Geckeler K.E., Nishide H. (Eds.) Advanced Nanomaterials

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4.4 Templated Self-Assembly on Nanopatterned Surfaces 125

Figure 4.7 Schematic representation of the

fabrication process of chemically

nanopatterned surfaces that template the

self - assembly of symmetric PS - b - PMMA

( M

= 104 000). (a) A self - assembled

monolayer of phenylethyltrichlorosilane is

deposited on a silicon wafer; (b) A photoresist

is then spin - coated and patterned with

alternating lines and spaces by ultraviolet

interferometric lithography (c); (d) The

topographic pattern is converted into a

chemical pattern by irradiation with soft

X - rays in the presence of oxygen; (e) After the

photoresist removal, a toluene solution of

PS - b - PMMA is spin - coated onto the patterned

SAM (f). (g) Thermal annealing facilitates

surface - directed self - assembly. Reproduced

Nature Publishing Group.

Figure 4.8 Cross - sectional images of

symmetric PS - b - PMMA ( M

= 104 000;

= 48 nm) ﬁ lms on unpatterned surfaces

(a) and chemically nanopatterned surfaces

with 47.5 nm periodicity (b), prepared as

reported in Figure 4.7 . When the surface

pattern is greater than L

(c), lamellae exhibit

an imperfect ordering. Reproduced with

Publishing Group.

126 4 Alignment and Ordering of Block Copolymer Morphologies

stacked one - dimensional ( 1 - D ) lamellar assembly along surfaces chemically stripe

patterned by conventional lithography [188] . A further optimization of blend

composition, polymer chemistry and lithographic techniques will make it pos-

sible to fabricate nonregular shaped structures of different types, which implicitly

afford the production of nanodevices requiring patterns more complex than

simple periodic arrays.

4.5

Epitaxy and Surface Interactions

Control of the orientation of microdomains in the microstructure of BCs can be

obtained through a bias ﬁ eld induced by surface interactions. It is well known that

a certain type of substrate strongly inﬂ uences the structure of polymers. A trivial

example is the action of nucleating agents on the crystallization, which has often

been attributed to epitaxy of the growing polymer crystal. The interactions between

the surfaces of a substrate or of conﬁ ning walls and the molecules of amorphous

or semicrystalline block copolymers, determine the orientation of domains on the

substrate. Different types of interaction can be established depending on the

nature of the surface and of the BC.

Speciﬁ c interactions, such as epitaxy and directional crystallization, are involved

in semicrystalline or amorphous BCs and crystalline substrates. It will be shown

in the following sections that epitaxy and/or graphoepitaxy can be used in combi-

nation with the directional crystallization providing powerful methods for creating

regular surface patterns in BC thin ﬁ lms.

4.5.1

Preferential Wetting and Homogeneous Surface Interactions

The microstructures in thin ﬁ lms block copolymers generally depend on addi-

tional variables such as thickness of the ﬁ lm and two types of surface interac-

tions – that is, interactions of the BC with the superstrate (often air) and with the

substrate. In particular, the behavior of BC thin ﬁ lms depends primarily on the

interfacial interactions and commensurability of the period of the BC with the ﬁ lm

thickness. The chemical modiﬁ cation of BCs and various surface - patterning tech-

niques (e.g., soft lithography and holography) allow a better control of the micro-

domain structures of BC thin ﬁ lms. The simplest interaction of a BC ﬁ lm deposited

on a substrate is the preferential wetting of one block at an interface so as to

minimize the interfacial and surface energies. As a consequence, a parallel orienta-

tion of microdomains, lamellae and cylinders is often induced at the interface, and

this orientation tends to propagate throughout the entire ﬁ lm [9, 189 – 200] . Quan-

tization of the ﬁ lm thickness occurs in thin ﬁ lms with dimensions of the order of

only a few microdomain repeats, when the thickness is incommensurate with the

natural period of the block copolymer. For lamellar - forming block copolymers,

4.5 Epitaxy and Surface Interactions 127

discrete integer or half - integer values of the repeat period occur, leading to the

formation of terraces (i.e., islands and holes) at the polymer/air interface

[193 – 196] .

The microstructure can be altered by variation of the ﬁ lm thickness on the

substrate and preferential interactions of blocks with the substrate [59, 198, 199,

201 – 203] . Symmetric boundary conditions are established when one of the blocks

interacts preferentially with both the substrate and the air surface [193] , whereas

asymmetric conditions pertain when one block is preferentially wetted by the

substrate and the other block by the superstrate [197] .

The control of orientation of the microdomains can also be achieved by conﬁ n-

ing a BC between two surfaces; that is, adding a superstrate to a BC ﬁ lm supported

on a substrate [204 – 207] . Strong or weak interactions of BCs with the surfaces can

be created by coating the surface walls with a homopolymer or a random copoly-

mer, respectively, containing the same chemical species as the conﬁ ned BC [206] .

In the case of a neutral surface, for example, by using a random copolymer, the

lamellar microdomains rearrange themselves so that the direction of periodicity

is parallel to the substrate [206, 208 – 210] . Moreover, decreasing the conﬁ ned ﬁ lm

thickness – that is, creating a large incompatibility strain of the natural domain

period of the BC and the ﬁ lm thickness – induces a heterogeneous in - plane struc-

ture where both parallel and perpendicular lamellae are located near the conﬁ ning

substrate [207] . Various theoretical studies have predicted the structural behavior

of BC thin ﬁ lms in a conﬁ ned geometry [211 – 220] and are basically consistent with

experimental results.

Great inﬂ uences of both ﬁ lm thickness and surface interaction on the orienta-

tions of the microdomains have also been found for BCs forming cylinder [190,

221 – 229] and sphere [230, 231] morphologies. A parallel - to - vertical transition of

cylindrical PB microdomains was observed, depending on ﬁ lm thickness [190, 223,

224, 228] . Moreover, strong preferential interactions between one block and the

substrate in the case of conﬁ ned and supported block copolymer thin ﬁ lm, induce

a transition from cylindrical microdomains to a layered structure near the sub-

strate surface [221, 222, 224] . It has also been shown that in cylinder - forming

PS - b - PB BC thin ﬁ lms, the PS cylinders transformed into a perforated interlayer,

penetrated by PB channels that connect the two outermost PB surface layers, for

ﬁ lm thicknesses that are signiﬁ cantly less than their respective unperturbed chain

dimensions [224] . For the reverse structure – that is, PB cylinders in a polystyrene

matrix – the cylinders transformed into spheres as the ﬁ lm thickness decreased,

then to hemispheres, and ﬁ nally to a bilayer of surface - segregated PB covering a

PS - rich interlayer [224] .

The alignment of microdomains in both substrate - supported and - conﬁ ned ﬁ lms

has also been achieved by tuning the speciﬁ c interaction between the BC and the

substrate through modiﬁ cation of the surface [27, 139, 210, 232, 238] . An example

is the application of a random copolymer brush anchored on the substrate, which

allows the orientation of the domains to be changed from parallel to perpendicular

by altering the composition of the random copolymer [238] . A new approach

128 4 Alignment and Ordering of Block Copolymer Morphologies

developed by Char and coworkers is based in the addition of a low - molecular - weight

surfactant, oleic acid, that has the effect to mediate the self - assembly of the BC thin

ﬁ lm (Figure 4.9 ) [239] . At the early stage of the thermal annealing, oleic acid (whose

acid groups have a preferential afﬁ nity with the hydrophobic part of the PMMA

block) segregates to the upper part of the ﬁ lm, and preferentially in the PMMA

domains. The energetically neutral conditions at the surface rapidly induce the

perpendicular orientation of microdomains into the inner ﬁ lm.

4.5.2

Epitaxy

Epitaxy is deﬁ ned as the oriented growth of a crystal on the surface of a crystal of

another substance (the substrate). The growth of the crystals occurs in one or more

strictly deﬁ ned crystallographic orientations deﬁ ned by the crystal lattice of the

crystalline substrate [240 – 242] . The resulting mutual orientation is due to a 2 - D

or, less frequently, a 1 - D structural analogy, with the lattice matching in the plane

of contact of the two species [240] . The term epitaxy, literally meaning “ on surface

arrangement, ” was introduced in the early theory of organized crystal growth

based on structural matching [240 – 242] . Discrepancy between atomic or molecular

spacings is measured by the quantity 100( d − d

)/ d

, where d and d

are the lattice

periodicities of the adsorbed phase and the substrate, respectively. In general

10 – 15% discrepancies are considered as an upper limit for epitaxy to occur in

polymers [242] .

Figure 4.9 Schematic on the surfactant - assisted orientation of

PS - b - PMMA thin ﬁ lm. Reproduced with permission from Ref.

4.5 Epitaxy and Surface Interactions 129

Inorganic substrates were ﬁ rst used for the epitaxial crystallization of polymers

[243 – 257] . Successive studies have demonstrated the epitaxial crystallizations of

polyethylene ( PE ) and linear polyesters onto crystals of organic substrates, such

as condensed aromatic hydrocarbons (naphthalene, anthracene, phenanthrene,

etc.), linear polyphenyls, and aromatic carboxylic acids [258 – 262] . In the case of

PE, a unique orientation of the crystals grown on all the substrates is observed,

with different contact planes depending on the substrate [258 – 260] .

An example of an epitaxial relationship between PE crystals and an organic

substrate is shown in Figure 4.10 , with the substrate constituted by a crystal of

benzoic acid (BA) [259] (monoclinic structure with a = 5.52 Å , b = 5.14 Å , c = 21.9 Å

and β = 97 ° , with a melting temperature of 123 ° C). A clear match between the PE

interchain distance (the b - axis of PE equal to 4.95 Å ) and the b - axis periodicity of

benzoic acid crystal (5.14 Å ), and between the c - axis periodicity of PE (2.5 Å ) and

the a - axis of benzoic acid crystal (5.52 Å ), produces the crystallization of PE onto

preformed crystals of benzoic acid with lamellae standing edge - on, that is, normal

to the surface of benzoic acid crystal (Figure 4.10 ). The PE polymer chains lie ﬂ at

on the substrate surface with their chain axis parallel to the substrate surface and

parallel to the a - axis of benzoic acid crystal, and the b - axis of PE parallel to the

b - axis of the benzoic acid crystal [259] . The (100) plane of PE is in contact with the

(001) exposed face of benzoic acid.

In order to apply epitaxial control, BCs need to have at least one crystalline

block, which can interact with a crystalline surface. The morphology of semic-

rystalline block copolymers is the result of the interaction between microphase

separation of the component blocks and crystallization of the crystallizable block.

The process pathway of structure formation is of primary importance, in the

sense that the forming structures set off those emerging to the described geometry

into which the new structure must evolve. The ﬁ nal morphology is therefore

path - dependent; different microdomain structures are obtained if the crystalliza-

tion occurs from a homogeneous melt (in this case the crystallization drives the

Figure 4.10 PE lamella oriented edge - on on the (001) face of

a BA crystal substrate after epitaxial crystallization. The (100)

plane of PE is in contact with the (001) plane of BA, and

b - and c - axes of PE are parallel to b - and a - axes of BA,

respectively [259] .

130 4 Alignment and Ordering of Block Copolymer Morphologies

microphase separation), or it occurs from an already microphase - separated het-

erogeneous melt (in this case microphase separation precedes crystallization and

provides a microstructure within which crystallization takes place.) In the latter

case, crystallization is conﬁ ned to occur within the pre - existing microseparated

domains; crystallization conﬁ ned in preformed lamellar, spherical or within and

outside cylindrical microdomains has been observed [12, 78, 80] . Different situ-

ations occur when the crystallization is controlled by epitaxy. Although the ver-

satility of epitaxy in the case of crystallization of polymers has clearly been shown,

the method of using organic substrates to control the crystallization and the

morphology of semicrystalline BCs was introduced only in 2000, when De Rosa

and coworkers [184 – 263] ﬁ rst used epitaxy to control the molecular and micro-

domain orientation of PE - b - PEP - b - PE and PS - b - PE semicrystalline BC thin ﬁ lms.

These authors used BA [184, 263, 264] or anthracene ( AN ) [264, 265] and obtained

precise control of the molecular orientation of the crystalline block and subsequent

overall long - range order of the BC microdomains.

The selected area electron diffraction pattern and the transmission electron

microscopy ( TEM ) bright - ﬁ eld image of a thin ﬁ lm of PE - b - PEP - b - PE epitaxially

crystallized onto a BA crystal are shown in Figure 4.11 a and b, respectively. The

diffraction pattern essentially presents only the 0 kl reﬂ ections of PE, and therefore

corresponds to the b * c * section of the reciprocal lattice of PE (Figure 4.11 a). This

indicates that the chain axis of the crystalline PE lies ﬂ at on the substrate surface

and is oriented parallel to the a - axis of the BA crystals, as in the case of the PE

homopolymer (Figure 4.10 ) [184] . The (100) plane of PE is in contact with the (001)

plane of BA; therefore, the crystalline PE lamellae stands edge - on on the substrate

surface, with the b - and c - axes of PE oriented parallel to the b - and a - axes of BA,

respectively. The bright - ﬁ eld TEM image (Figure 4.11 b) indicates that epitaxy has

produced, instead of a spherulitic structure, a highly aligned lamellar structure

with long, thin crystalline PE lamellae with a thickness of 10 – 15 nm, evidenced as

dark regions, oriented along the [010]

||[010]

direction. The dark - ﬁ eld image

created by using the strongest 110 reﬂ ection (see Figure 4.11 c) reveals the same

parallel array of crystalline edge - on PE lamellae oriented along the b - axis of BA

crystals. This can be seen as bright regions due to the lamellae all being arranged

in Bragg diffraction conditions determined by the 2 - D epitaxy [184] . A scheme of

the orientation of the PE - b - PEP - b - PE obtained on BA crystals is shown in Figure

4.12 [184] . The biaxial matching of the BA and PE lattices creates a highly ordered

lamellar BC microdomain state. The widths of the crystalline PE lamellae are

highly uniform, the PE crystals and the intervening noncrystalline PEP are all

parallel, and the orientations of both the c - and b - axes of PE crystals over many

micron - sized regions are very high [184] .

4.5.3

Directional Crystallization

In polymer – diluent binary mixtures, if both the polymer and solvent are crystal-

lizable above room temperature, then a eutectic - like behavior can be observed. In

4.5 Epitaxy and Surface Interactions 131

fact, the melting temperatures of both the polymer and solvent are depressed up

to the eutectic composition [266 – 271] .

The presence of solvent in a noncrystalline BC depresses the order – disorder

temperature of the BC, depending on the solvent quality. Several theories predict

the phase behavior of BC – organic solvent mixtures [272 – 274] . Therefore, it can be

expected that mixtures of BCs with crystallizable solvents exhibit eutectic behavior.

In theory, the two liquidus lines of the binary mixture of a block copolymer and

Figure 4.11 (a) Selected area electron

diffraction pattern, (b) TEM bright - ﬁ eld image,

and (c) TEM (110) dark - ﬁ eld image of a thin

ﬁ lm of PE - b - PEP - b - PE epitaxially crystallized

onto a BA crystal. In the TEM bright - ﬁ eld

image, the dark regions correspond to the

denser crystalline PE phase, which form long

lamellae standing edge - on on the substrate

surface and preferentially oriented with the

b - axis of PE parallel to the b - axis of the BA

(panel b). In the dark - ﬁ eld image, the bright

regions correspond to the crystalline PE

lamellae in the Bragg condition (panel c).

Reproduced with permission from Ref. [184] ;

132 4 Alignment and Ordering of Block Copolymer Morphologies

an organic diluent – that is, the freezing point depression curve of the organic

diluent and the order – disorder temperature depression curve of the BC – can meet

each other at a certain composition and induce the characteristic eutectic trans-

formation of a liquid to two solids: the crystalline solvent and the phase - separated

solid block copolymer. Since the order – disorder transition in a block copolymer

is a weak ﬁ rst - order transition, the phase - separated block copolymer at the invari-

ant point can have some nonzero diluent content, as seen in the mixtures of block

copolymer and solvents [274] . If this were the case, the phase separation at the

invariant point would be from homogeneous liquid into a pure solid (crystalline

solvent) and another solid (solvent - swollen BC microdomains). Park et al . [275]

used this hypothesis of eutectic formation to globally organize the eutectic mixture

for the ﬁ rst time and induce the alignment of microdomains in the solid BC. These

authors used organic diluents, such as BA and AN, and amorphous asymmetric

PS - b - PI and symmetric PS - b - PMMA diblock copolymers [275] . In this process, the

ﬁ rst requirement is that the diluent must dissolve the BC above the melting tem-

perature of the solvent. Second, the diluent must have a tendency to crystallize

directionally into large, plate - like crystals. When the organic diluent, which ini-

tially was a solvent for the BC, directionally crystallizes along its fast growth direc-

tion under a temperature gradient, the BC undergoes microphase separation, due

to a rapid decrease in the solvent concentration. At the same time, the orientation

of the microdomains nucleated from the eutectic transforming solution is deter-

mined by the fast directional growth of the organic diluent. In the case of BA and

AN, the fast growth directions are both b - axis, and consequently the intermaterial

dividing surface of the microdomains of the BC tends to orient along this direction,

which also corresponds to the temperature gradient direction [275] . A polarized

optical microscope image of directionally crystallized BA crystal is shown in Figure

4.13 a [275] . The BA crystal is elongated along the fast growth b - axis and presents

Figure 4.12 Schematic model of the

crystalline and amorphous microdomains in

the PE - b - PEP - b - PE triblock copolymer

epitaxially crystallized on the BA crystal. The

epitaxy shows the relative orientation of

crystalline PE lamellae on the BA crystal:

(100)

||(001)

and c

|| a

, b

|| b

Reproduced with permission from Ref. [184] ;

4.5 Epitaxy and Surface Interactions 133

a ﬂ at (001) surface. The different thicknesses of the BA crystals lead to the different

colors under the microscope. A schematic model of cylindrical microdomains well

aligned from the directional eutectic transformation of the homogeneous BC solu-

tion is shown in Figure 4.13 b [12] . This process occurs within a few seconds (the

growth velocity of the BA crystal is nearly 1 cm s

− 1

) and the microstructure is

formed and then kinetically trapped.

Examples of the ordered microstructures obtained by this process are shown

in Figure 4.14 for symmetric PS - b - PMMA (Figure 4.14 a) and asymmetric PS - b - PI

(Figure 4.14 b,c) diblock copolymers prepared by directional solidiﬁ cation with

BA crystals [275] . In the case of PS - b - PMMA, the darker regions correspond to

the RuO

- stained PS microdomains (Figure 4.14 a). Edge - on parallel alternating

lamellae of PS and PMMA are well aligned along the fast growth direction of

the BA crystals (the b - axis), as shown in the schematic model of Figure 4.14 d

[275] . The well - aligned parallel lamellae extend over regions larger than 50 μ m

The fast Fourier transform ( FFT ) power spectrum in the inset of Figure 4.14 a

shows a spotlike ﬁ rst reﬂ ection located on the meridian, indicating the nearly

Figure 4.13 (a) Polarized optical microscopy

image of directionally crystallized BA crystals.

The large, ﬂ at and elongated BA crystals are

aligned with the b - axis parallel to the growth

front direction. Reproduced with permission

Chemical Society; (b) Schematic model of the

microstructure formation of a cylinder

forming BC under directional crystallization of

the BA from homogeneous solution.

Reproduced with permission from Ref. [12] ;

134 4 Alignment and Ordering of Block Copolymer Morphologies

single - crystal - like microdomain structure. The fast directional microstructure

formation during the phase separation with a thin ﬁ lm thickness approximately

less than a half - lamellar period avoids preferential wetting of one of the blocks

on the substrate, leading to the oriented lamellae microdomain structure where

the interface of the microdomains is parallel to the normal of the substrate

surface [275] . The structure is kinetically driven and subsequently vitriﬁ ed at

room temperature. Importantly, for regions thicker than approximately a half -

lamellar period, the perpendicular lamellae orientation switches to an in - plane

parallel one, and large planar regions are produced. The bright - ﬁ eld TEM image

of a ﬁ lm of the asymmetric PS - b - PI with a thickness of approximately 50 nm,

Figure 4.14 TEM bright - ﬁ eld images of thin

ﬁ lms directionally solidiﬁ ed with BA of the

symmetric PS - b - PMMA (20 - nm thick) stained

with RuO

(a), the asymmetric PS - b - PI

stained with OsO

with a thickness of 50 nm

(b) and 20 nm (c). The dark regions

correspond to the stained PS lamellae (a),

parallel PI cylinders (b) and vertically oriented

PI cylinders (c) well aligned along the fast

growth direction of the BA crystals ( b - axis).

The insets show the FFT power spectrum of

the TEM micrographs. Schematic models of

the microstructures of PS - b - PMMA (d),

PS - b - PI (e) and ultrathin ﬁ lm of PS/PI (f)

processed with BA. Reproduced with

American Chemical Society; and with