Self-assembled material, in particular a polymeric or oligomeric material, having a non-centrosymmetric lamellar structure

Abstract

A material is provided having a lamellar, non-centrosymmetric macroscopic structure, essentially consisting of a mixture of at least two populations of objects that are heterogeneous in blocks along an axis, each object consisting of at least two blocks, characterized in that each of the objects is connected to adjacent objects via interactions that involve at least two mutually incompatible blocks of the object and two blocks that are compatible one-to-one with the first of the blocks, and mutually incompatible along the chain of each one of said adjacent objects. The objects can be, in particular, block co-oligomers or copolymers.

Claims

1. A material exhibiting a macroscopic structure of lamellar and non-centrosymmetric type, comprising: a mixture of at least two populations of objects which are heterogeneous by blocks along an axis, each formed by a chain of at least two different blocks, wherein each of said objects is bonded to adjacent objects via interactions involving at least two blocks which are incompatible with one another of said object and two blocks which are compatible one to one with the first said blocks and incompatible with one another arranged along the chain of each said adjacent object, wherein said structure is formed by a juxtaposition of cyclic linear arrangement of chains of said blocks offset with respect to one another in the direction of said chains, and wherein each said object is bonded to each adjacent object in all the directions of the material, with the exception of the direction perpendicular to the lamellae, via interactions involving at least two blocks which are incompatible with one another of said object and two blocks which are compatible one to one with the first said blocks and incompatible with one another arranged along the chain of each said adjacent object.

2. The material having a non-centrosymmetric lamellar structure as claimed in claim 1, further comprising a mixture of M populations of objects indexed by m, each said object being composed of a linear chain of P(m) blocks chosen from N individual units, with N_≧3, P(m) and M≧2, the adjacent individual units in each linear chain being chosen to be incompatible with one another.

3. The material having a non-centrosymmetric lamellar structure as claimed in claim 2, wherein each said linear chain of blocks constitutes a portion of length P(m)≧2 of a sequence obtained by periodic repetition of an orderly set of said individual units.

4. The material having a non-centrosymmetric lamellar structure as claimed in claim 3, further comprising a mixture of 3 populations of objects, each composed of a linear chain of 3 blocks chosen from 3 individual units, the adjacent individual units in each linear chain being chosen to be incompatible with one another.

5. The material as claimed in claim 1, wherein said populations of objects are mixed in substantially equal proportions.

6. A nanocomposite material comprising a matrix composed of a material having a non-centrosymmetric lamellar structure as claimed in claim 1 and polar or polarizable insertions.

7. The nanocomposite material as claimed in claim 6, wherein said insertions comprise Janus nanoparticles (NP) exhibiting a first side and a second side which are chemically different, said particles being positioned at the level of interfaces between two lamellae which are compatible with said first side and said second side respectively.

8. The nanocomposite material as claimed in claim 6, wherein said insertions comprise molecules (D) formed by two of said blocks constituting said copolymers or co-oligomers, positioned at the level of interfaces between two lamellae, each of which is compatible with one of the two said blocks.

9. The nanocomposite material as claimed in claim 6, wherein said insertions comprise linear chains exhibiting two ends formed by two of said blocks (A, B) constituting said objects, positioned at the level of interfaces between two lamellae, each of which is compatible with one of the two said blocks, and a central part (PC) which is incompatible with the two said ends.

10. The nanocomposite material as claimed in claim 7, wherein said insertions also comprise molecules (P) grafted between two said blocks of said objects.

11. The nanocomposite material as claimed in claim 6, in which said insertions exhibit a permanent magnetic and/or electric dipole moment.

12. The nanocomposite material as claimed in claim 6, wherein said insertions exhibit a linear or nonlinear electric, magnetic or optical susceptibility greater by at least a factor of 10 than that of said objects in the presence of the lamella structure in the nanocomposite material.

13. The material s claimed in claim 1, wherein said objects are block copolymers or co-oligomers.

14. The material having a non-centrosymmetric lamellar structure as claimed in claim 13, wherein said copolymers or co-oligomers exhibit a linear or comb-shaped chain.

15. The material as claimed in claim 13, formed by a stack of lamellae, each of said lamellae being formed of just one chemical entity constituting a said block, or else of chemical entities forming compatible blocks, the chains of said polymers or oligomers exhibiting an orientation generally perpendicular to said lamellae.

16. The material as claimed in claim 13, wherein said copolymers or co-oligomers exhibit substantially identical lengths, wherein a standard deviation of the lengths is less than 30%.

17. The material as claimed in claim 13, wherein the blocks which are identical or compatible with one another belonging to different copolymers or co-oligomers exhibit substantially identical lengths, wherein a standard deviation of the lengths is less than 30%.

18. The material as claimed in claim 13, wherein each of said copolymers or co-oligomers exhibits two end blocks (a, b, c) and one or more “central” blocks (A, B, C) between said end blocks; in which at least one central block of a said copolymer or co-oligomer is compatible with at least two end blocks of other said copolymers or co-oligomers, said end blocks exhibiting different closest neighbors, and in which said central block exhibits a length substantially equal to the sum of the end blocks of the other said copolymers or co-oligomers.

19. The material as claimed in claim 13, wherein the constituent blocks of said copolymers or co-oligomers are themselves composed of organic molecules, of mesogenic blocks, of organometallic molecules, of nucleotides, of amino acids or of saccharides.

20. The material as claimed in claim 1, wherein said objects are objects in the form of rods.

21. The material as claimed in claim 20, wherein said objects in the form of rods exhibit a length of less than or equal to 1 mm.

22. The material as claimed in claim 20, wherein said objects exhibit the same dimensions in a plane perpendicular to said axis and are obtained by permutation of three base blocks, indicated by A, B and C, the lengths Lj of which adhere to one of the following conditions: Lj(ABC)=Lj(BCA)=Lj(CAB) with j=A, B or C; and Lj(jkl)+Lj(klj)=Lj(ljk) with j,k,l=A B or C and j≠k≠l.

23. The material as claimed in claim 20, wherein said objects in the form of rods exhibit a length of less than or equal to 100 μm.

24. The material as claimed in claim 20, wherein said objects in the form of rods exhibit a length of less than or equal to 10 μm.

25. The nanocomposite material as claimed in claim 7, wherein said insertions also comprise molecules (P) grafted between the two sides of said Janus nanoparticles.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Other characteristics, details and advantages of the invention will emerge on reading the description, made with reference to the appended drawings, given as nonlimiting examples, in which:

(2) FIGS. 1A, 1B and 1C, which have already been described, respectively illustrate the lamellar structure formed by symmetric diblock copolymers according to the prior art, a theoretical nonsymmetric structure, which is not formed spontaneously by these copolymers, and the structure of a hypothetical defect of stacking of the layers of these copolymers, which does not appear to have ever been observed in practice;

(3) FIG. 2 illustrates the structure of a non-centrosymmetric material according to a first embodiment of the invention;

(4) FIG. 3 shows the structure of a defect necessary for the reversal of the polarity in the material of FIG. 2;

(5) FIG. 4 illustrates, in a highly diagrammatic manner, the structure of a non-centrosymmetric material according to a second embodiment of the invention;

(6) FIG. 5 illustrates, also in the highly diagrammatic manner, the structure of a non-centrosymmetric material according to a third embodiment of the invention;

(7) FIG. 6 shows the structure of a hybrid nanocomposite material composed of a lamellar matrix, of the type illustrated in FIG. 2, in which are dispersed oriented inclusions of three different natures; and

(8) FIG. 7 illustrates the structure of a non-centrosymmetric material according to a fourth embodiment, composed of “comb-shaped” copolymers.

DETAILED DESCRIPTION

(9) Out of concern for simplicity, in the continuation of the description, reference will be made exclusively to “polymers” but, unless otherwise indicated, everything which will be said will also relate to the oligomers.

(10) A material according to the invention is much more stable, both chemically and mechanically, than the NCS structures described above. This is because the structure of such a material is based entirely on dipolar interactions between parallel chemical dipoles, similar to the interactions between two adjacent molecules in the membrane of a diblock. Thus, for example, an ABC molecule can be associated with a CAB molecule via their common dipole AB. The relative directions of the two molecules are then linked. In a lamellar edifice, these molecules cannot be located at the same level. The lamellae are thus connected to one another and it is thus possible to speak of “dipolar interpenetration”. By analogy with ferromagnetic materials, this association of parallel chemical dipoles can itself be described as “ferrochemical”.

(11) A first example of ferrochemical material, illustrated in FIG. 2, is composed of a mixture in (substantially) equal proportions of three triblocks. The composition of each triblock is obtained by circular permutation of three immiscible entities A, B and C. In order to allow dipolar associations between all the molecules without creating stress in the medium, the end blocks are half the length of the central blocks; for this reason, the three triblocks are denoted by aBc, bCa, cAb. During an annealing of this mixture, the molecules can only be arranged as illustrated in FIG. 2.

(12) A concrete example of material of this type corresponds to the following choice: A/a: polyisoprene (or oligoisoprene); B/b: polybutadiene (or oligobutadiene); C/c: polystyrene (or oligostyrene).

(13) The three copolymers (polyisoprene/polybutadiene/polystyrene).sub.n, (polybutadiene/polystyrene/polyisoprene).sub.n and (polystyrene/polyisoprene/poly-butadiene).sub.n are known from the prior art: 36) Apostolos Avgeropoulos, Stella Paraskeva, Nikos Hadjichristidis and Edwin L. Thomas, Macromolecules, 2002, 35, 4030-4035; 37) Nikos Hadjichristidis, Marinos Pitsikalis and Hermis Iatrou, Adv. Polym. Sci. (2005), 189, 1-124.

(14) A second concrete example of material of this type corresponds to the following choice: A/a: poly(2-vinylpyridine) (or oligo(2-vinylpyridine)); B/b: polybutadiene (or oligobutadiene); C/c: polystyrene (or oligostyrene).

(15) The three copolymers (poly(2-vinylpyridine)/polybutadiene/polystyrene).sub.n, (polybutadiene/polystyrene/poly(2-vinylpyridine)).sub.n and (polystyrene/poly(2-vinylpyridine)/polybutadiene).sub.n are known from the prior art: 38) H. Hückstädt, A. Göpfert and V. Abetz, Polymer, 41 (2000), 9089-9094 39) Hiroshi Watanabe, Takatoshi Shimura, Tadao Kotaka and Matthew Tirrell, Macromolecules (1993), 26, 6338-6345.

(16) A third concrete example of material of this type corresponds to the following choice: A/a: polystyrene or oligostyrene; B/b: polyisoprene or oligoisoprene; C/c: polycyclohexadiene (or oligocyclohexadiene).

(17) The three copolymers (polystyrene/polyisoprene/polycyclohexadiene).sub.n, (polycyclohexadiene/polystyrene/polyisoprene).sub.n and (polyisoprene/polycyclo-hexadiene/polystyrene).sub.n are known from the prior art: 40) Xiaojun Wang, Jianfeng Xia, Junpo He, Fengping Yu, Ang Li, Jiangtao Xu, Hongbin Lu and Yuliang Yang, Macromolecules, 2006, 39, 6898-6904.

(18) A fourth concrete example of material of this type corresponds to the following choice: A/a: poly(methyl methacrylate) (or oligo(methyl methacrylate)); B/b: poly[hexa(ethylene glycol) methacrylate] (or oligo[hexa(ethylene glycol) methacrylate]); C/c: poly[2-(dimethylamino)ethyl methacrylate] (or oligo[2-(dimethyl-amino)ethyl methacrylate]).

(19) The three copolymers (poly(methyl methacrylate)/poly[hexa(ethylene glycol) methacrylate]/poly[2-(dimethylamino)ethyl methacrylate]).sub.n, (poly[2-(dimethylamino)ethyl methacrylate]/poly(methyl methacrylate/poly[hexa(ethylene glycol) methacrylate]).sub.n and (poly[hexa(ethylene glycol) methacrylate]/poly[2-(dimethylamino)ethyl methacrylate]/poly(methyl methacrylate)).sub.n are known from the prior art: 41) Aggeliki L. Triftaridou, Maria Vamvakaki and Costas S. Patrickios, Polymer, 43 (2002), 2921-2936.

(20) A fifth concrete example of material of this type corresponds to the following choice: A/a: polystyrene (or oligostyrene); B/b: poly(D,L-lactide) (or oligo(D,L-lactide)); C/c: polyisoprene or oligoisoprene.

(21) The three copolymers (polystyrene/poly(D,L-lactide)/polyisoprene).sub.n, (polyisoprene/polystyrene/poly(D,L-lactide)).sub.n and (poly(D,L-lactide)/polyisoprene/polystyrene).sub.n are known from the prior art: 42) David A. Olson, Liang Chen and Marc A. Hillmyer, Chem. Mater., 2008, 20, 869-890.

(22) Furthermore, by virtue of the recent advances in the techniques which allow them to be chemically synthesized, it is today accepted that it is possible for a person skilled in the art to manufacture virtually any arrangement of arbitrarily chosen blocks. The references below illustrate, by a few examples, the variety of the synthetic techniques available: 43) Kelly A. Davis and Krzysztof Matyjaszewski, Macromolecules, 34 (2001), pp. 2101-2107; 44) Holger Schmalz, Armin Knoll, Alejandro J. Müller and Volker Abetz, Macromolecules (2002), 35, 10004-10013; 45) Himabindu Nandivada, Xuwei Jiang and Joerg Lahann, Adv. Mater., 2007, 19, 2197-2208; 46) Patricia L. Golas and Krzysztof Matyjaszewski, Chem. Soc. Rev., 2010, 39, 1338-1354; 47) David Fournier, Richard Hoogenboom and Ulrich S. Schubert, Chem. Soc. Rev., 2007, 36, 1369-1380; 48) Ulrich Mansfeld, Christian Pietsch, Richard Hoogenboom, C. Remzi Becer and Ulrich S. Schubert, Polym. Chem., 2010, 1, 1560-1598; 49) Morten Meldal and Christian Wenzel Tornøe, Chem. Rev. (2008), 108, 2952-3015.

(23) The variety of the syntheses of sequential triblocks and multiblocks already carried out and of the self-assembled structures which result therefrom for the pure materials is, for example, illustrated by the following references: 50) Volker Abetz and Peter F. W. Simon, Adv. Polym. Sci. (2005), 189, 125-212; 51) Nikos Hadjichristidisa, Hermis Iatroua, Marinos Pitsikalisa, Stergios Pispasb and Apostolos Avgeropoulos, Prog. Polym. Sci., 30 (2005), 725-782.

(24) The copolymers can be mixed in the powder state; the mixture of powders can then be melted, left to stabilize and, finally, solidified by cooling. In an alternative form, the melting can be replaced by or combined with the dissolution by means of a solvent, which is subsequently evaporated to restore the solid material.

(25) Compared with all the lamellar structures provided to date, a major distinguishing feature of this structure is the decoupling between the position of the chemical domains and that of the centers of gravity of the molecules. Each domain can be viewed as an asymmetric bilayer 50% filled with similar “transmembrane” central blocks. Alternatively, the structure can be viewed as a juxtaposition of cyclic linear arrangements of chains of molecules aBc/cAb/bCa/aBc/cAb/bCa . . . offset with respect to one another by a half-period, in staggered fashion, as are rows of bricks in a wall. Since each molecule acts therein as a hook for the neighboring molecules, this structure exhibits a resistance to shearing which is considerably higher than that of the normal lamellar structures.

(26) The only competing symmetric structure corresponds to a phase-separated state in which each entity forms a monodomain. From a dynamic viewpoint, considering that the lamellar edifice is put in order by propagation of a local order, it is virtually impossible for such a phase separation to be able to take place starting from a homogeneous mixture of the three entities. Furthermore, from a static viewpoint, the configuration of the chains in each monodomain is identical to its configuration in the mixture since the constraints are the same there. The entropy of the mixture and of the phase-separated state are thus identical. On the other hand, the entropy of the mixture is greater than that of the phase-separated state, with the result that, all in all, the free energy of the phase-separated system is greater than that of the mixture. The NCS structure proposed is thus particularly stable.

(27) This high thermodynamic stability is necessary in order to make possible the formation of macroscopic “monodomain” samples with NCS order but it is not sufficient. This is because it is necessary for the defects capable of reversing the polarity of the NCS structure to be sufficiently rare, which implies that they have a sufficiently high energy cost. FIG. 3 illustrates the defect of reversal which is most “economical” energetically.

(28) This defect is constructed arbitrarily around the entity C. It is reflected by the presence of three lamellae of abnormal thickness. If I now denotes the thickness of a chemical domain and thus 2I the height of a molecule, the thickness of the domain C at the core of the interface is I/2 and that of the domains A located on either side of the interface is 3I/4. The structure is thus disturbed over a total thickness of 2I and, over this thickness, three interfaces between immiscible entities are found, whereas the same thickness comprises two thereof in bulk. The excess energy per unit of surface area of the defect is thus Y and the volume energy density averaged over the thickness of the defect is 1.5 times that of the material in bulk. This energy is considerable. It is, for example, entirely comparable to that of the defect of stacking in the lamellar structure of a symmetric diblock copolymer represented in FIG. 1C, where an additional AB interface is also included in the region of the defect, i.e. three interfaces over the disturbed thickness 2I instead of two in bulk. In point of fact, it is well known that such defects of stacking in diblocks are rare and easily avoided. The “ferrochemical” materials are thus capable of exhibiting NCS orders without defects over large volumes.

(29) The structure of the interface between the ferrochemical material and a flat solid is also given by FIG. 3, in which only a single one of the two symmetric parts then has to be considered, the dotted axis now representing the solid surface. This structure corresponds to a homeotropic anchoring of the material. The term “homeotropic” reminds us that the ferrochemical structure, when it is liquid, is that of a smectite and more specifically of a smectite A, the molecules being substantially perpendicular to the lamellae. The polar smectic order (that is to say, non-centrosymmetric) is novel.

(30) The composition of the “ferrochemical” material of FIG. 2 can be generalized.

(31) First, the invention is not limited to the use of three triblock polymers (or oligomers) but can be generalized to mixtures of M sequential copolymers or oligomers exhibiting main chains obtained by circular permutation or extracted as parts of said permutations, optionally repeated as many times as necessary, of N individual units or blocks, with 2≦M and N≧3, M=2 and N=3 being excluded and it being possible for some nonneighboring blocks to be similar (for example, it is possible to have a mixture of the following block copolymers: ABAC, ACAD, ADAB, where the “A” block appears twice in each chain in nonadjacent positions, or else ABA′C, ACA′D, ADA′B, where “A” and “A′” are blocks which are similar and compatible but not identical to one another). The proportions of these copolymers or oligomers should ideally be equal, with a tolerance of ±10% or better still of ±2%, but this is not essential.

(32) The blocks indicated by one and the same letter (“A/a”, “B/b”, and the like) are not necessarily composed of one and the same chemical entity; it is sufficient that they are compatible blocks, within the meaning indicated above. This is important, for example, in the case where the individual units or blocks are composed of polymers or more generally of macromolecules: it is known that, in these cases, the replacement of certain groups by others may only slightly affect the physical and/or chemical properties of the molecule.

(33) The notion of compatibility of the polymers is studied in particular in the papers by Sonja Krause: 52) Pure and Appl. Chem., Vol. 58, No. 12, pp. 1553-1560, 1986; and 53) “Polymer Compatibility”, Polymer Reviews, Volume 7, Issue 2, 1972, pages 251-314.

(34) The following handbook: 54) “Polymer data handbook”, Oxford University Press, 1999, shows the polymers compatible with a given polymer.

(35) A degree of polydispersity in the chain lengths of the different blocks is accepted. The polydispersity is even capable of promoting the organization of the medium; for example, the polydispersity index PI can be less than or equal to 1.7, preferably less than or equal to 1.4, preferably less than or equal to 1.1, more preferably less than or equal to 1.05.

(36) Furthermore, it is not essential for the various “central” blocks to exhibit the same length. Nor is it essential either for the end blocks to exhibit a length equal to half that of said central blocks. The term “dual blocks” describes chemically similar end blocks having a different closest neighbor; this is, for example, the case of the “a” blocks in the “aBc” and “bCa” triblocks. The sum of the lengths of these dual blocks has to be substantially equal to the mean length of the central block which is chemically similar to them (“A” in “bAc”), to within about 50%, preferably to within about 20%, more preferably to within about 10%.

(37) It is even possible to exclusively use polymers (oligomers) in which all the similar or compatible blocks having similar or compatible neighboring blocks are substantially equal in length between them, without shorter end blocks. By way of example, FIG. 4 shows, in a highly diagrammatic manner, a ferrochemical material composed of a mixture in equal proportions of three triblocks with blocks of the same length. FIG. 5 shows the structure obtained from a mixture of two complementary tetrablocks, ABCD and CDAB.

(38) These two edifices are less harmonious than the preceding one because the end blocks contribute to the creation of interfaces between immiscible entities.

(39) The ferrochemical materials can be used as matrices for the preparation of nanocomposite materials, exhibiting electrically and/or magnetically polar or hyperpolarizable inclusions.

(40) It is known from the prior art to magnify the nonlinear optical properties of polymer materials by introducing hyperpolarizable molecules into the polymer matrix and by orienting them “hot” under an electric field (poling), the combination subsequently being frozen at normal temperature. The molecules are thus maintained in an arrangement contrary to equilibrium. This results in problems of temperature stability and in particular of aging. The same fatigue problems are encountered with piezoelectric, ferroelectric, pyroelectric or ferromagnetic materials.

(41) FIG. 6 shows how, on the contrary, polar or polarizable inserts can be oriented at equilibrium by a ferrochemical matrix. Four solutions are represented in the figure. In the first, a DB diblock, composed of two of the three entities present in the matrix and carrying an electric or magnetic dipole, or a highly polarizable group, is positioned astride the interface between two lamellae. In the second, the insert is composed of a nanoparticle NP, the two hemispheres of which are lined with two different functional groups, FB, FC, exhibiting a preferred affinity with the chemical entities B and C respectively (“Janus grain”); it should be pointed out that, in this case, the nanoparticles are located at the interfaces and not at the core of the lamellae, as often takes place with isotropic nanoparticles, and their orientation is “chemically” forced by the matrix. See, in this connection: 55) Li-Tang Yan, Nicole Popp, Sujit-Kumar Ghosh and Alexander Böker, ACS Nano, Vol. 4 (2), pp. 913-920 (2010); 56) Xue Li, Hui Yang, Limei Xu, Xiaoning Fu, Huanwang Guo and Xiaokai Zhang, Macromol. Chem. Phys., 2010, 211, 297-302; 57) Andreas Walther, Kerstin Matussek and Axel H. E. Müller, ACS Nano, 2008, 2 (6), pp. 1167-1178; 58) Frederik Wurm and Andreas F. M. Kilbinger, Angew. Chem. Int. Ed., 2009, 48, 8412-8421; 59) Jaeup U. Kim and Mark W. Matsen, Phys. Rev. Letters, 102, 078303 (2009).

(42) In the third case, the dipole or hyperpolarizable group P is installed chemically “as a bridge” between two adjacent blocks of a copolymer component of the mixture.

(43) In the fourth case, the insertion is provided in the form of a linear chain exhibiting two ends formed by two of the blocks making up said copolymers or co-oligomers (A and B), positioned at the level of interfaces between two lamellae, each of which is compatible with one of the two said blocks, and a central part PC incompatible with both said ends and which, due to its incompatibility, gathered up in the form of a ball or drop. The central part can be or comprise a block, a chain of blocks, or one or more nanoparticles.

(44) Until now, only the case of materials composed of linear copolymers or co-oligomers has been considered but this is not an essential limitation. FIG. 7 shows the structure of a material according to a fourth embodiment of the invention, obtained by mixing, in identical or similar molar proportions, three “comb-shaped” copolymers respectively composed: of a main chain A carrying linear sequential diblock chains BC; of a main chain C carrying linear sequential diblock chains AB; and of a main chain B carrying linear sequential diblock chains CA.

(45) It is also possible to envisage materials obtained by mixing linear and comb-shaped copolymers/co-oligomers.

(46) In an alternative form, a material according to the invention can be obtained by mixing, in solution, three populations of solid objects, which are optionally flexible, for example rods, in equal proportions. Each object can be organic, dielectric (for example silica) or metallic (for example gold or silver), or semiconducting, or composed of a rigid synthetic or natural polymer (for example xanthan or tobacco virus). It is composed of several sections (for example three), the compatibility or incompatibility of which is controlled by varying their composition (in bulk) or their surface properties, for example by virtue of ion implantation or electron beam irradiation techniques or by cold plasma techniques, or also by techniques for selective grafting or selective absorption of short molecules on their surface after reversible deposition on a support or in a microreactor. These techniques can be applied to objects reversibly deposited for this end on a support.

(47) Preferably, the populations of rods are each obtained by permutation of the sections (for example: ABC, BCA or CAB) and, when their diameter is identical, the lengths of the sections adhere to (in the preferred case of three sections): either L.sub.j(ABC)=L.sub.j(BCA)=L.sub.j(CAB), with j=A, B or C or L.sub.j(jkl)+L.sub.j(klj)=L.sub.j(ljk) with k=A, B or C and l=A, B or C and j≠k≠l

(48) Preferably, the total length of the objects in the form of rods can be less than or equal to 1 mm, preferably indeed even less than or equal to 100 μm or even less than or equal to 10 μm.

(49) For the manufacture of such objects, reference may be made to: 60) Matthew J. Banholzer et al., ACS Nano, Vol. 4, No. 9, pp. 5446-5452.