Besancon, Green - 2007 - Dewetting Dynamics in Miscible Polymer-polymer Thin Film Mixtures-Annotated

8/2/2019 Besancon, Green - 2007 - Dewetting Dynamics in Miscible Polymer-polymer Thin Film Mixtures-Annotated

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Dewetting dynamics in miscible polymer-polymer thin film mixtures

Brian M. BesanconDepartment of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712

Peter F. Greena

Department of Materials Science, University of Michigan at Ann Arbor, Ann Arbor, Michigan 48109

Received 6 February 2007; accepted 11 April 2007; published online 13 June 2007

Thin polystyrene films supported by oxidized silicon SiOx/ Si substrates may be unstable ormetastable, depending on the film thickness, h, and can ultimately dewet the substrate when heated

above their glass transition. In the metastable regime, holes nucleate throughout the film and

subsequently grow due to capillary driving forces. Recent studies have shown that the addition of

a second component, such as a copolymer or miscible polymer, can suppress the dewetting process

and stabilize the film. We examined the hole growth dynamics and the hole morphology in thin film

mixtures composed of polystyrene and tetramethyl bisphenol-A polycarbonate TMPC supportedby SiOx/ Si substrates. The hole growth velocity decreased with increasing TMPC content beyond

that expected from changes in the bulk viscosity. The authors show that the suppression of the

dewetting velocity is primarily due to reductions in the capillary driving force for dewetting and to

increased friction at the substrate-polymer interface. The viscosity, as determined from the hole

growth dynamics, decreases with decreasing film thickness, and is connected to a depression of the

glass transition of the film. 2007 American Institute of Physics. DOI: 10.1063/1.2737043

INTRODUCTION

Thin polymer films in the thickness range of nanometers,

or tens of nanometers, exhibit thickness dependent proper-

ties: glass transition,118

viscosity,1925

and vibrational

dynamics.2631

These thickness dependencies are due to the

influence of interfacial interactions and confinement.3234

Structural instabilities, leading to dewetting, are ubiqui-

tous in liquid or molten thin films.3540

While impurities and

residual stresses are important factors that affect the struc-

tural stability and morphology of thin films, long-range vander Waals forces acting across the film are often fundamen-

tally responsible for structural destabilization.4143

One

method for changing the intermolecular interactions to

promote stability is to modify the chemical composition of

the substrate. An alternative to modifying the substrate

chemistry is to add a second component, such as a miscible

homopolymer,44

copolymer,45

dendrimer,46

or

nanoparticles,47

to the polymer.

In the case of mixtures where the second component is a

copolymer or homopolymer that preferentially adsorbs to the

substrate, the dewetting dynamics are modified due to the

interactions of the second component with the substrate and

with the host polymer. In entangled polymer systems, whereslip at a polymer/substrate interface is an important factor in

the dynamics, changes in the friction between the polymer

and substrate play a significant role in the dynamics.4850

Oslanec et al. showed that the addition of PS-b-PMMA co-

polymers to PS resulted in a retardation of the dewetting

process due to entanglements between the adsorbed chains

and the dewetting PS chains and a reduction in the capillary

driving force for dewetting.45

Kropka and Green recently

examined the effect of adding a second miscible component,

TMPC, on the structural stability of PS thin films.44

They

showed that very small TMPC concentrations kinetically sta-

bilized the PS films against the nucleation and growth of

holes.

In this paper we examine the influence of tetramethyl

bisphenol-A polycarbonate TMPC on the kinetics of holegrowth and on the morphology of growing holes in thin PS-

TMPC films containing weight fractions of TMPC, wTMPC

0.03. It was difficult to get statistically meaningful datafrom samples containing appreciably larger concentrations of

TMPC because such films were kinetically stable. We ob-

served large reductions in the hole growth velocity in the

PS/TMPC films, over an order of magnitude in excess of that

which would be expected from an increase in the viscosity

due to the presence of TMPC. We suggest that this decrease

in dewetting velocity stems from both a reduction in the

driving force for dewetting and from an increase in the fric-

tional resistance at the polymer-substrate interface, associ-

ated with the strong preferential interactions between TMPC

and the substrate.44

The morphologies of the rims surround-

ing the growing holes in the PS/TMPC films are fundamen-

tally different from those in PS films. In addition we showthat the viscosities of the films, as determined from the de-

wetting dynamics, decrease with decreasing film thickness;

this decrease is associated with a reduction of the glass tran-

sition and not due to shear shinning.

EXPERIMENT

Thin film mixtures of TMPC Mw =37 900 g/mol;Mw/Mn =2.75 obtained from Bayer Corp., and fully deuter-ated polystyrene d8-PS, Mw =139 900 g/mol; Mw/Mn

aAuthor to whom correspondence should be addressed. Electronic mail:

[email protected]

THE JOURNAL OF CHEMICAL PHYSICS 126, 224903 2007

0021-9606/2007/12622/224903/9/$23.00 2007 American Institute of Physics126, 224903-1

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=1.06 purchased from Polymer Source, Inc. were dissolvedin toluene. The mixtures contained 0, 1, 2, and 3 wt %

TMPC; compositions greater than 3 wt % TMPC did not

readily dewet and were not examined.44

Note that PS has a lower surface tension than TMPC and

will preferentially enrich the free surface; TMPC, on the

other hand, preferentially enriches the substrate.44

In fact, an

autophobic layer rich in TMPC, compared to the bulk, re-

mains at the substrate after dewetting. This thin layer in-creases slightly in thickness with increasing TMPC.

44

Solutions of TMPC and PS were spin cast onto acid-

cleaned 100 silicon wafers, which had a native oxide layerof 1.5 nm as determined by ellipsometry. The films were

then annealed 30 K above their Tgs for at least 4 h. Film

thicknesses between 20 and 70 nm, as measured by ellip-

sometry, were prepared by adjusting the solution concentra-

tion and spin rate.

Analyses of the topographies of the films were per-

formed using scanning force microscopy SFM AutoprobeCP atomic force microscope from TM Microscopes. Ex situSFM scans were made employing the contact mode. Each

film was scored after deposition to expose the underlyingsubstrate so that the same hole could be easily found and the

local film thickness could be determined from the SFM scans

of the edges. These values agreed well with those from el-

lipsometry. The films were subsequently annealed at 180 C

under vacuum and periodically quenched and analyzed using

SFM.

RESULTS AND DISCUSSION

The structural stability of a polymer thin film on a sub-

strate is reasonably well understood.42,43

The excess free en-

ergy of interaction per unit area between the liquid/substrateand liquid/free surface interfaces separated by a distance, h,

is determined by a combination of short- and long-ranged

intermolecular interactions. These are often represented by

an effective interface potential, h = Asvl/12h2 +h.

The first term in the potential describes the long-ranged van

der Waals contribution to the interaction; Asvl is the Hamaker

constant, which describes the strength of the interaction be-

tween the substrate/polymer and polymer/free surface inter-

faces. The second term, h, describes short-range forcesassociated with molecules in contact. A net attraction exists

between the solid-liquid and liquid-vacuum interfaces when

the Hamaker constant is positive and the film is inherently

unstable.42,43,51

For the Si/SiOx/ PS system, the effective Ha-maker constant is positive, and thin PS films are typically

unstable or metastable, depending on their initial film thick-

ness. For larger thicknesses 10 nm thin PS films onSi/SiOx substrates are known to be metastable.

43,52In this

metastable regime, the PS films dewet via the nucleation and

subsequent growth of holes. In this case there exists a global

minimum in the effective interface potential that implies a

stable layer on the order of a nanometer on top of which the

melt will dewet.43,53

At high temperatures, the thin adsorbed

layer is thought to remain stable while it destabilizes as the

temperature is decreased leading to the formation of nano-

droplets adsorbed to the substrate.24,44,53,54

The nucleation of holes occurs with the formation of a

local depression in the film at the free surface. This local

depression penetrates into the film and impinges on the sub-

strate. When a hole forms on the substrate, capillary forces

negative spreading coefficient, S =svlvsl, where sv,lv, and sl are the solid-vapor, liquid-vapor, and solid-liquid

interfacial energies, respectively are responsible for itsgrowth. As a hole grows, the rim at the perimeter of the hole

increases in size due to the accumulation of chains. The cap-illary forces driving hole growth are opposed by two pro-

cesses: the dissipation of energy within the film due to vis-

cous resistance and the resistance due to friction at the

substrate/liquid interface. If friction at the substrate/liquid

interface is the dominant mode of dissipation, then for suffi-

ciently small rim widths, the hole radius, r, grows linearly in

time.55

rS

b

h1/2t. 1

In Eq. 1, is the viscosity and b is the hydrodynamic

extrapolation slip length, which is determined by the ratioof the viscosity and the monomer friction coefficient be-tween the polymer and the substrate, k k=/b.56 The ve-locity is constant initially because the driving force is con-

stant and the resistance due to friction, which depends on the

rim size, is small. While the radius of the hole increases

linearly with time, the width of the rim increases as the

square root of time due to volume conservation. Eventually,

as time progresses, the hole growth velocity decreases be-

cause the frictional resistance increases with the size of the

growing rim while the driving force remains constant. In this

long time regime, the hole size increases as55

r= lv

2/3

E5/3b2

h 1/3

t2/3 , 2

where lv is the liquid-vapor surface tension, and E is the

equilibrium contact angle of droplets formed on the substrate

after dewetting. This description of the hole growth55

is con-

sistent with previous data for PS films dewetting off a

SiOx/ Si substrate.19,20,45,54,57

As this model of hole growth demonstrates, the friction

at the substrate-polymer interface is an important factor in

determining the growth rate of holes. In order to understand

how the friction at the substrate affects the dewetting veloc-

ity, we investigated the hole growth dynamics of miscible

thin film mixtures of PS and small concentrations of TMPC.TMPC exhibits a strong preferential affinity for the substrate

and PS, which has the lower surface energy, dominates the

free surface.

The time dependencies of the radii of holes for various

thicknesses shown for the pure PS thin films in Fig. 1a areconsistent with an initial linear growth stage followed by

power law growth.19,20,45,54,55,57

Similar qualitative hole

growth behavior is also observed for the 1 and 2 wt %

TMPC-PS mixtures. In thin PS films, the time dependence of

the rim width also transitions from t1/2 to t1/3 at roughly the

same hole size as the transition from linear to power law

growth of the hole radii.54,55

These data indicate that holes

224903-2 B. M. Besancon and P. F. Green J. Chem. Phys. 126, 224903 2007



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grow by a slip process, and the hole growth dynamics are

qualitatively consistent with Eqs. 1 and 2. With largerTMPC concentrations, the hole growth behavior changes. As

Fig. 1b shows, the time dependence of the hole radii for thethicker 3 wt % TMPC/PS thin films exhibits an initial linear

growth stage followed by slower growth at later times in

which the hole growth is arrested and the radius essentially

reaches a plateau value. However, for all mixture composi-

tions studied, the holes grow at a faster rate with decreasing

film thickness consistent with results for hole growth on sup-

ported substrates20,52,58

and in freestanding films.22,23

Fur-

thermore, the time dependence of the hole radii decreases

strongly with increasing TMPC concentration, as is shown in

Fig. 2 for h = 30 nm thick films. The reasons for the observed

reduction in dewetting velocity with TMPC composition are

investigated in the following sections.Using Eq. 1, we calculated the velocity of hole growth

as a function of composition and thickness for the linear

growth regime. These initial hole growth velocities are plot-

ted in Fig. 3 as a function of film thickness for all four

compositions. These data reveal that the addition of small

amounts of TMPC leads to large decreases in the hole

growth velocity; the reductions are beyond that expected

from increases in the mixture viscosity due to the addition of

TMPC. The ratio of the hole growth velocities is shown in

Table I for films of h =50 nm. The relative hole growth ve-

locity, VPS/VPS-TMPC, is roughly independent of h within the

errors of our measurements. Figure 3 also shows that, for all

compositions, the hole growth velocity increases with de-

creasing thickness in excess of that predicted by Eq. 1. Thethickness dependence scales as roughly h2 and is consistent

with previous data on pure PS.19,20

The excess thickness de-

pendence, relative to the h1/2 prediction of Eq. 1, has beenpreviously rationalized in terms of a thickness dependent

viscosity.19,20

As we will show later, these data are consistent

with that hypothesis.

As shown in Eqs. 1 and 2, the primary factors influ-encing the hole growth rate are the viscosity, , the spread-

ing coefficient S =lv1cos E, and the slip extrapolationlength, b, which is determined by the ratio of the viscosity to

the friction at the substrate. The contributions of these three

TABLE I. The values of the experimentally measured and calculated ratio of

the dewetting velocities are compared. The ratios of the relevant parameters

affecting the dewetting velocity according to Eq. 3 are shown.

PS 1% TMPC 2% TMPC 3% TMPC

VPS/VPS-TMPC Expt. 1 1.96 4.02 8.03

VPS/VPS-TMPC Calc. 1 1.64 2.52 6.11

PS-TMPC/PS 1 1.03 1.07 1.10

SPS/SPS-TMPC 1 1.30 1.62 2.94

bPS/bPS-TMPC1/2 1 1.22 1.46 1.89

FIG. 1. The hole radius as a function of time and film thickness is shown for

the a 152 kg/mol PS films and b the 3 wt % TMPC/152 kg/mol PS filmmixtures.

FIG. 2. The hole radius as a function of time and mixture composition is

shown for films with thickness h 30 nm.

FIG. 3. The initial linear velocity is plotted as a function of film thickness

and shown to decrease with increasing TMPC concentration.

224903-3 Dewetting dynamics J. Chem. Phys. 126, 224903 2007



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factors to the dewetting velocity can be examined using

Eq. 1. The hole growth velocity of the pure PS relative to aPS-TMPC mixture is given by

VPS

VPS-TMPC=

SPS

SPS-TMPC

PS-TMPC

PS bPS

bPS-TMPC1/2 . 3

The viscosity of bulk PS-TMPC blends has been measured

independently by Wisniewski et al. as a function of

composition.59 Interpolation of their data shows that additionof 3 wt % TMPC only increases the viscosity by a factor of

10%, which is small compared to the observed changes inthe hole growth velocity. Kropka and Green measured the

equilibrium contact angle, E, as a function of TMPC com-

position in thin film mixtures of 4 kg/mol PS and TMPC.44

The equilibrium contact angle was found to decrease with

increasing TMPC composition.44

Since the spreading coeffi-

cient is determined by the value of the contact angle via S

=lv1cos E, the magnitude of the spreading coefficientdecreases significantly upon addition of 3 wt % TMPC, de-

creasing by a factor of roughly 3. We do not expect signifi-

cant differences in the droplet contact angles due to the dif-

ferences in molecular weight between the two systems.

Furthermore, extrapolation of the contact angle data of

Kropka and Green suggests that a transition, wherein there

was no evidence of hole formation, occurs near a value of

5 wt % TMPC this suppression is believed to be kinetic.Accordingly, we did not observe consistent, or appreciable,

hole formation in films containing more than 3 wt % TMPC.

The third factor affecting the hole growth velocity, the

slip extrapolation length, can be calculated from the

equation49,58,60

bti = 3Vtiwti/0.5lvti , 4

where wti is the rim width, Vti is the velocity, and ti isthe dynamic contact angle, which is directly measured byatomic force microscopy at time ti. The value of the viscos-

ity, , used was PS =2.1104 Pa s,

61and the viscosity in-

creased with TMPC concentration59

by the factor listed in

Table I. The slip extrapolation length did not show an appre-

ciable dependence on time for the pure PS, 1 wt % TMPC

films, or 2 wt % TMPC films. Furthermore, there was no

appreciable dependence of b on the film thickness, as one

would expect. In the 3 wt % TMPC films, however, b was

initially constant and then decreased with further anneal

time. The average value of the slip extrapolation length ob-

tained from the time-independent regime is plotted as a func-

tion of TMPC composition in Fig. 4. The slip length de-creases with TMPC composition for the four compositions

shown. The slip lengths are considerably less than their the-

oretical values 20 m;19,56 the substrate is not smoothand passive

56as evidenced by the adsorption of PS and

TMPC chains at the substrate demonstrated by the presence

of secondary droplets adhered to the substrate.44,53,54

The ratios of the three parameters , S, and b primarilyaffecting the hole growth velocity as defined in Eq. 3 areshown in Table I. While the agreement between the calcu-

lated and measured hole growth velocity ratios is not exact,

the data in Table I indicate that the largest factors contribut-

ing to the reduction in dewetting velocity arise from changes

in the substrate-liquid interactions. TMPC adheres to the

substrate due to preferential interactions with the oxide sub-

strate, with which it hydrogen bonds.13,15,17,62

The spreading

coefficient primarily the polar component of S44 thuschanges because TMPC alters the liquid-substrate interfacial

energy. However, the bare surface energy remains invariant,

or with negligible changes, because PS has a lower surface

tension63

and the concentrations of TMPC are small. Addi-

tional factors contributing to the reduction in the dewetting

velocity could be due to the energy cost associated with

stretching and pulling out adsorbed chains.45

Nevertheless

the key point is that the slip lengths in the mixtures are small

compared to that of pure PS.

We now explore the reasons for the decrease in the slip

extrapolation length with increasing TMPC composition

Fig. 4. The slip length is the ratio of the viscosity to thefriction coefficient b =/k indicating that addition ofTMPC chains to PS films results in an increase in the friction

at the polymer/substrate interface beyond the increase in vis-

cosity due to addition of TMPC. In addition to a reduction in

the calculated value of the slip extrapolation length Fig. 4,an increase in friction is also manifested in the reduction ofb

with time as mentioned earlier for the 3 wt % TMPC films.

Reiter and Khanna examined the slip length as a function of

time for PDMS films dewetting off a densely grafted poly-

dimethyl siloxane PDMS brush layer and a weakly ad-sorbed PDMS layer.

58For dewetting of a layer from the

densely grafted layer, the slip length calculated by Eq. 4

was independent of time, whereas for dewetting from theweakly adsorbed layer, b, decreased with annealing time.

The decrease of b was attributed to increased interpenetra-

tion of the adsorbed layer with the dewetting melt. This re-

sult is similar to our results for the 3 wt % TMPC mixtures

where TMPC adsorbs to the substrate and interacts with the

melt. Both the decrease of the slip length with increasing

time for larger TMPC concentrations and the decrease in the

average slip length with increasing TMPC concentration in-

dicate increased friction at the polymer/substrate interface.

Bruinsma proposed a two-fluid model to describe the

case in which polymer chains near the substrate possess re-

duced mobility relative to chains in the remainder of the

FIG. 4. The slip extrapolation length calculated from Eq. 4 is plotted as afunction of TMPC concentration.




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film.48

Due to the excess TMPC at the substrate, this would

to be the case for our PS-TMPC system. Bruinsma postu-lated that as the film thickness becomes comparable to Rg, an

increasing fraction of the polymers in the film will have con-

tacts with the substrate termed attached chains resultingin a reduction in their mobility. The remaining fraction of the

chains have no contact with the substrate unattachedchains. Transport of the chains in contact with the substrateoccurs through a slip mechanism. These chains form a po-

rous medium through which the unattached chains diffuse.

The resistance to diffusion of these chains through the po-

rous medium is described by the monomeric friction factor,

which is distinct from the friction coefficient, k, at the solid/

liquid interface due to slip. The dewetting velocity of the

melt is then determined by the sum of the friction coefficientdue to slip and the friction factor of the chains transported

through the network. To account for the reduced mobility of

the polymers near the substrate, a new friction coefficient

was defined, k=fk, where f is the ratio of the monomer

mobility in the bulk to that near the substrate. Diffusion stud-

ies in thin films have suggested that f could be on the order

of 100.64,65

Alternatively, one could redefine the slip extrapo-

lation length as b=f1b. In the case of the PS-TMPC sys-

tem, b would be the value of b for the mixture. With in-

creasing TMPC concentration, we might expect the mobility

of the layer near the substrate to decrease relative to the bulk

of the film because of the TMPC surface excess at the

substrate and because the dynamics of TMPC are slowcompared to PS. The value of 1/f would thus continually

decrease with increasing TMPC concentration. The data in

Fig. 4 show that the compositional dependence of b is con-

sistent with this hypothesis.

Thickness dependence of the hole growth velocity

As we showed earlier, the thickness dependence of the

hole growth velocity is considerably larger than predicted by

theory, which suggests V h1/2.55 The viscosity of the filmscan be calculated from Eq. 1 similar qualitative results areobtained if the late time, power law regime given by Eq. 2

is used. The reduced viscosities normalized to their values ath =50 nm are presented in Fig. 5. The viscosity decreases

with decreasing film thickness as suggested by Masson and

Green.19,20

The thickness dependence of the viscosity19,20

is

thought to arise from a decrease in the glass transition tem-

perature of the films with decreasing thickness.1,9

Whereas

this hypothesis was formed by rationalizing the thickness

dependence of the hole growth velocity, Herminghaus and

co-workers examined the dewetting dynamics of very thin25 nm, low molecular weight 2 kg/mol PS films thatunderwent spinodal dewetting.

21They calculated the viscos-

ity from the characteristic growth time of the amplitude of

the spinodal wavelength, ,66

and obtained values of

that were many orders of magnitude lower than expected.

The Tg of the material calculated from the difference in vis-

cosity via the Vogel-Fulcher equation67

agreed well with

changes in the Tg of the material measured by ellipsometry

that were extrapolated to these very small thicknesses.21

To calculate the Tg of these thin film mixtures from the

dewetting data, we used the Williams-Landel-Ferry WLFequivalent to the Vogel-Fulcher equation equation to calcu-

late the Tg depression at each thickness relative to the valueof thick films. Subtracting the logarithm of the shift factor

for a film of thickness, h, from a film of thickness h

=50 nm yields an expression that accounts for the depression

in the viscosity as a function of the Tg of the system at a

given thickness,

logh=50 nmThT

= C1 T Tgh = 50 nm

C2 + T Tgh = 50 nm

T Tgh

C2 + T Tgh .5

In this expression, hT is the viscosity and Tgh is theglass transition temperature of a film of thickness, h, at the

anneal temperature T=180 C. The WLF constants, C1 and

C2, are material constants assumed to be 13.7 and 50 K,67

respectively, for all materials in this study. Here we have also

assumed that the viscosity at Tg is by definition the same for

any thickness and concentration.

From Eq. 5 and the data presented in Fig. 5, we havecalculated values of Tg that account for the depression in the

viscosity. These values are shown in Fig. 6. The solid line in

Fig. 6 was calculated from the equation of Keddie et al.,1

Tgh = Tg1 Ah

. 6In this equation, Tg is the glass transition temperature atlarge thicknesses, indicates the extent to which Tg de-

creases with film thickness, h, and A is a length scale. There

is good agreement between the values of Tg from our de-

wetting measurements and those from ellipsometry measure-

ments. Deviations could arise from differences in the WLF

constants that may depend on film thickness and/or as a

function of depth within the sample. As we have discussed in

the previous section, the dynamics appear to be depth depen-

dent and this could influence the analysis.

FIG. 5. The viscosity is shown to decrease relative to its thick film values

for each composition. The viscosity at h 50 nm was chosen as the normal-izing value since 3 wt % TMPC films did not readily dewet above this

thickness.




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Although the thickness dependence of the viscosity ap-

pears to be well accounted for by changes in Tgh, shearthinning has also been suggested as a mechanism to rational-

ize the reduction in viscosity observed in dewetting experi-

ments on thin, freestanding PS films.22,23

We now demon-

strate that our observations cannot be reconciled with shear

thinning. In our supported films, the shear rate at the edge of

the hole can be calculated the shear stress at the edge of the

hole using the spreading coefficient, viscosity, and film thick-

ness. In the model of Brochard-Wyart et al., the shear stress

at the edge of the hole is S/h, and the resulting shear rate is

S/h.55

We calculated shear rates in this manner to be at

most on the order of 101 s1.19

Incidentally, this is in agree-

ment with values obtained from the Herminghaus model de-

scribing the shape of the rim profiles.

Graessley proposed that the extent to which shear thin-

ning effects are important is determined by the dimensionless

parameter, ,68

given by the expression

=0Mw

RT. 7

Here, 0 is the zero-shear viscosity, Mw is the weight average

molecular weight, is the shear rate, is the density, R is the

gas constant, and T is the temperature. Shear thinning effectsbecome important for 10.

68With shear rates on the order

of 101 s1 and viscosities of 2.1104 Pa s,59,61

the values of

for even the thinnest films are on the order of 102, which

is well below the threshold value of 10. In hole growthexperiments on freestanding films, Dutcher and co-workers

obtained much larger values of ranging from 103 to 1011because their experiments were carried out at temperatures

close to, and in some cases below, the bulk Tg resulting in

extremely large viscosities and thus large values of.22,23

In

our system, we can safely assume that the dewetting mea-

surements yield values of the zero-shear viscosity and that

shear thinning effects are not important.

Effect of TMPC on the morphology of the rims

The effect of TMPC on the dewetting of PS thin films is

also manifested in the morphology of the rim surrounding

the hole. The morphology of the rim is believed to be influ-

enced by the friction at the substrate/polymer interface,6972

and by the viscoelastic properties of the film.38,73,74

Figure

7a shows the profiles of a rim in a 50 nm thick PS filmM=152 kg/ mol at different times during annealing. Theheight of the rim increases with time, as material from the

interior of the growing hole is transported to the rim. The

driving force for hole growth remains constant because the

angle of contact remains constant; this is consistent with the

data of others.73

A damped oscillatory profile develops away

from the maximum of the rim, into the interior of the film.

Such oscillations surrounding growing rims have previously

been observed for low molecular weight 2 kg/mol PS filmson SiOx/ Si.

38,73However, the amplitude of the oscillation for

those oligomeric PS films is considerably larger than ob-

served in higher molecular weight PS films.38

The differ-

ences may be related to the fact that the higher molecular

weight films are entangled and possess a larger viscoelasticcomponent and, moreover, larger viscosity. The relative in-

fluence of the polymer/substrate friction, the viscosity, and

viscoelasticity on the shape of the rims is further explored

below in the PS/TMPC system.

Quantitative differences exist between the morphologies

of holes in the PS/TMPC films Figs. 7b7d and the purePS films Fig. 7a of comparable thickness. We begin withthe mixtures containing 1 wt % TMPC, PS/TMPC0.001.While the sizes of the rims in the PS and the PS/

TMPC0.001 films increase throughout the same time inter-val, from 20 min to 4 h, the maximum heights of the

rims in the PS/TMPC1001 films are smaller than those ofpure PS films at any given time. Moreover, the differences

between the rim maxima in these two systems increase with

increasing time. This behavior is reconcilable with the dif-

ferences between the growth rates in the two systems, shown

earlier in Fig. 3. The growth rate of a hole determines the

rate of transport of material into its surrounding rim. If the

rate at which material is transported away from the rims into

the PS and into the PS/TMPC0.001 films is comparable,then the rims in the PS films are expected to be larger due tothe larger hole growth rate in PS. We will examine this issuein further detail below, after we complete the discussion of

the findings for the other films containing larger amounts of

TMPC.

The maximum height of the rim for the PS/

TMPC0.002 sample, shown in Fig. 7c, exhibits only aslight increase between 3 and 4 h. With a further increase in

time, the rim height subsequently decreases and the oscilla-

tions in the vicinity of the rim are further dampened com-

pared to the PS and to the PS/TMPC0.001 sample. In thePS/TMPC0.003 sample, only a decrease of the rim heightis observed throughout the entire time interval, from

1 to 25.5 h. The amplitude of the oscillations surrounding

the rims in the PS/TMPC0.003 samples is diminished com-pared to the other samples, at any instant in time.

FIG. 6. The values of Tg obtained from the reduction in viscosity via the

WLF equation are shown to agree adequately with the values of Tg from

spectroscopic ellipsometry measurements. The solid line is a fit of equation

4.8 to 590 kg/mol PS Tg data from Pham Ref. 75. The constants usedwere Tg =112 C, A =3.9 nm, and =1.112.




7/9

A rim will form immediately when a depression is cre-

ated in a film due to a conservation of mass; when the de-

pression reaches the substrate, or the autophobic layer, the

rim will rapidly increase in size. Two competing processes

subsequently control the size of the rims: 1 the transportrate of chains from the growing hole into the rim and 2transport of chains away from the rim into the film. Due to

the increasing friction between the melt and the substrate and

the reduced spreading coefficient44

in the PS/TMPC system,

the hole growth rate drops appreciably with increasing

TMPC. Consequently, the flux of chains transported into the

rim decreases. The addition of TMPC, at these concentra-

tions, has a negligible effect on the composition in the near

surface region of the film for two reasons: 1 enrichment ofTMPC at the substrate depletes the interior and 2 PS has alower surface energy and will always dominate the surface.

Consequently transport of mass into the rims particularlydue to a Laplace pressure, associated with the surface ten-

sion, that would dampen the height fluctuations remainscomparatively constant with increasing TMPC. In short, the

hole growth rate decreases by an order of magnitude over the

composition range, while the transport rate of mass from the

rim into the film, particular at the surface region, remains

relatively unperturbed. These competing effects would ex-

plain why the rim growth rate was most rapid in pure PS and

decreased in the PS/TMPC systems with increasing TMPC

concentration. The amplitude of the oscillations around the

rims decreased because the rate of transport from the rims

was sufficiently rapid compared to the rate of transport of

mass into the rims.

Viscoelastic effects have been proposed to account for

the dampening of the oscillatory profile in the vicinity of the

rims. While the modulus of TMPC is an order of magnitude

larger than that of PS and for 3 wt % mixtures, and the

modulus is 20% larger than PS,59

we argue that in the PS/

TMPC system, such effects would not account for the damp-

ening oscillatory profile. The transition of the rim width from

a damped oscillatory structure to a monotonic decay that we

observe is similar to the observations of Herminghaus et al.38

In their experiments, an increase in molecular weight from

2 to 600 kg/ mol resulted in a transition of the rim shape

from oscillatory to monotonic decay. They argued that since

the only difference in the materials was the molecular

weight, the changes in the rim shape were due to the vis-

coelasticity of the film materials. In fact, by incorporating

viscoelastic effects into a lubrication model derived from the

Navier-Stokes equations, they were able to extract the modu-

lus of their PS films. We attempted to extract the modulus

from the PS/TMPC films and found that the moduli did not

differ with composition when plotted against the size of thehole; in fact, we found that it decreased with time. Clearly

FIG. 7. ad: The rim profiles are shown as a function of anneal time and distance from the contact line, xN, for a a 52 nm, 152 kg/mol PS film, b47 nm, 1 wt % TMPC/152 kg/mol PS film, c 60 nm, 2 wt % TMPC/152 kg/mol PS film, and d 48 nm, 3 wt % TMPC/152 kg/mol PS film.




8/9

an enhancement of the viscoelasticity with increasing TMPC

cannot account for the dampening profiles in the vicinity of

the rim in the TMPC/PS mixtures.

Finally, we note that Blossey et al. recently examined the

effects of slippage and viscoelasticity on the morphology of

spinodal instabilities that developed in thin polymer films

and found that in both the weak and strong slippage regimes,

viscoelastic relaxation had no distinguishable effect on the

unstable modes.72

Kargupta et al. recently used simulationsto examine the effect of slippage on the morphology of spin-

odal decomposition at the free surface.69

When the instabili-

ties impinged on the substrate, rims formed at the edge of the

holes. They found that strong slippage resulted in rim forma-

tions that were not as pronounced as in the weakly slipping

case.

CONCLUSIONS

We have shown that the hole growth velocity in PS-

TMPC thin film mixtures is suppressed beyond that expected

from changes in the viscosity of the film. The decrease in the

velocity is due to increases in the substrate-polymer interac-tions that reduce the magnitude of the spreading coefficient

and increase the friction at the substrate-polymer interface.

The excess of TMPC chains near the substrate and the result-

ant reduction in the slippage length is consistent with Bruin-

smas two-fluid model. An additional effect of TMPC was

also manifested in changes in the morphology of the rim

surrounding the growing holes. The differences in the rim

shapes in the pure PS and the PS/TMPC films appear to be

connected to differences between the transport rates of

chains to the rim controlled by the hole growth rate andhence TMPC composition and the transport rate of chainsaway from the rims controlled by the PS composition.

The velocity of hole growth exhibited a film thicknessdependence, Vh, in excess of that predicted by theory. Thisexcess h dependence was shown to arise from thickness de-

pendent changes in the viscosity, h, which in turn is con-nected to a h-dependent Tg in this system. The glass transi-

tion temperatures deduced from the dewetting experiments

correspond well to those measured by spectroscopic ellip-

sometry. Shear thinning effects appear too unimportant in

our system in contrast to the case of freestanding films.

ACKNOWLEDGMENT

This work is supported by the National Science Founda-

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Besancon, Green - 2007 - Dewetting Dynamics in Miscible Polymer-polymer Thin Film Mixtures-Annotated

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