Table Of Content5 Diverse Spreading Behavior of Binary Polymer Nanodroplets
0
0
2
David R. Heine, Gary S. Grest, Edmund B. Webb III
n
a
J 2nd February 2008
9
1
] Sandia National Laboratories, Albuquerque, New Mexi
o 87185
t
f
o
s
.
at Abstra
t
m
Mole
ular dynami
s simulations are used to study the spreading of binary polymer nanodroplets in
-
d
a
ylindri
al geometry. The polymers, des
ribed by the bead-spring model, spread on a (cid:29)at surfa
e
n
o with a surfa
e-
oupled Langevin thermostat to mimi
the e(cid:27)e
ts of a
orrugated surfa
e. Ea
h droplet
c ∼350000
[
onsistsof
hainsoflength10or100monomerswith monomerstotal. Thequalitativefeatures
1 of the spreading dynami
s are presented for di(cid:27)eren
es in
hain length, surfa
e intera
tion strength,
v
7 and
omposition. When the
omponents of the droplet di(cid:27)er only in surfa
e intera
tion strength, the
5
4 more strongly wetting
omponent forms a monolayer (cid:28)lm on the surfa
e even when both materials are
1
0 aboveorbelowthewettingtransition. Inthe
asewheretheonlydi(cid:27)eren
eisthepolymer
hainlength,
5
the monolayer (cid:28)lm beneath the droplet is
omposed of an equal amount of short
hain and long
hain
0
/
t monomers evenwhen one
omponent(the shorter
hain length) is above the wetting transition and the
a
m otherisnot. Thefra
tionofshortandlong
hainsinthepre
ursorfoot dependsonwhetherornotboth
-
d the short and long
hains are in the wetting regime. Diluting the
on
entration of the strongly wetting
n
omponentin a mixturewith a weaklywetting
omponentde
reases therate of di(cid:27)usion of thewetting
o
c
material to the surfa
e and limits the spreading rate of the pre
ursor foot, but the bulk spreading rate
:
v
i is nota(cid:27)e
ted untilthemore strongly wetting
omponentis removed
ompletely.
X
r
a
1 Introdu
tion
The spreading of liquid dropletson a surfa
e is an important issuefor severalindustries in
luding adhesion,
lubri
ation,
oatings,and printing. Emerging nanote
hnologyin areassu
haslithographyand mi
ro(cid:29)uidi
s
make the issue of droplet spreading on small length s
ales even more relevant.
Just as blending bulk polymers
an improve the physi
al properties of the resulting material, adding a
se
ond
omponentto aspreadingdroplet
anprodu
eadesired
hangein surfa
etensionorwettability. For
1
example, adding a surfa
tant to a droplet that ordinarily does not wet a surfa
e
an give a produ
t that
1
doeswet the surfa
e. In general,adding ase
ond
omponentprovidesmoreparameterswithwhi
hto tune
thematerialproperties,but italsointrodu
esmore
omplexphenomenasu
hastheinterdi(cid:27)usionofthetwo
omponents and possible preferential wetting of one at either the liquid/solid or liquid/vapor interfa
e due
to the di(cid:27)eren
e in surfa
e tension.
Compared to homogeneous systems, the published literature on binary droplets is limited. Experiments
on binary droplets have been
on
erned primarily with a nonwetting polymer solute in a wetting solvent.
2
These experiments explored the
on
entration dependen
e of the equilibrium
onta
t angle and found a
3,4 5
leak-out transition where a (cid:28)lm of pure solvent is in equilibrium with the droplet. Other experimental
6,7
and theoreti
al papers fo
us on the equilibrium behavior of binary mixtures. The surfa
e segregation of
8(cid:21)10
two-
omponent polymer (cid:28)lms has been studied using mole
ular dynami
s (MD) simulation as well as
11(cid:21)13
numeri
al te
hniques based on Ising-likemodels. Some MD simulations of droplet spreading have been
4000
14,15 16
performed for mixtures of solvent and oligomers with monomers or mixtures of two oligomers
25000
withupto monomers,thoughevenlargersystemsizesarerequiredtoadequatelymodelthespreading
17
dynami
s. Oneworkbythe
urrentauthorsexploredrea
tivewettingofbinarydropletsinmetalli
systems.
Results therein demonstrated a di(cid:27)eren
e in substrate dissolution rate with varying droplet
omposition,
whi
h in turn resulted in di(cid:27)erent wetting kineti
s and equilibria. However, the
ombined phenomena of
substratedissolutionwithwettingpreventsdire
tly
onne
tingthoseresultstonon-rea
tivewettingofbinary
polymer droplets.
This paper presents mole
ular dynami
s simulations of binary polymer nanodroplets di(cid:27)ering in either
polymer
hainlengthorsurfa
eintera
tionstrength. Weexplorethe qualitativedi(cid:27)eren
esin thespreading
behavior, surfa
e monomer
omposition, and pre
ursor foot
omposition for several systems. We also vary
the relative
on
entration of the two
omponents and analyze the velo
ity distributions of the spreading
∼ 350000
droplets. All of the simulations presented here are for droplets of monomers, whi
h for single
18,19
omponent droplets is su(cid:30)
iently large to over
ome(cid:28)nite size e(cid:27)e
ts.
This paper is organized as follows. Se
tion 2 presents a brief summary of the mole
ular dynami
s
simulation te
hniques and the appli
ation of the surfa
e-
oupled Langevin thermostat. It also des
ribes
the methods used to analyze the simulation results. The methods of analysis are des
ribed in more detail
18,19
elsewhere. Se
tion3
ontainsthesimulationresultsforbinarypolymernanodropletsfordi(cid:27)erentpolymer
hain lengths and surfa
e intera
tion strengths, and dis
usses the e(cid:27)e
ts of varying the mole fra
tion of
strongly wetting and weakly wetting
omponents. Con
lusions drawn from these simulations are presented
in Se
. 4.
2
2 Simulation Details
Mole
ular dynami
s simulations are performed using the standard
oarse-grainedmodel for polymer
hains
m
in whi
h the polymer is represented by spheri
al beads of mass atta
hed by springs. We use a trun
ated
Lennard-Jones (LJ) potential to des
ribe the intera
tion between the monomers. The LJ potential is given
by
12 6
ULJ(R)= 4εh(cid:0)σr(cid:1) −(cid:0)σr(cid:1) i r ≤rc
(1)
0 r >r
c
ε σ r = 2.5σ
c
where and are the LJ units of energy and length and the
uto(cid:27) is set to . The monomer-
ε σ
monomer intera
tion is used as the referen
e and all monomers have the same diameter . For bonded
monomers, we apply an additional potential where ea
h bond is des
ribed by the (cid:28)nite extensible nonlinear
20 k=30ε R0 =1.5σ
elasti
(FENE) potential with and .
18
The substrate is modeled as a (cid:29)at surfa
e sin
e it was found previously that with the proper
hoi
e of
thermostat, the simulations using a (cid:29)at surfa
e exhibit the same behavior as those using a realisti
atomi
substrate. Sin
e simulating a realisti
substrate requires several times the total number of atoms in the
simulation, using the (cid:29)at surfa
e greatly improves the
omputational e(cid:30)
ien
y. The intera
tions between
z
thesurfa
eandthemonomersinthedropletatadistan
e fromthesurfa
earemodeledusinganintegrated
LJ potential,
ULwJall(z)= 2π3εw h125(cid:0)σz(cid:1)9−(cid:0)σz(cid:1)3i z ≤zc (2)
0 z >z
c
ε z =2.2σ.
w c
where is the monomer-surfa
e intera
tion strength and
We apply the Langevin thermostat to provide a realisti
representation of the transfer of energy in the
droplet. The Langevinthermostat simulates a heat bath by adding Gaussian white noise and fri
tion terms
to the equation of motion,
m¨r =−∆U −m γ r˙ +W (t),
i i i i L i i
(3)
m i γ −∆U
i L i
where is the mass of monomer , is the fri
tion parameter for the Langevin thermostat, is
i W (t)
i
the for
e a
ting on monomer due to the potentials de(cid:28)ned above, and is a Gaussian white noise
21
term. Coupling all of the monomersto the Langevinthermostat hasthe unphysi
al e(cid:27)e
t of s
reening the
hydrodynami
intera
tions in the droplet and not damping the monomers near the surfa
e stronger than
3
those in the bulk. To over
ome this, we use a Langevin
oupling term with a damping rate that de
reases
γ (z)=γs exp(σ−z) γs
exponentiallyawayfromthesubstrate.22 We
hoosetheform L L where L isthesurfa
e
z γs = 10.0τ−1
Langevin
oupling and is the distan
e from the substrate. We generally use values of L and
3.0τ−1 ε =2.0ε 3.0ε
w 18
for and , respe
tively, based on earlier work mat
hing the di(cid:27)usion
onstant of the
γs
pre
ursor foot for (cid:29)at and atomisti
substrates. The larger L
orresponds to an atomisti
substrate with
larger
orrugation and hen
e largerdissipation and slowerdi(cid:27)usion near the substrate.
19
All of the droplets presented here are modeled as hemi
ylinders as des
ribed previously. The droplets
x y L = 40σ
y
spread in the dire
tion and ea
h system is periodi
in the dire
tion with length and open
in the other two dire
tions. This allows a larger droplet radius to be studied in the
ylindri
al geometry
than in the spheri
al geometry using the same number of monomers. The binary droplets
onsist of either
N = 10 N = 100 ε
w
mixtures of
hain length and polymers with the same surfa
e intera
tion strength or
N = 10 ε
w
mixtures of
hain length with varying . Unless expli
itly stated, the binary droplets
ontain an
R0 = 80σ
equal number of monomers of ea
h
omponent with initial droplet radius of for a total size of
∼350000
18
monomers. These droplets are large enough that (cid:28)nite droplet size e(cid:27)e
ts are minimal.
∆t =
The equations of motion are integrated using a velo
ity-Verlet algorithm. We use a time step of
0.01 τ τ = σ m 1/2 T = ε/k
where (cid:0)ε(cid:1) . The simulations are performed at a temperature B using the lammps
48 64
23
ode. Most of the simulations were run on to pro
essors of Sandia's ICC Intel Xeon
luster. One
350000 37 48
million steps for a wetting drop of monomers takes hours on pro
essors.
Forthesimulationspresentedhere,theinstantaneous
onta
tradiiforthepre
ursorfootandbulkregions
400τ
areextra
tedevery . The
onta
t radius is
al
ulatedby de(cid:28)ning aone-dimensional radialdistribution
18
fun
tion, as des
ribed previously. The pre
ursor foot radius
al
ulation in
ludes all monomers that are
1.5σ 4.5 6.0σ
within of the surfa
e whereas the bulk radius
al
ulation uses monomers between and from
the surfa
e.
3 Results and Dis
ussion
The additional degrees of freedom for binary droplets leads to a number of qualitatively distin
t spreading
hara
teristi
s. In the following (cid:28)gures, we show snapshots of several di(cid:27)erent droplets as they wet the
substrate. In ea
h
ase, the droplets start in roughly the same
on(cid:28)guration with a
onta
t angle near
90o
, but they ea
h show di(cid:27)eren
es in the pre
ursor foot
omposition and spreading rate as well as the
omposition of the (cid:28)rst layerabove the substrate.
4
N = 10 ε = 1.0ε
w
Figure 1: Pro(cid:28)les for binary droplets
omposed of equal mixtures of
hain length with
ε =2.0ε t=40000τ t=80000τ ε =2.0ε
w w
(yellow)and (blue) at (top) and (middle). Pro(cid:28)lefor (yellow)
ε = 3.0ε t = 40000τ 600σ
w
4a0ndσ (blueγ)sa=t 10.0τ−1 (bottom). The substrate (red) has a length of and a width of
in ea
h pro(cid:28)le. L .
3.1 Substrate Intera
tion Strength
N =10
ThetoptwodropletsinFig. 1showapro(cid:28)leofaspreadingdropletforthemixtureof
hainlength in
ε =1.0ε ε =2.0ε
w w
whi
hhalfofthe
hainsintera
twiththe substratewith andhalfwith fortwodi(cid:27)erent
N = 10
times. Previously we have shown that the wetting transition for droplets of
hain length o
urs at
εc ≃ 1.75ε N = 10 ε = 1.0ε
w . This droplet is a mixture of a wetting and nonwetting polymer.18 For , w has
θ0 ∼=90o
a (cid:28)nite
onta
t angle of . At early times, a monolayer of the wetting
omponent forms at the solid
interfa
e and wets the substrate. However, unlike the
ase of a homogeneousdroplet in whi
h all monomers
ε =2.0ε
w 19
intera
twiththesubstratewith , thepre
ursorfootinthis
asedoesnotseparatefromthemain
droplet. Both
omponents of the droplet follow the monolayer as it wets the substrate, but the spreading
rate of the droplet is limited by the spreading rate of the monolayer. The evolution of the
onta
t angle
ε = 1.0ε ε = 2.0ε
w w
for the binary droplet with and is
ompared to the single
omponent droplet with
ε = 2.0ε ε
w w
in Fig. 2. In this
ase, adding the lower
omponent slightly de
reases the spreading rate of
19
the droplet. This de
rease is su(cid:30)
ient to produ
e a better (cid:28)t to the hydrodynami
spreading model as
ε =2.0ε
w
ompared to the pure system.
Di(cid:27)erent behavior is observed when both
omponents wet the surfa
e as shown in the bottom panel of
ε = 2.0ε 3.0ε
w
Fig. 1 for a mixture with and . Despite the fa
t that both
omponents wet the substrate,
5
80
60
oθ []40
20
0
0 10000 20000 30000 40000 50000
time [τ]
ε =0.5ε ε =1.5ε
w w
Figure 2: Dynami
onta
tangleforthe binary systemswith an equalmixture of and
ε = 1.0ε ε = 2.0ε
w w
(triangles) andεan=e1q.u5aεl mixture of ε =2a.n0dε N(s=qu1a0resγ)s
=om1p0a.0reτd−1to the single
omponent
droplets with w (diamonds) and w (
ir
les). , L .
ε =3.0ε
w
a monolayer of the
omponent still forms at the solid interfa
e sin
e that is the strongly favored
intera
tion. Although earlier simulations showed an a
umulation of the more strongly wetting
omponent
16
in the (cid:28)rst layer above the substrate, here the (cid:28)rst layer
onsists entirely of the more strongly wetting
ε =1.0ε/2.0ε
w
omponent. Unlike the
ase,the spreading rate ofthe pre
ursorfoot is fastenough to allow
it to advan
e well ahead of the bulk of the droplet similar to the leak-out behavior observed experimentally
3,4
for polymer/solvent mixtures. A depletion region forms near the edges of the bulk droplet be
ause the
di(cid:27)usionrateofthewetting
omponentinthebulkisinsu(cid:30)
ienttorepla
ethematerialformingthepre
ursor
foot. In Se
tion 3.3 we return to this
ase for varying
omposition of the two
omponents.
ε = 0.5ε
w
We also
onsider the
ase of a droplet
ontaining a mixture of two nonwetting
omponents,
ε = 1.5ε N = 10
w
and for . As in the previous
ases, a monolayer of the more wetting
omponent forms
between the droplet and the substrate. In this
ase, the droplet rea
hes an equilibrium
onta
t angle of
θ0 ∼= 64o 20000τ
after . The evolution of the
onta
t angle for this nonwetting system is
ompared to the
ε = 1.5ε
w
single
omponent system in Figure 2. The single
omponent droplets have equilibrium
onta
t
θ0 ∼= 120o εw = 0.5ε 44o εw = 1.5ε
angles of for and for . Thus the
onta
t angle of the binary system is
more strongly in(cid:29)uen
ed by the material that forms a monolayeron the substrate.
3.2 Polymer Chain Length
For droplets
omposed of two
hain lengths of the same type of polymer, the spreading behavior is qualita-
N = 10
tively di(cid:27)erent. The top two droplets in Fig. 3 show pro(cid:28)les for the mixture of
hain lengths and
100 ε = 2.0ε γs = 10.0τ−1 ε = 2.0ε
with w and L . Although w for both
omponents, the longer
hains are in
6
N =10
FigurNe3=: 1P0r0o(cid:28)lesforbinarydroplets
εom=pos2e.0dεofequaγlsn=um1b0e.0rτo−fm1 onotm=er4s0o0f0
0haτinlength t = 80(b00lu0eτ)
and (yellow) polymerεs w=ith3.0wε γsa=nd3.0Lτ−1 att= 40000τ (top) and
(middle). Same as above with w and L taken at (bottom). The substrate
800σ 40σ
(red) has a length of and a width of in ea
h pro(cid:28)le.
εc ≃ 2.25ε
the nonwetting regime ( w )19 whereas the shorter
hains are slightly above the wetting transition
εc ≃ 1.75ε N = 10
( w ). As a result, a slow pre
ursor foot
onsisting of approximately 80% monomers and
N =100
20% monomers extends from the bulk region. This is somewhat similar to the (cid:16)leak-out(cid:17) behavior
observed experimentally in mixtures of polymer and solvent where the pre
ursor foot
onsists entirely of
3,4
solvent. Unlike Fig. 1, a monolayer of the wetting
omponent does not form on the substrate below
the bulk region of the droplet. Instead, the (cid:28)rst monolayer at the substrate beneath the droplet
onsists
of an equal fra
tion of the two
omponents. This
an be understood by noting that the longer
hains are
nonwetting in this
ase due to their greatersurfa
e tension. The
hains that areburied beneath the droplet
feel no in(cid:29)uen
e of the liquid/vapor interfa
e, so there is no preferen
e as to whi
h
hain length is in
on-
ta
t with the substrate. The
hains at the upper surfa
e of the droplet, both in the bulk region and the
pre
ursorfoot, are in(cid:29)uen
ed by the liquid/vapor interfa
e and there one (cid:28)nds an abundan
e of the shorter
N = 10 N = 100
hains. The liquid/vapor surfa
e tensions for the and
hains were previously found to
0.84 0.96±0.02ε/σ2 10/100
19
be and , respe
tively. The surfa
e tension for the mixture was found to be
0.90±0.02ε/σ2
indi
atingaroughlyequalin(cid:29)uen
ebyea
h
omponentonthesurfa
etensionofthemixture.
Thus, the surfa
e tension
al
ulation is not pre
ise enough to a
ount for the abundan
e of shorter
hains
at the liquid/vapor interfa
e.
ε
w
If is in
reased so that both
hain lengths are in the wetting regime, the behavior is similar to that of
N =10
a single-
omponent droplet. This is shown in the bottom of Fig. 3 for the mixture of
hain lengths
7
60
(a)
40
20
σ] 0
z [ (b)
40
20
0
0 40 80 120 160
x [σ]
N = 10 N = 100
Figure 4: Velo
ity pro(cid:28)les of half of the droεple=t s3h.0owεing thγes =3.0τ−1
haint=len2g0t0h0(0aτ), and the
hain length (b), for the binary droplet with w and L at .
100 ε = 3.0ε γs = 3.0τ−1
and where w and L . Here, both
hain lengths are in the wetting regime and the
rapidlyspreadingpre
ursorfootis
omposedofanequalnumberofmonomersofthetwo
hainlengths. One
N =100 N =10
onsequen
eofthisisthe
hainsdi(cid:27)usea
rossthesubstratemorerapidlywhenmixedwith
N = 100
hains than in the pure droplet. Although the longer
hains have a higher surfa
e tension, the
0o
equilibriumstateforboth
omponentsisa
onta
tanglesothereisnosegregationofthetwo
omponents
in thepre
ursorfoot asthis droplet spreads. The la
kofsegregationforamixture oftwo
hainlengths with
ε 8 16
w 16
the same was previously reported by Voué et al. for
hain lengths and .
The droplet velo
ity pro(cid:28)les provides another method to analyze the dynami
s of the spreading droplet.
10 100
Figure 4showsthe velo
itypro(cid:28)lesforthe mixture of
hainlengths and . Although both
omponents
showthe samespreading pathway,the shorter
hainlengths tend to moveslightly fasterat the liquid/vapor
and liquid/solid interfa
es.
3.3 Varying Composition
The ability to form a (cid:28)lm from a non- or weakly wetting polymer by adding a wetting
omponent is of
signi(cid:28)
ant pra
ti
al interest. To analyze the e(cid:27)e
ts of the
on
entration of the two
omponents on the
ε =3.0ε
w
spreading dynami
s, we simulate droplets
ontaining a strongly wetting
omponent ( ) at di(cid:27)erent
x = 0.10 0.25 0.50 ε = 2.0ε N = 10
wet w
mole fra
tions, , , and with a weakly wetting
omponent ( ). Sin
e
for both, the only di(cid:27)eren
e in the two
omponents is the surfa
e intera
tion. Pro(cid:28)les of the spreading
60000τ
droplets after are shown in Figure 5. In ea
h
ase, a monolayer of the strongly wetting
omponent
forms on the surfa
e and spreads outward. The rest of the drop then spreads on this layer. However, for
x = 0.10
wet
, the surfa
e monolayer never be
omes fully homogeneous as a segment of the weakly wetting
omponentremainsat the edgeofthefoot and
ontinuestogetpushed outwardasthedropletspreads. The
x
wet
size of the depletion region at the droplet edge in
reasesas de
reases sin
e less of the strongly wetting
8
N = 10 ε = 2.0ε ε = 3.0ε
w w
Figure 5: Pro(cid:28)les of three binary droplets of
hain length with (yellow) and
x =0.10 0.25 0.50
wet
(blue). Thet=mo6l0e0fr0a0
τtioγnss=of1th0.e0sτt−ro1nglywetting
omponentare 800(σtop), (middl4e)0,σand
(bottom). , L . The substrate(red) hasalengthof and awidth of in ea
h
pro(cid:28)le.
polymer is available to form the pre
ursor foot. The rate of spreading of the pre
ursor foot de
reases as
x
wet
de
reases be
ause the supply rate of the strongly wetting material from the bulk to the surfa
e limits
the spreading rate of the pre
ursor foot. This is more
learly demonstrated in Fig. 6 where the
onta
t
radii of both the foot and bulk regions are shown as a fun
tion of time for ea
h of the three
ompositions
x = 0
19 wet
and
ompared to previous results for . Figure 6a shows that the pre
ursor foot spreading rate
x D = 1drf2
de
reases as wet is redu
ed. The e(cid:27)e
tive di(cid:27)usion
onstant of the pre
ursor foot, eff 2 dt , de
reases
4.7 3.8 2.6 0.6σ2/τ x 0.50 0.25 0.10 0.0
wet
from to , and as de
reases from to , and , respe
tively. Figure
x
wet
6b shows no signi(cid:28)
ant e(cid:27)e
t of on the bulk droplet spreading rate for the duration of the simulation
x = 0.5 x = 0.1
wet wet
for to . However, there is a strong e(cid:27)e
t on the spreading rate when in
reasing the
x =0.0 x =0.1 tx
wet wet
on
entrationfrom to . Inall ofthese
ases,thebulk
onta
tradiusspreadsas with
∼
x=1/5
19
, whi
h is expe
ted from the kineti
model for spreading in the
ylindri
al geometry used here.
t = 70000τ
The velo
ity pro(cid:28)les of the strongly wetting and weakly wetting
omponents at are shown
x = 0.25
wet
in Fig. 7 for . After the foot has extended and a depletion region has formed at the edge of
the droplet, Fig. 7a shows that the weakly wetting material moves down from the liquid/vapor surfa
e
and up from the solid/liquid surfa
e to allow the monolayer of the strongly wetting material to form. Very
little motion is seen in the
enter of the droplet. In Fig. 7b, the strongly wetting material shows similar
behavior at the liquid/vapor surfa
e, but the data is noisier due to the smaller mole fra
tion of strongly
wetting material. This material moves through the depletion region at the edge of the droplet and onto
9
6.0
(a)
2σ]
40 4.0
1
2R) [02.0
(r-f
0.0
(b)
2σ] 1.5
40
1
2R) [0 1
(r-b0.5
0
0 20000 40000 60000 80000
time [τ]
x = 0
wet
Figure 6: Conta
t radii of the pre
ursor foot (a) and bulk (b) for the droplets
omposed of
x = 0.10 0.25 0.50
wet
(dotted
urves), (dashed
urves), (dot-dashed
urves), and (dot-dash-dashed
urves).
ε = 2.0ε ε = 3.0ε N = 10
w w
γs =10.0τf−o1r the weakly wetting
omponent and for the strongly wetting
omponent. ,
L .
the pre
ursorfoot where it rapidlydi(cid:27)uses outward. The same qualitativebehavioris observedfor di(cid:27)erent
x x
wet wet
values of , though the data be
omes in
reasingly noisy as de
reases.
4 Con
lusions
The spreading dynami
s of binary polymer nanodroplets are studied using mole
ular dynami
s simulation.
We demonstrate qualitative di(cid:27)eren
es in the spreading behavior of binary droplets due to di(cid:27)eren
es in
surfa
e intera
tion strength, polymer
hain length, and
omposition.
When the twodroplet
omponents di(cid:27)er in surfa
e intera
tion strength, the more stronglywetting
om-
ponentformsamonolayer(cid:28)lmonthesurfa
eevenwhenbothmaterialsareeitheraboveorbelowthewetting
transition. For
ases that also produ
e a rapidly spreading pre
ursor foot, a depletion region of the more
strongly wetting
omponent forms starting at the edge of the droplet sin
e the interdi(cid:27)usion rate in the
droplet is slowerthan the rate at whi
h material is withdrawn into the pre
ursorfoot.
For di(cid:27)eren
es in the polymer
hain length, the monolayer (cid:28)lm beneath the droplet is
omposed of an
equal amount of short
hain and long
hain monomers. This is true even when one
omponent (the shorter
hainlength)isabovethewettingtransitionandtheotherisnot. Inthis
ase,thepre
ursorfootis
omposed
primarily of the wetting
omponent. When both
omponents are above the wetting transition, the surfa
e
monolayer and pre
ursor foot are both
omposed of an equal amount of short and long
hain monomers.
The formation of a monolayer of the more strongly wetting
omponent is studied in greater detail by
onsidering di(cid:27)erent
ompositions of the mixture of strongly wetting and weakly wetting
omponents. For
10
