Article pubs.acs.org/Macromolecules
Ferrochemical Materials Dominique Ausserré* UMR CNRS 6087, “Molecular Landscapes, Biophotonic Horizons” Group, Université du Maine, Avenue Olivier Messiaen, BP 535, F-72085 Le Mans Cedex, France ABSTRACT: Amphiphilic molecules such as phospholipids, smectic liquid crystals or diblock copolymers are chemical dipoles which, under appropriate conditions, spontaneously line up side by side in a ferro-like arrangement to form stable monolayers. In three dimensions, these monolayers stack in a head-to-tail or antiferro-like arrangement, which favors monopolar contact between similar species. It results in a symmetric bilayered lamellar material. Here we show that dipolar chemical interactions can be extended in the direction normal to the lamellae by the use of triphilic rather than amphiphilic molecules, so that stable self-assembled smectic stacks may be designed with a fully polar, hence noncentrosymmetric, ordering. We describe in details a generic model of such materials. It is made of a mixture of three triblock copolymers aBc, bCa, and cAb with their end blocks twice sorter than the corresponding middle block. Because each constitutive molecule extends over three different chemical layers, all pairs of adjacent layers are linked and oriented via dipolar interactions. As a consequence, a polar structure with remarkable thermodynamic and mechanical stabilities is expected. We name these materials “ferrochemicals” because any given triblock molecule of the blend is oriented the same way through the whole sample due to chemical dipole interactions with all neighboring molecules. In the polymer case, the polar lamellar stacks can also be used as organic matrices hosting and orienting inorganic Janus particles in order to get a large variety of hybrid polar materials with interesting nonlinear optical, ferromagnetic, or ferroelectric properties.
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yielding materials where symmetric and nonsymmetric domains coexist that show at best a weak NCS order preference, which means that it is brittle and that it cannot extend over a useful scale. These attempts have involved only lamellar structures. In this case, the expected NCS order is one-dimensional, i.e., simply polar. We stress that the term “polar” applies to the organization in its chemical composition, which is a first reason to call it “ferrochemical”. In this article, we theoretically describe the composition and structure of a new self-assembled polar material that is expected to be mechanically and thermodynamically extremely stable, that is to say more stable than previous self-assembled lamellar materials by orders of magnitude. These structural properties, and the consequent physical properties, lie on the fact that all adjacent layers in it are linked via chemical dipoles. Two attached blocks in a copolymer chain may be viewed as a chemical dipole. Two adjacent molecules into a membrane layer are pair wise associated via chemical dipoles. In the new material described, composed of a blend of three complementary triblock copolymers, all neighboring molecules belonging to adjacent, hence different, layers are also pair wise associated via chemical dipoles. This original structural feature gives us another reason to call it “ferrochemical”.
elf-assembled structures play an important part in the development of new nanostructured materials. Among them, materials formed spontaneously by block copolymers1 are probably the simplest and the best defined. They are also easy to process because they adopt after simple annealing very regular periodic composite structures under the form of lamellae, cylinders or spheres2 which are maintained in the solid state after being cooled back to normal temperature. The mechanisms that underlie this self-assembling are very independent of the precise chemical nature of the copolymers and the structure period can be adjusted between 10 and 100 nm through the length of the blocks. Block copolymers allow a wide range of applications and present a great chemical variety.3,4 They are used, for instance as interfacial agents,5 to make very tough plastics,6 to structure surfaces at nanometer scales,7 or to realize meso-porous materials8 or photonic crystals.9 However, some important applications, requiring noncentrosymmetric (NCS) structures, cannot benefit from their use because these block copolymers prefer to form selfassembled and centro-symmetric structures. For example, nonlinear optical components used in optical communications and integrated optics require a strong second-order nonlinear optical susceptibility, i.e., a strong χ2, and thus a NCS structure. That is why research has been specifically engaged over the last 2 decades to imagine tricks that drive block copolymers to adopt spontaneous NCS structures, 10−13 unnatural for amphiphilic molecules. Different molecule compositions, blend formulations, and block sequences have been tried, © 2012 American Chemical Society
Received: October 9, 2011 Revised: January 27, 2012 Published: February 27, 2012 2478
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Figure 1. Bulk structure of a lamellar diblock copolymer. In the first two boxes (a and b), copolymer molecules are shown in a realistic way on the left (1) part of the box, where they are entangled, and in a simplified way on the right (2), where they are artificially split and compressed. Box a schematizes the symmetric order always observed in volume. Box b shows a hypothetical polar order, in practice never observed in the bulk; Box c shows a stack defect in the symmetric order, with the appearance of an additional AB interface, in the simplified representation (2).
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RESULTS AND DISCUSSION
composed of a blend of ABC triblock and ac diblock copolymers, with small letters representing much shorter blocks than those written with capital letters. The interfacial tension between two similar species (γAA or γaa) is not strictly zero, though its value is always very low compared to that between immiscible species (γAB). For simplicity we will assume γAB = γAC = γBC ≡ γ. The interfacial tension between two blocks with the same chemistry, but different lengths (γAa) is slightly lower than the average ([γAA + γaa]/2). As a consequence, the ABC/ca/ABC/ca... stacking is slightly better than the ABC/ CBA/ac/ca/ABC/CBA/ac/ca... stack or any other stack composed of bilayers, and the NCS structure is predominant. Thus, in these materials, the NCS order only relies on a very slight preference among the various monopolar interactions. Furthermore, the insertion of a simple bilayer like ac/ca. in the structure is enough to change the ABC order in CBA, so that this solution cannot apply for the manufacturing of big NCS monodomains samples. An alternative has been recently suggested by Erukimovich and co-workers.13 It consists in reinforcing the preference for the contact between similar chains with different lengths (like A and a) by the insertion of donor and acceptor interactions between long and short chains. However, there is no reason why the additional interaction would modify the ordering process of the material; consequently a lot of donor/acceptor pairs are likely to ignore each other indefinitely in a metastable structure containing many symmetric domains. Another example of a material with a NCS preference has been obtained by Takano et al.11 The material is pure and composed of ABCA tetrablocks with two A blocks of the same length. It aligns preferably in a polar ABCA/ ABCA/ABCA... lamellar sequence rather than in the symmetric ABCA/ACBA/ABCA... sequence. This is due to a slight dissymmetry between the lengths of B and C blocks, which leads the A end blocks respectively attached to B and C to adopt different stretching rates, and to behave as if they did not present the same length. The mechanism is thus very similar to the one described in the previous example, and the energy difference between the symmetric and the nonsymmetric structure is in the same range. In this case too, rival symmetric structures persist and the preference for the NCS order is very weak. In addition, in both situations the layers are disconnected
Figure.1a shows the lamellar structure of an AB diblock copolymer self-organized in the liquid state. We assume that the two blocks are immiscible, which is generally the case when two polymers are presenting a different chemical nature. Furthermore, we assume that they have the same length and the same volume. In order to form as few AB interfaces as possible, the lamellar structure is periodic and composed of bilayers. It is an AB/BA/AB/BA... symmetric structure. The free energy F per chain of this system, the minimum of which describes the equilibrium configuration, is the sum of two terms:13−18 F = γAB∑ + Fel. The first term is the contact energy between A and B. It is the product of their interfacial tension and of the contact area per chain. It decreases when the chains stretch perpendicularly to the lamellae and this elastic stretching is expressed by the second term. At equilibrium, these two terms respect the rule of equipartition in the three directions of space. They represent respectively 2/3 and 1/3 of the total energy, so that F = (3/2)γAB∑. If we divide the energy per chain by the molecular volume l∑, where l is the height of an AB monolayer, we get a very simple expression of the free energy density of the material: f = (3/2)γAB/l. The free energy density of the rival nonsymmetric structure AB/AB/AB/AB..., shown in Figure 1b, is almost twice that of the symmetric one since it contains almost twice more AB interfaces per volume unit (“almost” because the lamellar equilibrium layer is bigger, which is not shown in Figure 1). Hence, f is proportional to the number of AB interfaces per unit volume. In more general terms, the sequences of block copolymers are organized as follows: two sequences that are chemically similar tend to gather and two sequences chemically different tend to split. The association of similar sequences happens both laterally (entangling two similar neighbor blocks) and longitudinally (similar end blocks interpenetrating each other). Notice that in lamellar structures of diblock copolymers, elementary bilayers are linked via monopolar block associations and hence are topologically disconnected from each other, which leads to bad resistance of the material to shearing. Goldacker et al.10 created the first material with block copolymers presenting a NCS structure. This structure is 2479
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Figure 2. Nonsymmetric ternary blend of triblock copolymer chains. The most realistic picture in part a shows that each molecule is connected to its neighbors by a chemical dipole, including molecules located at an upper or a lower level. As a result, the orientation of the molecules in the blend is the same everywhere. In the topologic picture (b), molecules are compacted. The structure is that of a brick wall made with three colors and organized to maximize each color domain size. Each tricolor rectangle represents the volume of a chain. Picture c underlines the relative organization of the three kinds of chemical dipoles, which are attached in pairs along the z direction. The staggered arrangement of the rows insures a ferrochemical order between adjacent lamellae. Color dots at the center of rectangles represent the center of mass of the molecules.
and can slip easily, rendering the materials mechanically fragile. Abetz and co-workers12 obtained a third type of material with a tendency NCS order by using a blend of two triblocks (or “terpolymers”) ABC and AbC with the same composition but middle blocks with different lengths. The structure is lamellar but B and b blocks stretching rates differ widely. They become incompatible and the sequence ABC/CbA/ABC/CbA is locally observed. However, again this NCS order is delicate and coexists with symmetric stacks. Finally, a fourth solution was suggested by Stupp and co-workers19−21 with a different approach, supra-molecular self-assembly. In these systems, the association of the molecules happens at different length scales. The diblock or triblock copolymers contain rigid sequences that associate into tight bundles. The other blocks are flexible, they do not easily cohabitate laterally, and the aggregate takes the form of a bunch of flowers that can receive only a finite number of molecules. Bunches then structure themselves in a head-to-tail fashion to fill the space homogeneously and the result is a NCS material. The chemical synthesis of this material is complex and does not allow many possibilities to host impurities, which, as we will discuss below, is essential in applications. The material that we have imagined is based on self-assembly as were the systems just described. However, it is qualitatively different because it is made of triphilic rather than amphiphilic molecules and because all associations between molecules are dipolar in nature, in the sense explained previously. For instance, an ABC linear triblock copolymer and a CAB linear triblock copolymer can join together via their common AB dipole so that their orientation becomes linked. However, those molecules presenting different compositions, cannot take place on the same z level in a lamellar structure, the z axis being normal to the lamellae. As a consequence, adjacent lamellae become interconnected and we can talk of “dipolar inter-
penetration” between lamellae by contrast with the usual monopolar interpenetration. The triblock molecules that compose these lamellae may order themselves step by step in a three-dimensional way, each given molecule of the mixture finding always the same orientation, similar to the organization of the physical dipoles in ideal ferromagnetic or ferroelectric materials.22 The model for the ferrochemical materials is composed of a blend of three triblock copolymers in equal proportions. The composition of each triblock is obtained thanks to a circular permutation of three immiscible species A, B, and C. To allow every molecule to form dipolar connections and avoid the appearance of constraints in the structure, end blocks are twice shorter than middle blocks, which we write as aBc, bCa, and cAb. During the annealing of this blend, copolymer chains can only order as shown in Figure 2. In this structure, the position of the chemical domains is decoupled from that of the copolymer’s centers of mass. The whole material can be seen as a stacking of asymmetric bilayers (e.g., bAc/cBa) half filled with transmembrane middle molecules (e.g., aCb). In a plane perpendicular to the lamellae, the structure can also be viewed as the juxtaposition of similar columns composed of periodic linear arrangements aBc/cAb/ bCa/aBc/cAb/bCa of copolymer chains ... that are shifted half a period with respect to each other like rows of bricks in a wall. Since each molecule acts as a staple for its neighbors, this system is expected to present very unusual mechanical properties for a lamellar structure. The material is very easy to obtain by mixing thoroughly the three components in the powder, and subsequently melt the system by heating. Selfassembly occurs spontaneously in the liquid state and the order is maintained after cooling back to room temperature. The only competing symmetric structure we could think of is that of a demixed state in which each species forms a bilayered monodomain (as aBc/cBa). From a static point of view, the 2480
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Figure 3. Homeotropic interfaces. Left panel: Polarity reversal. The bulk organization dictated by chemical dipolar combinations is polar, so the two z directions are not equivalent. The material polarity cannot be reversed unless a defect occurs in the stacking. The drawing shows the energetically cheapest defect with in-plane invariance that we could imagine. The dotted line at the middle of the perturbed area represents the plane of symmetry. Solid lines represent interfaces between immiscible polymer species. Considering the dashed dot line as the surface of a continuous medium, the upper (or lower) part of the same drawing illustrates how the material surface in the homeotropic material orientation can self-organize against a solid, the air, or an immiscible liquid. Right panel: Ferrochemical membrane. A ferrochemical membrane has two interfaces with similar topology; the drawing displays the thinnest stoichiometric membrane that can be formed by the ternary blend, with homeotropic orientation at both interfaces. It is worth noticing that the membrane is asymmetric. The bulk structure is recalled by the superimposed pattern of solid lines.
is even a higher fraction of it. Hence the secondary free energy minimum corresponding to the competing demixed state is well above that of the ideal mixture. It gives a lot of space for playing with chain lengths around their optimal values. Reminding that in a block copolymer system the relative increase of the free energy is one-third of the relative change of the total chain length, the same rule holding for each block, one expects the ferrochemical structure to accept deviations up to several 10% of the relative block lengths with respect to their targeted values without demixing. Hence, if chemically possible, the synthesis of the three constituent should not be too demanding. Finally, in order to proof that the synthesis of the three triblock permutations of three given A, B, and C components is feasible, we cite an example. It is taken from the work described in ref 23 by Hückstädt, Göpfert, and Abetz on one side, where the synthesis of polystyrene-b-polybutadiene-b-poly-2-vinylpyridine (SBV) and VSB terpolymers was reported, and from the work described in ref 24 by Watanabe, Shimura, Kotaka, and Tirrell on the other side, where the complementary synthesis of BVS terpolymers was reported. Unusual physical properties for a lamellar structure derive from the absence of symmetry of the ferrochemical structure, especially a second-order nonlinear optical susceptibility that will be found interesting for optical telecommunication. These kinds of applications require the production of large NCS samples, which is made possible by the high thermodynamic stability of the ferrochemicals, but also the absence of any defect that could reverse the polarity within the NCS structure. We will now use the very simple rule of the minimum number of interfaces per unit volume explained at the beginning of this article to study the energetic cost of such a defect. This will be also useful in order to anticipate the behavior of this material at an interface with a solid. Figure 3a shows in a simplified representation of the NCS structure the topology of the least energy consuming reversal
arrangement of the chains in each of these monodomains is expected to be the same as their arrangement in the blend. In addition, demixing decreases the entropy of the blend and thus increases the free energy. From a dynamical point of view, since the ordering mechanism of the lamellar structure takes place through the propagation of a local order, demixing is very unlikely to happen. We may conclude that the NCS structure of this system is particularly stable. In the above description, we considered an ideal 3 × 1/3 mixture of perfect monodisperse terpolymer constituents, each block having an ideal relative length. When envisaging the synthesis of these materials, one must estimate how sensitive the structure will be toward a variation of the length ratio of the different blocks. Although any quantitative treatment remains beyond the scope of the present paper, we will give two arguments showing that a high margin of tolerance is expected in the system composition. The first argument is based on the property that two complementary tails such as two end blocks “a” of the aBc and bCa terpolymer chains with hypothetical lengths xN and (1 − x)N behave exactly the same and contribute to space filling with the same monomer distribution as the central block A in the terpolymer chain cAb. As a consequence, the structure remains unperturbed as long as the sum of the lengths of two complementary end blocks in two given constituent triblock molecules equals the length of the corresponding central block in the third molecule. This property provides flexibility in the polymer synthesis. The second argument is obtained by considering the equilibrium energy of the main competing structure, which is the demixed lamellar state. A demixed state will result in confining one constituent terpolymer in a third of the available volume V. The associated energy penalty will be −kBT ln[(V/3)/V], that is to say roughly kBT per molecule. For long copolymer chains, where N is of order 100, this is typically 5 to 10% of the molecular free energy in the lamellar state. For shorter chains, it 2481
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defect that we could imagine. This defect is arbitrarily built around the C block. It leads the formation of three lamellae with deviant thickness. If h is the thickness of a chemical domain, hence 2h the height of a molecule, the thickness of a C domain in the middle of the interface is h/2 and the thickness of the domains located on each side of the interface is 3h/4. So, the structure is perturbed over a total thickness of 2h that contains three interfaces between immiscible species while elsewhere the same thickness contains two such interfaces. In the defect, the excess free energy per unit area is γ and the averaged bulk free energy density of the defect is 1.5 times that of the bulk material. The difference is considerable and is comparable to the amount of free energy stored by a stack defect in the lamellar structure of symmetric diblock copolymers shown in Figure 1c, where an additional AB interface also appears in the defect area, which makes three interfaces in the perturbed thickness 2l instead of two elsewhere. It is well-known that this kind of stacking defect in diblock copolymers rarely happens and can easily be avoided. Given that the energy released by polarity reversal defects in ferrochemicals is rather similar, we can conclude that these materials are able to present faultless NCS order over large distances. The scheme on the left in Figure 3 also describes the structure of an interface between a ferrochemical and a solid surface if the dashed line represents the solid surface and we consider only one-half of the image. This structure corresponds to homeotropic anchorage of the material. The term “homeotropic” reminds us that, in a liquid state, the structure of the ferrochemical is that of a smectic A liquid crystal. This spontaneous polar smectic order is remarkable in that it is obtained with non chiral molecules that are orthogonal to the lamellae and moreover present a radial symmetry. With a ferroelectric order between adjacent layers, it corresponds to the SmAPF phase of the C∞V symmetry group. Such a level of symmetry in smectic liquid crystals has never been obtained, even with bent-core ferroelectrics.25 In a generic way, we show that this is made possible by introducing of a new kind of dipolar interactions, namely ferrochemical interactions, between adjacent layers. The scheme in Figure 3b illustrates that a very thin layer of the material will naturally form a nonsymmetric membrane. The example given in the figure is the thinnest membrane compatible with the material composition. In polymer materials used for nonlinear optical applications, sought-after optical properties are improved by the presence of hyper-polarizable molecules. These molecules are introduced in the polymer matrix and oriented by annealing under electric or electromagnetic fields, the whole structure is then quenched to room temperature while maintaining the field (poling).26 With the same method, permanent dipoles, whether magnetic or electric, can also be oriented.27 In this way molecules are maintained in an out of equilibrium28 arrangement, resulting in a material that is sensitive to heating and especially to aging.29 Figure 4 shows how permanent dipoles can be oriented at equilibrium by a ferrochemical matrix. The three situations described by this scheme are also valid for induced dipoles, whether electric or magnetic. On the right, the dipole is placed chemically between two adjacent blocks of a copolymer in the blend. On the left, the dipole is inserted via a diblock composed of two of the three species constituting the matrix: it acts as a cosurfactant. In the center, the dipole is carried by a Janus grain covered with two different species on its two hemispheres,30,31 both species being compatible with a component of the matrix.
Figure 4. Nanocomposite hybrid material. A nanocomposite hybrid material at equilibrium is obtained by the introduction between two blocks of diblock surfactants (on the left), of Janus grains (in the middle), or of grafted bridges (on the right). The black arrows represent dipoles or hyperpolarizable molecules. The physical dipoles carried by the impurities are all parallel to the AC, CB and BA chemical dipoles.
In the latter example, the nanocomposite self-assembled material is different from materials containing isotropic particules,32−38 because the nanoparticules prefer to settle at interfaces rather than in the center of the lamellae,39,40 and because their orientation is now imposed by the polar chemical structure of the matrix. This structure appears sufficiently robust to sustain unfavorable interactions between parallel dipoles (by contrast with antiparallel), even at high dipole densities. Thus, the matrix organizes the dipoles in space, while the latter bring the sought-after physical properties. Therefore, ferrochemical interactions appear to be a powerful concept in order to design useful new materials. To summarize, we predict that a blend of aBc, bCa and cAb triblock copolymers in equal proportions, with a = A/2 ..., will self- organize in a polar (NCS) lamellar structure. This material presents several unique features: dipolar interpenetration of juxtaposed layers, which couples their relative positions; dipolar association between the constituent molecules along their main axis, which confers on each constituent molecule a unique orientation in the entire sample; equal distribution of the molecule centers of mass among the lamellae filled with the three chemical species, which guarantees remarkable mechanical properties. We expect the total asymmetry of this selfassembled material to generate interesting physical properties such as second-order nonlinear optical susceptibility, ferroelectrics or piezoelectricity.41 We use “ferrochemical” to qualify this material because of the ferro-like arrangement of identical molecules. We also use “ferrochemical” to qualify the pairwise association of chemical dipoles sustaining the polar structure. Other organic NCS materials can also be envisaged on the basis of the same principles with other blends of molecules, each of them being formed with at least three blocks. These molecules are for instance co-oligomers,42,43 copolypeptides,44 copolynucleotides45−48 or comesogenic groups.49 In particular, the latter might form ferroelectric smectic materials23 with short 2482
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switching times for display applications. In each of these families, there exists a great number of possible chemical species, and we expect the emergence of a broad range of new materials.50 Making real examples of such materials certainly requires physicists and synthetic chemists working hand in hand.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work is respectfully dedicated to the memory of P. G. de Gennes. We are indebted to Taco Nicolai ̈ for critical reading of the manuscript.
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dx.doi.org/10.1021/ma202262m | Macromolecules 2012, 45, 2478−2484
