Stains from freeze-dried drops

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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers

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 dicult 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 lidication 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

ACS Paragon Plus Environment 1

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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

inuence 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 conrms 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 coecient

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-magnication 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 prole (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


t0 ≈ tf /2

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 reection 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 . prole, 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 conned 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 prolometer

β = D (ρsat − ρ∞ ) /ρice with D the water diusion coecient, ρsat the vapor saturation concentration over ice, ρ∞ the vapor concentration at innity 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 modies 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 inuences 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 specic 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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Page 4 of 10

(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 prole (white dashed line).

The images include the reection 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 conrming

If this packing fraction is constant throughout

that our stains have a reasonably constant porosity. We


Page 5 of 10 (a)

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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 dened 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 solidication 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 solidied 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


30%

of

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(a)

Page 6 of 10

(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 solidica-

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 conrming

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 signicant inuence 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


Page 7 of 10

(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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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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Page 10 of 10

Graphical TOC Entry frozen droplet of colloidal suspension

dry air

200 μm

cold substrate Ice sublimation

stain


Stains from freeze-dried drops

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