before the
deposition, the suspension was ultrasonically stirred for 10 min to ensure that the microparticles were
homogeneously dispersed. Once the droplet was deposited onto the surface, OCA 20 system (precision: ? 0.1?, from
Dataphysics, Germany) equipped with a high-resolution camera was immediately adjusted to record droplet
evaporation at 0.5 fps. The environmental temperature and relative humidity (RH) are 23? 1 ?C and 53 ? 3%,
respectively. To ensure the reproducibility, each experiment was repeated six times. Finally, the deposition
patterns after evaporation were measured using laser scanning confocal microscope (Keyence VK-X260, Japan).
Evaporation of both water and ethanol/water mixture droplets containing larger PS?microparticles was
experimentally investigated. The evaporation of ethanol/water mixture droplet containing PS microparticles exhibits a
Hamaker constant of PS microparticle
Hamaker constant of PDMS
Hamaker constant of water
Hamaker constant between the PS
microparticle and PDMS in water
Surface tension of water
Minimum separation distance
Permittivity of water
Surface potential of PS
Surface potential of PDMS
Dynamic viscosity of water
Velocity of water in evaporating droplet
Reciprocal of the Debye length
different way from that of pure water droplet. When the concentration of microparticle is low, the contact radius
decreases throughout the whole process while the contact angle increases at first to a maximum, then keeps almost
constant, and finally decreases sharply. However, the evaporation of ethanol/water mixture droplet with higher
concentration of microparticle behaviors more complex. The settling of microparticles inside the evaporating
droplet was theoretically analyzed and compared with the experimental observation. At last, deposition patterns of
microparticles were analyzed. It is found that at low microparticle concentration, a compact monolayer deposition
of microparticles was obtained, while a multi-layer deposition pattern were formed for higher one. Small addition
of ethanol brings a stronger flow inside evaporating droplet, yet has little influence on the deposition pattern.
This research was supposed by the Natural Science Foundation of China (Grant No. 11572114), the Chinese
Academy of Sciences (CAS) Key Research Program of Frontier Sciences (Grant No. QYZDJ-SSW-JSC019),
the CAS Strategic Priority Research Program (Grant No. XDB22040401) and the opening fund of State Key
Laboratory of Nonlinear Mechanics (LNM). We also thank Prof. Quanzi Yuan from State Key Laboratory of
Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences and Prof. Fengchao Wang from
Department of Modern Mechanics, University of Science and Technology of China for helpful discussion.
Y.S.Y. supervised the research. Y.S.Y. and M.C.W. designed the experiments. Y.S.Y. and M.C.W. performed the
experiments and analyzed the data. All authors discussed the results and wrote the manuscript.
Supplementary information accompanies this paper at https://doi.org/10.1038/s41598-017-14593-5.
Competing Interests: The authors declare that they have no competing interests.
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