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Stains from freeze-dried drops Etienne Jambon-Puillet Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00084 • Publication Date (Web): 01 Apr 2019 Downloaded from http://pubs.acs.org on April 7, 2019
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Langmuir
Stains from freeze-dried drops ∗,†,‡ Etienne Jambon-Puillet
†Institute
of Physics, Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands
‡Present
address: Department of Chemical and Biological Engineering, Princeton University,Princeton, New-Jersey 08540, USA
E-mail:
[email protected] Abstract
frozen drop sublimated
(a)
(b)
liquid drop evaporated
The evaporation of droplets of colloidal suspensions onto a surface is a common tool to achieve surface coatings and self-assembly. Yet, because of the spontaneous ow developing within an evaporating drop, the deposit is di cult to control and an unwanted ring-like structure often forms, with particles aggregating along the drop edge. Here, by freezing the drops before sublimating them in dry air we propose a new approach that pro-
Figure 1: Stains left by drops dried while frozen
duces a dierent kind of stains where most particles are
liquid (supercooled)
clustered in the center of the drops instead. We demon-
(b)
conditions: droplet volume
strate that these deposits can be continuously tuned
Ts = −5◦ C, 0.5 mm. at
from wide but thin to concentrated and thick by varying the droplet's aspect ratio. Unlike evaporated liquid
(a)
or
under identical experimental
V ≈ 1 µL, glass RH = 5%.
relative humidity
substrate Scale bar
drops, stains from freeze-dried drops do not depend on the drying conditions or substrate roughness and possess a porous and branched microstructure somewhat
drops of aqueous colloidal suspensions by cooling the
reminiscent of freeze-casted ceramics. These stains be-
substrate and sublimate them in dry air, while frozen.
ing governed by the freezing process rather than the
In contrast with common coee stains obtained from
drying, it opens alternative ways to control colloidal de-
dried liquid drops, this approach yields a deposit in
posits.
which most particles are concentrated in the center [Fig-
Introduction
ure 1(a)].
Spilled coee, tea or red wine left to dry usually leaves a
stain solely and non-linearly depends on the initial drop
stain that is darkest around its edge. This so-called cof-
aspect ratio; the strength of the particle accumulation
fee ring [Figure 1(b)] forms when a sessile drop contain-
can be tuned to produce stains whose aspect ratio varies
ing non-volatile solutes evaporates with a pinned con-
over several orders of magnitude. Electron microscopy
tact line, a situation encountered on most substrates.
images further reveal a porous and branched microstruc-
We systematically varied the drop volume
as well as the substrate wettability, temperature and roughness and show that within these parameters, the
1,2
In these circumstances, a capillary ow transporting the
ture dierent from the compact deposits obtained from
solute develops toward the drop edge to compensate the
evaporated liquid drops
9,17 and closer to freeze-casted
18,19 where the particles are repelled by the soceramics 2027 The clustering we observe in our lidi cation front.
14 Since drying drops are stronger evaporation there. 5 6,7 used in many applications such as coating, printing,
8,9 and biomedical assays, 10,11 achieving a
stains is in fact caused by the transport of the particles
good understanding and control of the deposit forma-
toward the apex of the drop as the freezing front prop-
tion is an important challenge. As a result, intense re-
agates upward. The stains from freeze-dried drops are
search eorts to understand and control the deposits
therefore sensitive to parameters governing the freezing
left by dried liquid drops have yielded many innovative
front-particle interaction rather than those determining
strategies, which all have limitations (see recent reviews
common coee-stain type of deposits, thus oering a
on drop evaporation and deposition patterns
new approach to control non-volatile solute deposition.
self-assembly
1216 ).
We present here a new approach in which we freeze
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Stain analysis
Experimental section
Materials The
Page 2 of 10
Once the ice droplets have completely dried, we remove the stains from the climatic chamber and use a 3D laser
aqueous
suspension
is
prepared
by
diluting
scanning confocal microscope (Keyence VK-X1000) to
R mimonodisperse polystyrene particles (Polybead
acquire both microscopy images (focus stacked, coaxial
465 ± 11
illumination) and height maps of the stains. The sur-
nm in Milli-Q water (Millipore) at 0.08% wt (volume
faces being quite irregular due to their microstructure,
crospheres from Polysciences, Inc) of diameter fraction
φ = 8 × 10−4 ).
Although non functionalized,
we t them with 2D Gaussians in Matlab to quantify
the particles contain a slight anionic charge and traces
the global stain shape [see Figure 4(a)]. The deposit av-
of surfactant (the suspension and pure water have simi-
erage height
lar contact angles). Our substrates are thin glass cover
while its radius
slips (Menzel-Gläser # 1, thickness
0.13-0.16
mm) ei-
in the principal directions. The stains are then coated
ther raw or coated with Parylene-C (SCS Labcoter PDS 2010, additional coating thickness
∼ 1 µm).
h is extracted from the Gaussian amplitude r is the sum of the standard deviations
with chromium or titanium (thickness
∼ 20
nm) and
We further
imaged with a high-resolution scanning electron micro-
plasma treat both of the surfaces (Diener Zepto) and
scope (FEI Verios 460) to observe their microstructure.
use them at various degrees of ageing to continuously vary the wettability (18
< θ (deg) < 103).
Results and discussion
To test the
in uence of surface roughness, we sand plain glass cover slips (arithmetical mean deviation
Sa ≈ 0.5 µm).
As for most suspension-substrate combinations,
Sublimation experiment
1,2 dry-
ing liquids drops of our suspension, either at room temperature or supercooled below the melting point as in
×
Figure 1(b), always leaves a pronounced coee rings.
0.5×0.7 m) where the relative humidity (with respect to ◦ the ambient air at T0 = 24 C) RH is monitored with a thermo-hygrometer Testo 645 (accuracy ±2%) and kept
This con rms that the contact line pins, and that ther-
The experiment is conducted in an acrylic box (0.4
mal and solutal Marangoni ows that could arise due to the small amount of surfactants in solution are negligible. Moreover, since both the particles and our sub-
constant at a value low enough to sublimate our coldest drops (∼
5%)
strates are slightly negatively charged, the DLVO inter-
by gently blowing dry nitrogen. The
action are repulsive and particles do not deposit on the
physically relevant relative humidity at the frozen drop' surface
RHice
substrate to form a uniform lm.
is much higher and varies with the sub-
and form a crystalline packing.
28 The calculated from equations (7) and (10) of Ref.
the liquid-air interface as it would also result in a more uniform deposit.
D(T0 )
29 Figure 78 and is calculated with the equation in Ref the ice density is taken as
ρice = 918.9
kg m
−3
shots of a typical experiment are shown in Figure 2(a).
.
Once frozen, a sharp tip develops on top of the drop due to the expansion of water upon freezing.
system (Anton Paar TEK 150P-C) with thermal grease.
1 µL
to
50 µL
of the suspension are then de-
liquid water evaporating under the same conditions.
spheroidal shape after roughly half of the total evapo-
to its minimal value, therefore decreasing the substrate troller permits it until the drop freezes (≈ rough glass and a rate
∼1
◦
≈ −23◦ C
−18
and
min). This shape is
37
As the contact line retracts, particles at the drop edge
for the smooth substrates at
are gradually deposited onto the substrate.
C/min). Then we set the Peltier to the de-
−2◦ C
t = 42
then maintained until the end of the drying process.
C on
sired sublimation temperature (reached in less than s), between
ration time (see Figure 2(a)
as quickly as the Peltier's feedback con-
◦
37
It rst loses its sharp regions (tip and edges) to reach a
ods of time, we rst set the Peltier's target temperature
Ts
3436 The
frozen drop then sublimates at a rate similar to that of
posited. As our drops remain supercooled for long peri-
temperature
8,32,33
Now turning to the drops dried while frozen, snap-
The cover slips are attached to a water-cooled Peltier Drops of
9,31 Finally, the presence
of the ring shows that the particle do not accumulate at
water vapor concentrations are then calculated from the ideal gas law, the water-air diusion coe cient
30 Instead, they are
rapidly advected by the capillary ow at the drop edge
ice water (Ts ) (T0 )/Psat strate temperature: RH = RH Psat where the saturation pressures over ice and water are ice
It seems
that as the ice sublimates, particles are released on the
10
drop surface and move along with it until they touch
−15◦ C.
the substrate (see Movies S1 & S2).
The sublimation process is followed by means of
We rst look at the drying dynamics in Figure 2(b)
side-view images recorded with a Nikon D5600 cam-
where we plot the height
era mounted with a high-magni cation objective (Nav-
H
and contact radius
R
of the
drop as it sublimates. Except at the beggining of drying
itar). The images are analyzed using ImageJ and Mat-
where the drop is still pointy, both parameters scale as
lab; drop volumes are measured by numerically inte-
R(t) ∼ H(t) ∼ (tf − t)1/2
grating their pro le (assuming axisymmetry) and their
with tf the total drying time.
This behavior is similar to that of liquid drops evaporat-
contact angle with the tangent method.
ing with a constant contact angle.
38 But unlike liquid
drops, the dynamics after the drop becomes spheroidal (for
t > t0
with
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the smoothing time or equiv-
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Langmuir
(a)
(b)
1.2
1
0.8
0.6
0.4
0.2
0
Figure 2:
(a)
0
10
20
30
40
50
60
70
Sequence of images showing the evaporation of the frozen drop whose stain is shown in Figure 1(a).
The images include the re ection of the drop on the substrate. The white dashed curve is the initial liquid drop
1 mm. (b) Radius R (red circles) and height H (blue squares) of the same drop as a t. The dashed and solid curves are the spheroid evaporation model: equation (1) with t0 = 30 β = 7 × 10−11 m2 s−1 . pro le, scale bar
function
of time
min and
alently
tˆ ≡ t − t0 > 0)
can be described by a closed-
left by frozen drops, each with a volume of
5 µL,
on
form equation. We derive this equation by modeling the
substrates of increasing hydrophobicity (see also Movie
diusion-limited sublimation of self-similar spheroids:
S1 and S2). The stain of the low contact angle drop, is
R(tˆ) =
q
37
relatively thin and looks uniform from the side while the
R02 − 2β (C0 /H0 ) tˆ
ones resulting from the drops with a higher contact an(1)
gle leaves a macroscopic spot-like residue in the center
H(tˆ) = (H0 /R0 ) R(tˆ).
of the stain. Figure 3(g)-(f ) shows the same stains seen from above with an optical microscope. We observe an
C is the electrostatic capacitance: √ . p R2 − H 2 arcsin 1 − (H/R)2 . √ C= √ 2 H 2 − R2 ln H+√H 2 −R2 2 2 H− H −R
Here,
outer region of varying size with a very thin layer of particles (dark grey) and a thicker central core (white).
if R > H
Gradually decreasing the wettability results in the par-
if R < H
ticles increasingly accumulating in the core which be-
(2)
comes more con ned and thicker.The thin outer region'
(i.e.
size concurrently decreases but with a lot more vari-
In equation (1), all thermodynamic quanti-
ability. To quantify this behavior we use a pro lometer
β = D (ρsat − ρ∞ ) /ρice with D the water diusion coe cient, ρsat the vapor saturation concentration over ice, ρ∞ the vapor concentration at in nity and ρice the ice density. We plot equation (1)
to measure the stain topography [see Figure 3(g)-(i)].
and the subscript 0 denotes the value at
t = t0 ).
tˆ = 0
ties are enclosed within
While the outer region is always only a few particles high, the core region evolves from a collection of separated towers of a few tenths of microns at very low contact angles to a more compact half millimeter high
along with the experimental data in Figure 2(b) and nd a very good agreement with
β
spot at larger contact angles. Increasing the drop vol-
tted within the ex-
perimental uncertainties (error margin of
20%
ume increases the stain size as one would expect from
resulting
mass conservation, but it also modi es its aspect ratio
from the humidity probe accuracy). We nd that dier-
at large volumes, when the drop starts to get attened
ent substrate temperatures result in dierent drying
by gravity (see Supplementary Information). This sug-
We now turn to the stains. speeds: drops at
◦
−15
C take about
evaporate than drops at model
37 since
β
−2
◦
10
gests that it is not the substrate wettability
times longer to
C, as expected from the
is reduced by roughly a factor
10
θ which dic-
tates the strength of particle clustering in the core but the drop aspect ratio
and
H/R.
Finally, since the substrate
However, we nd that the nal stains are
roughness in uences the pinning for liquid drops and in
very similar (see Supplementary Information), indicat-
return their stains, we sand glass cover slips to check
ing that the deposit is insensitive to the sublimation
roughness eects on our freeze-dried drops. No pinning
rate.
This opens the opportunity of performing the
of the ice contact line is observed and the stains are sim-
drying step at enhanced sublimation rates using partial
ilar to the one sublimated on smooth substrates (at con-
vacuum and a condenser as in freeze-drying applications
stant drop aspect ratio) suggesting that the roughness
tf ∼ 1/β .
(tf
∼ 1/β ∼ 1/D ∼ P ,
with
P
does not induce speci c particle-substrate interactions.
the pressure). In stark
contrast, changing the substrate wettability dramati-
To characterize the aggregation of particles in the core
cally alters the stain. Figure 3(a)-(c) shows three stains
of the stain, we t the height maps with 2D Gaussians as
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(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
0
5
10
15
20
25
30
35
0
20
40
60
80
100
Figure 3: Eect of wettability on the stains [(a)(d)(g): glass,
V ≈ 5 µL]. (a)-(c)
Height maps of the stains (in
µm)
h
section).
and radius
(b)(e)(h):
Scale bars:
color coded between
shown in Figure 4(a). We then extract the core average height
r
0
from the ts (see Experimental
ferent temperatures, we plot the core aspect ratio as a function of the drop aspect ratio
plasma parylene
200
250
(c)(f )(i):
300
parylene,
1
(d)-(f )
mm.
H/R
h
h/r
V 1/3
in Figure
The data fall on a single master curve indicat-
r V 1/3
[see inset Figure 4(b)] reveals a power law dependence that we t to get
Since we know
a = 0.55 and α = 4.0.
h
and radius
r.
, we
a
and
α
(3)
(4)
from the initial t, only the
ϕ
is unknown and it can
be extracted from the prefactors.
Since the
We plot the dimensionless stain radius in Figure 4(c)
stains are reasonably Gaussian, their volume is roughly
πhr2 /2. Conservation ϕπhr2 /2 ≈ φV with ϕ
α
h/r = a (H/R)
1/3 2α/3 2φ H =a , πϕ R 1/3 −α/3 H 2φ −1/3 . =a πϕ R 2/3
average stain packing fraction
We can then couple this empirical t to mass conservation to disentangle the height
Microscopy images of the stains.
stain height and radius:
drop shape. Plotting the same data on a log-log scale
tion.
150
expect the following power laws for the dimensionless
ing that the stain shape solely depends on the initial
α
100
our experiments, then using that
Aggregating all our data for drops of dier-
h/r = a (H/R)
50
and the maximum height on each image.
ent volumes on dierent substrates sublimated at dif-
4(b).
0
Backlit side-view pictures of the nal stain with the unfrozen drop pro le (white dashed line).
The images include the re ection on the substrate.
(g)-(i)
120
and height in Figure 4(d) as a function of the drop as-
of the particles therefore gives
pect ratio.
the average stain packing frac-
The data collapse on power laws with the
exponents given by equations (3)(4), thus con rming
If this packing fraction is constant throughout
that our stains have a reasonably constant porosity. We
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Langmuir 350 exp
300
particles aggregated together to form an interconnected
fit
network with larges holes (black regions).
The core's
250
center [Figure 5(c)] contains the same kind of clumps
200
but stacked together in a more compact way. Details of the clumps themselves are shown in Figure 5(d): they
150
are compact with a short-range hexagonal order. The
100
stain's porosity therefore comes from the irregular clus-
50
tering of the clumps. Finally, we discuss the physical mechanism responsi-
0 -2000
-1500
5
(b)
10
-1000 15
-500 20
0
25
500 30
1000
35
40
1500 45
2000
ble for the particular structure of our frozen stains. The
50
particles can not be homogeneously distributed within
2 1.8
the frozen drop and simply deposited on the surface be-
101
1.6
100
low during sublimation. If that was the case, we would
1.4
10-1
expect stains with an aspect ratio roughly equal to the
10-2
drop aspect ratio itself and not the very non-linear de-
1.2 1 0.8 0.6
10-3
pendence observed in Figure 4(b).
10-4 10-1
As the ice subli-
mates, particles are released on top of the drop surface
10 0
0.4
and more or less follow the interface until they reach
0.2 0 0
0.2
0.4
0.6
0.8
1
1.2
the substrate (see Movie S1 & S2).
1.4
It is well known
that liquid interfaces can capture particles, transport
(c)
2
them and self-assemble them in various structures (e.g.
1.6
Ref ). Here analogously, by preventing the particles to
1.2
roll o from the curved solid surface through adhesion
0.8
and/or friction, this interfacial capture constitute a rst
0.05
0.4
mechanism to cause central aggregation. However, this
0
0
0.3
(d)
parylene plasma parylene glass plasma glass sanded glass
0.25 0.2 0.15 0.1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
8
0
0.2
0.4
0.6
0.8
1
1.2
mechanism is not very strong since thin drops still pro-
1.4
duce thin stains and this would not explain the particFigure 4:
(a)
ular microstructure observed as we would rather expect
Horizontal cross section of the stains
an homogeneous stain with particles in random loose
shown in Figure 3 with the Gaussian ts superimposed. How
(b)
r
and
h
packing. Another mechanism must therefore be respon-
are de ned is schematised in inset.
sible for the clustering and microstructure observed.
h/r as a function of the frozen droplet's aspect ratio H/R for all our experiments. The Stain aspect ratio
As solidi cation fronts propagate, they exert thermomolecular forces on impurities suspended in the melt.
colors code the initial drop volume, while the symbols code for the substrate used (see legend in (c)).
Depending on the front velocity
(d)
(c)
a particle is ei-
ther repelled by the front or engulfed.
dashed curve is a power law t. Inset: same data on a log scale. Dimensionless deposit height
v,
2023,25 Although 2325 models exist for the case of individual particles,
The
and radius
the behavior of suspensions where particles interact
as a function of the drop aspect ratio for the same
with each other is still unclear.
data. The dashed curves are derived from the t in (b)
26,27,41 Various engulf-
ment patterns have been observed with particles aggre-
through mass conservation.
gated in bands parallel to planar fronts,
41 between den-
42 In the last decades, drites, or at grain boundaries. this particle-front interaction has been used to produce highly anisotropic porous structures after dry-
then simply t their prefactor and get an average stain packing fraction of
ϕ = 0.19 ± 0.07,
ing/dissolving the solidi ed matrix, a technique now
showing that our
called freeze-casting.
stains are quite porous, much more than typical coee
tures, although much more regular and anisotropic,
9 or ball-like deposits obtained with a depinning 39,40 (for which ϕ ∼ 0.4 − 0.7 17 ). strategy rings
share some similarities with the microstructure of our stains. The dierences probably come from the absence
We investigate this particular porous microstructure with electron microscopy.
of binders in our drops to hold the particles in place and
Figure 5(a) shows an
overview of a representative stain.
18,19,43 These freeze-casted struc-
therefore, part of the structure collapses on itself during
The spot-like core
the drying and is perhaps transported on the receding
where most of the particles accumulate is very distin-
interface. These similarities strongly suggests that here
guishable from the outer region. The outer region con-
also, the particle-front interaction is responsible for the
sists of concentric stripes of small aggregates which be-
stain microstructure.
come smaller and more isotropic as we move away from
Consequently, we now focus on the freezing process.
the core, toward the stain edge. The core itself consists
Because our drops are supercooled, they freeze in two
of a rather compact central spot with a more porous
stages (see Movie S3). They rst go through a recales-
edge with concentric voids much larger than the parti-
cence stage where a very fast front (v
cles. The core's edge [Figure 5(b)] consists of clumps of
∼ 0.2
m/s) prop-
agates on the whole droplet and freezes about
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(a)
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(c)
200 µm
(b)
10 µm
(d)
5 µm
10 µm
Figure 5: Electron microscopy images of the stain in Figure 3(b)(e)(h) which as an intermediate aspect ratio:
µm, r = 469 µm. (a)
Overview of the stain.
(b)
Close-up view of the edge of the core region.
(c,d)
h = 66.5
Close-up views
of the center of the core.
the water while the drop temperature rises to
0◦ C. 4448
get trapped.
26
This creates a mushy water-ice mixture where the re-
We therefore propose a scenario for the stain for-
maining liquid water is trapped in a dendritic ice lat-
mation which combines the two mechanisms discussed
tice.
above.
48 Next, the main steady-state freezing front prop-
During recalescence, the front velocity is too
agates upward in the mushy drop until complete freez-
high and captures some particles within the dendritic
ing.
ice lattice. Then, the main front propagates more slowly
5 µL
We track the main front during the freezing of drops on glass and parylene and nd a quasi-
constant velocity
v ≈ 250 µm/s
upward and repels the particles in a liquid lens.
35,36
irrespective of the sub-
At the latter stages of freezing, the pushed particles
At the onset of freezing, the sus-
accumulate in a compacted layer above the solidi ca-
pension is very dilute and the main front propagates
tion front visible in Movie S3 [Figure 6(a), the ice lat-
at equilibrium.
tice from recalescence is not drawn for clarity]. When
strate wettability.
We can therefore estimate the critical
front velocity to repel the particles
vc
from models de-
veloped for single particles. The most recent
this layer becomes thick enough, particles start to get
25 predicts
continuously engulfed
26 but not homogeneously. The
vc ≈ 25 µm/s (see Supple10 times lower than our
front is not smooth on the microscale [Figure 6(b)]; as
mentary Information), a value
observed in freeze-casting,
main front velocity. Yet, a bright layer is visible above
agating ahead of the front leave the regularly spaced
the front during the freezing in Movie S3 indicating a
large voids observed while small dendrites capture the
higher concentration of particle there, thus con rming
particles in small, compact aggregates:
that the particles are initially repelled.
a critical engulfment velocity
18,19,43 large lamellas prop-
18,27 the clumps
Perhaps the
forming the stain. The particles are thus not distributed
particle slight charge and surfactants, not accounted in
homogeneously within the frozen drop. They are more
the model have a signi cant in uence here, especially on
concentrated at its apex and the strength of this con-
the magnitude of the DLVO force between the front and
centration depends on the shape of the liquid lens when
particle. Nonetheless, as the particle concentrate addi-
the particles engulfment starts, which depends on the
tional forces comes into play and the particle eventually
drop aspect ratio. Finally, as the drop sublimates, the
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(a)
water
tion, self-assembly or biomedical assays as they produce a unique porous spot-like structure which is sensitive to a dierent set of parameters (e.g.
ice
front velocity, par-
ticle size or thermal conductivity) that needs further exploration. A better understanding and control of the front-particle interaction during freezing and interfacial capture mechanism during drying could allow the pro-
(b)
duction of ball-like stains with highly ordered porosity similar to the ones recently developed using droplets in solution.
Close-up
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Langmuir
4952
Acknowledgement
I am grateful to D. Bonn and
N. Shahidzadeh for fruitful discussions and support. I also thank F. van Veen for his help with preliminary experiments and P. Kolpakov for the SEM images.
I
thank Shell Global Research for funding
ice dendrite
Supporting Information Available
ice lamella
Discussion on the eect of the substrate temperature Figure 6:
and drop volume on the stains, calculation of the critical
Schematic representation of the proposed
physical process.
(a)
engulfment velocity based on the model of Ref
Macroscale: as the freezing front
propagates upwards, it expels most of the particles toward the top of the drop.
bic (Movie S1) and a hydrophilic substrate (Movie S2).
The particles thus aggre-
Movie of a drop freezing highlighting the clustering of
gate in the center and the aggregation strength depends
particles toward the drop apex (Movie S3).
on the curvature of the liquid lens (which depends on the drop's aspect ratio).
(b)
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Graphical TOC Entry frozen droplet of colloidal suspension
dry air
200 μm
cold substrate Ice sublimation
stain
ACS Paragon Plus Environment 10
