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Of major importance is the question concerning the role of spa-tial and temporal order, in particular, the application of concepts developedon macroscopic and microscopic scales to struc

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Editors: R Hull R M Osgood, Jr J Parisi H Warlimont

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of all important classes of materials.

88 Introduction

to Wave Scattering, Localization

and Mesoscopic Phenomena

By P Sheng

89 Magneto-Science

Magnetic Field Effects on Materials:

Fundamentals and Applications

Editors: M Yamaguchi and Y Tanimoto

90 Internal Friction in Metallic Materials

A Reference Book

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H Neuh¨auser, and H.-R Sinning

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99 Self-Organized Morphology

in Nanostructured Materials

Editors: K Al-Shamery and J Parisi

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102 Photonic Crystal Fibers

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Editor: A.S Alexandrov

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Professor J¨urgen Parisi

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To Uschi

While scientists still marvel about the economical potential of the omnipresentnanomaterials promising a billion dollar market, nature is still miles ahead of

us in nanotechnology Already 500 million years ago, co-development of tor and prey coloration as well as the development of visual systems were aconsequence of diversification of life forms and were produced from mesoscop-ically ordered nanostructures For example, arm ossicles from light-sensitivespecies of brittlestar consist of arrays of calcite microlenses with each lens min-imizing spherical aberration and birefringence when focussing light towardsnerve bundles Spectacular are iridescent colors of certain insects, birds, andflowers to make them visible on ultra-long ranges The metallic blue of thewings of the tropical butterfly called “morpho rhetenor” is produced whenlight is diffracted at regularly ramified nanorods ordered with defined dis-tances However, there are many other complex examples basing on the sameprinciples: nature uses the properties of so-called photonic bandgap materials,consisting of dielectric media with periodical index modulation that inhibitpropagation of light with certain colors over a range of scattering angles.People, therefore, have started to produce materials consisting of mesoscopi-cally ordered molecules or nanoparticles, exhibiting intriguing new properties

preda-as compared with the single building blocks The latter is also known preda-as

a novel “bottom-up” approach for nanolithography First examples on howknowledge of the fabrication of such new materials is transferred to commer-cial products within a few years exist But also, from the basic research aspect,these materials rise a lot of new questions to be dealt with in the future Theinfluence of morphological changes developing at a nanometer scale on theoptical near field with implications on the far field is by far well understood.Artificial materials not known to nature, such as metamaterials with a nega-tive refractive index, may be produced by bottom up methods soon They willallow to build the perfect lens allowing to look at objects with light at atomicresolution or to make material invisible within a certain wavelength regime

In this volume, the question will be addressed, how to manufacture ically ordered materials Special emphasis will be put on to compare ordering

mesoscop-phenomena under nonequilibrium situations, usually called self-organizedstructures, with those arising under situations close to equilibrium via self-assembly Analogies are pointed out, differences are characterized, and effortswill be made to find common features in the mechanistic description of thosephenomena Of major importance is the question concerning the role of spa-tial and temporal order, in particular, the application of concepts developed

on macroscopic and microscopic scales to structure formation occurring onnanoscales, which stands in the focus of interest on the frontiers of science.How optical properties of materials can be tuned is demonstrated in a firstexample on the formation of one-dimensional waveguides from nanoaggre-gates of single organic building blocks The formation of highly ordered two-and three-dimensional supramolecular structures is related to the chemicalproperties of the single building blocks in a second chapter Furthermore, self-assembly of surfactants is used to produce nanomaterials of high monodisper-sity, enabling the self-organization of hexagonal networks of “supra” crystals,rings, tubes, dots, and labyrinths (Chaps 2.5 and 4) Properties of the soformed mesoscopical materials can be tuned also by changing the size of thenanoscopic building blocks The volume finally ends with treating how spa-tially periodic, temporally stationary turning patterns can be constructed out

of nanodroplets, thus, combining elements of self-assembly with aspects ofself-organization in the nonequilibrium pattern formation, arising out of theinterplay between reaction and diffusion embedded in the self-assembled pat-tern In a second example, it is shown how honeycomb carbon networks can

be formed when applying the proper knowledge on transport and structuring.Finally, the book ends with a description how waves are transported in livingsystems

The editors would like to thank all authors for constructive efforts to pare their manuscripts and to contribute to the rich variety of topics included

pre-in this volume Special thanks are due to Claus Ascheron and others fromSpringer Heidelberg for continuous commitment, efficient support, and skillfultechnical assistance The editors would like to thank our colleague Stefan C.M¨uller (University of Magdeburg) for fruitful collaboration throughout draft-ing the concept of the book, for valuable discussions, input and support With-out him the realisation of the book would not have been possible Furthermorethe editors are grateful to all authors for constructive efforts

1 Organic Crystalline Nanofibers

1.1 Introduction 1

1.2 Growth of Ultrathin Films: Molecular Orientation Control 2

1.3 Needle Films on Dedicated Templates: Mutual Orientation and Morphology Control of Nanoaggregates 6

1.3.1 Plain Mica 6

1.3.2 Au-Modified Mica 8

1.3.3 Water-Treated Mica 9

1.4 Selected Applications in Nano- and Microoptics 9

1.5 Summary and Outlook: Future Devices From Organic Nanofibers 14

References 15

2 Titanium-Based Molecular Architectures Formed by Self-Assembled Reactions 2.1 Introduction 17

2.1.1 Results and Discussion 19

2.2 Formation of Molecular Architectures 19

2.3 Molecular Architectures Accompanied by Radical Induced C–C Coupling Reactions 33

2.4 Molecular Architectures Based on C–C Coupling Reactions Initiated by C–H Bond Activation Reactions 38

2.5 Conclusion and Future Directions 42

References 43

3 Self-Assemblies of Organic and Inorganic Materials 3.1 Introduction 47

3.2 Structure of Colloidal Self-Assemblies Made of Surfactants and Used as Templates 49

3.3 Production of Nanocrystals by Using Colloidal Solutions as Templates and Their Limitations 51

3.4 Self-Organization of Nanocrystals 55

3.5 Colloidal Nanolithography by Using Nanocrystals Organized

in a Given Structure as Masks [83] 61

3.6 Conclusion 64

References 64

4 Self-Assembled Nanoparticle Rings 4.1 Introduction 67

4.2 Experimental Formation of Nanoparticle Rings 68

4.2.1 Spreading of Polymer Solution on Water Surface 68

4.2.2 HDA Pancake Structures 69

4.2.3 CoPt3Nanoparticle Rings 72

4.3 Model for the Formation of HDA Pancakes 74

4.3.1 Phase Separation of Binary Solution 74

4.3.2 Rupture of Thin HDA Film into Micrometer-Size Pancakes 78

4.4 Formation of a Nanoparticle Ring at the Edge of an HDA Pancake 81

4.4.1 Pinning of an HDA Micrometer-Size Pancake 81

4.4.2 Forces Acting on the Nanoparticle Located in the Interior of Pancake 82

4.4.3 Forces Acting on the Nanoparticle Located at the Edge of Pancake 84

4.5 Summary and Conclusions 85

References 86

5 Patterns of Nanodroplets: The Belousov–Zhabotinsky-Aerosol OT-Microemulsion System 5.1 Introduction 89

5.2 The BZ-AOT System 90

5.2.1 The BZ Reaction 90

5.2.2 AOT Microemulsions 91

5.2.3 The BZ-AOT System 93

5.3 Experimental Results 94

5.3.1 Experimental Configuration 94

5.3.2 Turing Patterns 95

5.3.3 Patterns Associated with a Fast-Diffusing Activator 97

5.3.4 Complex Patterns – Dashes and Segments 100

5.3.5 Localized Patterns 101

5.4 Theoretical Considerations 103

5.5 Constructing a Model 104

5.5.1 Linear Stability Analysis and Types of Bifurcations 106

5.5.2 Results of Numerical Simulations 108

5.6 Conclusion and Future Directions 109

References 112

6 Honeycomb Carbon Networks: Preparation, Structure,

and Transport

6.1 Introduction 115

6.2 Experimental Formation of Polymer Honeycomb Structures 118

6.2.1 Spreading of One Liquid on Another 118

6.2.2 Production of Polymer Networks 119

6.2.3 Structural Forms of Nitrocellulose Networks 120

6.2.4 Structural Forms of Poly(p-phenylenevinylene) and Poly (3-octylthiophene) Networks 123

6.3 Model for the Formation of Honeycomb Structures in Polymer Films 125

6.3.1 Water Droplet on the Fluid Polymer Layer 125

6.4 Nitrocellulose Networks as Precursor for Carbon Networks 132

6.4.1 Temperature Dependence of Hopping Transport in Carbon Networks 133

6.4.2 Electrical Field Dependence of Hopping Transport in Carbon Networks 142

6.5 Summary and Conclusions 150

References 151

7 Chemical Waves in Living Cells 7.1 Introduction 155

7.2 Waves of Metabolic Activity 156

7.3 Calcium Signaling Waves 160

7.4 Conclusions 164

References 166

Index 169

R Beckhaus

Institute of Pure and Applied

Chemistry, University of Oldenburg

Department of Chemistry and Volen

Center for Comlex Systems, MS 015,

of Michigan Medical SchoolAnn Arbor, MI 48105USA

hpetty@umich.edu

M.P Pileni

Laboratoire LM2N, URA CNRS

7070, Universit´e P et M Curie(Paris VI)

BP 52, 4 place Jussieu

75252 Paris cedex 05France

H.-G Rubahn

Mads Clausen Institute,NanoSYD, University of SouthernDenmark

Waltham, MA 02454USA

vanag@brandeis.edu

Organic Crystalline Nanofibers

H.-G Rubahn

Summary. Organic crystalline nanofibers are a new class of nanoscaled organicmaterials that bear high potential as model systems for optics and photonics atthe diffraction limit In addition, due to the possibility to tailor to a large extentmorphology as well as optoelectronic properties, organic nanofibers are promisingelements for future integrated devices In this chapter the specific growth conditionsare discussed that make the fabrication of this kind of matter possible as well as arange of applications in nano- and microoptics

1.1 Introduction

Nanooptics is about understanding and mastering the interface between themicro- and the macroworld using optical methods In doing so new opticalproperties are found which are based on the dimensional confinement that is

a characteristic of nanoscaled materials Metallic “quantum dots” such as Aunanoclusters are a good example of this domain, where changes in the size

of the objects result in drastic changes of the optical properties [1] Thesequantum dots have been well-studied in order to understand the fundamen-tals of the optoelectronic response in the nanodomain In the meantime, theyare also already used for, e.g., enhancing the brightness and stability of fluo-rophores for biological imaging and are as such commercially available [2] Thisillustrates the speed with which basic research results transfer into industrialproducts in this field

Another example – now based on dielectric materials – is photonic bandgap (PBG) materials [3] Here, a periodic index modulation is manufactured indielectric slabs (e.g., by laser- or electron-beam-drilling a matrix of submicron-sized holes) which in the following inhibits the propagation of light of cer-tain colors over a large range of scattering angles In analogy to solid statephysics this is called an “optical band structure.” Again, the commercializa-tion occurred on the very short time scale of a few years, and optical fibersimplementing the PBG effect are now available for a wide range of applica-tions [4] In contrast to the above-mentioned quantum dots the PBG effect

can be quantitatively understood using classical electrodynamics And indeedthe possibility to model the optical behavior of submicron-scaled materialsusing classical methods is often encountered in the context of nanooptics.The above examples from metallic and dielectric nanoscaled systemsshould not give the impression that optics in the subwavelength size regime

is well understood The influence of morphological changes on a scale on the optical near field and from that on the resulting far field needs

nanometer-to be as well investigated as the corresponding influence on the spectroscopicproperties, the waveguiding or the intrinsic dynamics of optical excitations innanoaggregates On the application side, a thorough understanding of mor-phology dependencies is an important prerequisite for the controlled build-up

of new nanoscaled optoelectronic elements such as light emitting devices orfield effect transistors

In this chapter we describe generation and control of organic crystalline

nanofibers, which constitute a recently developed model system that bears

a high application potential Using organic molecules instead of inorganiccompounds to build up nanostructures has the advantage of being able to workwith higher luminescence efficiency per material density, higher flexibility interms of spectroscopic properties as well as easier and cheaper processing sincecontrolled self assembled growth can be implemented

This chapter begins with a discussion of the growth of ultrathin organicfilms on well defined, single crystalline substrates It will be shown that thegrowth in general depends on both molecular parameters such as chain length

as well as substrate parameters such as surface free energy, polarity, roughness,etc Depending on the exact growth conditions such as substrate temperature

or growth rate, films can be generated that consist of molecules with ent orientations with respect to the surface normal, namely nearly parallel(“upright”) or perpendicular (“laying”) Further optimization of the growthconditions results in the generation of needle-like but nonoriented structures

differ-on alkali halide crystals Finally, by the use of the most appropriate substrateand fully optimized growth parameters, either dense arrays of nanofibers orisolated nanofibers are grown Once this has been achieved, the substrate sur-face serves mainly as a template for producing tailored nanoaggregates, which

in a next step are transferred onto other substrate surfaces

1.2 Growth of Ultrathin Films: Molecular

Orientation Control

In the past, various light emitting organic molecules have been investigated

in terms of their abilities to form well-organized, ultrathin films for cations in optics or organic electronics [5] Among those are thiophenes [6],

appli-PTCDA [7], pentacene [8], para-phenylenes [9], or anthraquinone [10] (Fig 1.1).

Up to now para-phenylenes have been found to provide us with the most

Fig 1.1. Some organic molecules that have been used for building up

d, para-hexaphenylene; e, anthraquinone

promising nanoaggregates, and therefore we will concentrate here on this class

of molecules

The short-chain para-phenylenes (p-nP, n = 4–6) form semiconducting

films or aggregates with rather delocalized π-electrons, and they emit bluelight after excitation with either UV light (around 360 nm) or electrons Films

of this material have attracted a great deal of attention over the last years [11].Because of their promising chemical and optical properties [12–14] they arewell-suited candidates for building up active layers in organic light-emittingdiodes (OLEDs) [15, 16], organic field effect transistors (OFETs) [17], andother electronic and optoelectronic devices [18]

In principle, the molecules might be oriented either normal to the substrate

or they might be aligned parallel to the substrate surface The orientation has

a strong influence on the device properties of the resulting films or

nanoaggre-gates For example, the electrical conductivity for p-6P is highest

perpendicu-larly to the molecules long axes since the HOMO has highest electron densitynear the middle of the molecule As a result, films of oriented molecules con-duct also better in the direction perpendicular to the molecular axes [19].Therefore one needs to characterize and optimize the molecular orientation.The characterization is rather simple in the case of a single crystalline filmwith large domains since the individual molecules possess a well-defined ori-entation with respect to the surface plane In addition the main optical tran-sition dipole moment is usually oriented along the long axes of the moleculesand thus polarized absorption and emission studies can reveal the molecularorientations For example, if all the molecules are oriented upright on the sur-face, then excitation under normal incidence will not result in light absorptionand thus also not in luminescence

Figure 1.2 demonstrates that characteristic features in the absorption tra allow one to distinguish between upright and laying molecules A pro-nounced absorption maximum at 280 nm characterizes upright molecules Theposition of this maximum is independent of the substrate material A maxi-mum at 340 nm characterizes laying molecules Both maxima shift with chainlength of the molecules to the red spectral regime, in agreement with theoreti-cal predictions [20] Another way to determine the orientation of the molecules

spec-is atomic force microscopy (AFM) Examples for a continuous film of upright

oriented p-4P molecules and a part of a needle-like structures (“nanofiber,” see later) made of laying p-6P molecules are shown in Figs 1.3a, b Height

scans indicate in the case of the continuous film terraces with height distancesthat correspond to tilted, normal oriented molecules (1.8 nm effective length).For the nanofiber (Fig 1.3b) no domains with characteristic corrugation of

2.5 nm (the length of a normal oriented and tilted p-6P molecule) are found.

These conclusions agree with local optical measurements

In order to obtain well-defined single crystalline organic films on tric substrates subtle deposition control is needed We have used a high vac-uum system (base pressure 10−9mbar) equipped with a fast entry lock and a

dielec-multi-channelplate low energy electron diffraction spectrometer for the sition of organic molecules and characterization of the resulting films Mus-covite mica and alkali halide single crystals were cleaved in air, transferredinto the apparatus, and were outgassed thoroughly at temperatures around

depo-370 K The substrates could be heated by a tungsten filament, and tion took place at substrate temperatures between room temperature and

deposi-420 K via sublimation of the organic compounds from a Knudsen cell sition rate and final thickness of the organic films were controlled via a gold-plated and water-cooled quartz microbalance Following deposition, LEEDpatterns were recorded in situ to verify the growth of single crystalline films ornanoaggregates Depending on deposition rate, substrate type, and substrate

Depo-250 300 350 400 450 0.0

Fig 1.2.Measured absorption spectra for films of upright oriented p-4P molecules

on NaCl and laying p-6P molecules on KCl The absorption is given in arbitrary

units and thus not to be mutually compared

Fig 1.3.(a) AFM image (2.17 × 2.17 µm2) of a film of standing p-4P molecules on

lithium fluoride Height information is given as a linescan in the inset (b) Same as

30 nm) We observe a modulation with 30 nm periodicity (black lines) which is due

to the crystalline phase of the aggregates and not correlated to height variations due

to individual molecules

Fig 1.4. Needle film of p-5P on NaCl, generated at surface temperature of 330 K.

temperature, films with molecules oriented normal or parallel to the surfacecan be obtained

For example, if one adsorbs para-phenylenes at high deposition rates

(0.5 nm s−1) films of molecules oriented parallel to the surface are found in

general [21] At low deposition rates (0.02 nm s−1) the molecules are oriented

normal to alkali halide surfaces if the deposition is performed at high peratures At room temperature films of parallel oriented molecules are gen-erated on alkali halides, whereas on mica molecules are oriented normal tothe surface If one modifies the mica surface by, e.g., rinsing it in water ormethanol, then a wetting layer of normal oriented molecules is generated even

tem-at high tempertem-atures and tem-at low deposition rtem-ates [22]

A closer look at the alkali halides (Fig 1.4) shows that in addition to

a continuous film of p-5P molecules needle-like aggregates can be generated.

The needles have widths of the order of a few hundred nanometers and heights

of the order of a few ten nanometers They are statistically distributed overthe surface Similar needle growth is observed on other surfaces such as TiO2,too [23] Since the needles show waveguiding properties we will use the term

nanofibers as an acronym.

1.3 Needle Films on Dedicated Templates: Mutual

Orientation and Morphology Control of Nanoaggregates

1.3.1 Plain Mica

Under certain growth conditions oriented needle growth is observed on

muscovite mica surfaces (Fig 1.5) [24, 25] Whereas height and width of theneedles are similar to those found on alkali halides, they are much longer

Fig 1.5. Hexaphenyl nanofibers on mica, generated at a surface

tempera-ture of 400 K Left-hand-side: epifluorescence image Right-hand-side: AFM image

(up to several hundred micrometers) and they are very well mutually oriented.Detailed investigations via electron diffraction and using optical methods haveshown that the growth mechanism of the needles is influenced by strong elec-tric dipole fields that are induced on the mica surface upon cleavage [25].These dipole fields possess two possible orientations on a cleavage plane ofmica (three, if one takes into account lower lying planes), and they do notexist on alkali halide surfaces The dipole fields induce a dipole moment inthe polarizable organic molecules, leading to an attraction via dipole-induceddipole forces and thus to an alignment of the individual organic moleculesalong the surface dipole orientations Subsequent molecules grow side-by-side

on the adsorbed molecules on the mica surface if they possess enough surfacemobility (i.e., if the surface is warm enough), leading to the generation ofaligned, needle-like aggregates with very well-defined molecular orientations.The needle growth process is thus dictated by the strength and orienta-tion of the dipole fields on the surface, the polarisability of the molecules andtheir mobility on the surface Domains with specific dipole directions can behuge on mica (of the order of square millimeters to centimeters) and conse-quently huge domains with parallel oriented nanoaggregates can be formed.The temperature window for the growth of long needles within which thesurface has to be kept is only of the order of 20–30 K; at lower temperaturesquasicontinuous films consisting of very short, dense needles are formed Thisstrong temperature dependence allows one to grow the needles at predefinedspots on the surface via, e.g., local laser heating [26], and enables controlover the environment of individual needles In other words, large areas withequally distributed needles of the same morphology can be generated, but also

Fig 1.6 Influence of an ultrathin Au film on the morphology (height (a), length

(b)), and orientation (c) of para-hexaphenyl nanofibers on mica (d) Epifluorescence

image of the sample with 2 nm Au [27]

areas that contain just a few, uniquely identifiable needles Both extremes areinteresting in terms of fundamental nanooptical studies

1.3.2 Au-Modified Mica

Besides control over mutual orientations and density, control over the phology of individual nanoaggregates is also important In general it is foundthat height and width of the nanoaggregates can be set rather independent

mor-of each other, i.e., needles mor-of constant height but with variable width can begenerated by adjusting the growth conditions on plain mica surfaces However,one usually pays for this variability with a very wide length distribution.More controllable results are obtained by modification of the mica sur-face before starting the organic film growth with, e.g., an ultrathin film ofgold nanoclusters Figure 1.6 demonstrates the influence of such a layer on

the morphology and orientation of p-6P nanofibers The plotted height has

been determined by atomic force microscopy, whereas length and mutual entation have been determined with the help of epifluorescence microscopy

ori-As seen, increasing the Au thickness results in a drastic decrease of lengths ofthe nanofibers as well as a significant increase in heights The degree of mutualorientation of the nanofibers, however, described via the standard deviationfrom a global orientation angle with respect to the substrate orientation doesdegrade only weakly

If one further increases the Au thickness to 5 nm, this behavior changesdrastically, the spread in orientation angle increases to 40◦ and the length

decreases to a few micrometers Thus especially the slight modification with

a very thin film leads to the most useful results It is also noted that theoverall luminescence efficiency of the needle film depends on the Au clusterdecoration With increasing Au film thickness the luminescence first decreases,but then for film thicknesses larger than 5 nm it increases again and becomeseven stronger than the luminescence without Au decoration [27] Apparently

Fig 1.7. Bent organic nanofibers (p-6P) on hydrophilized mica: (a) AFM image

(60× 60 µm2

of the order of 100 nm [22]

the Au film acts as a rough mirror and channels the emitted light along thesurface normal

1.3.3 Water-Treated Mica

As demonstrated before, a strong modification of the mica surface with, e.g., a

Au cluster film results in less straight nanofibers However, we do not observesignificantly bent nanoaggregates such as rings Ring-formation occurs if onerinses the mica surface before organic film growth with water and thus changesthe surface hydrophobicity In that case curved needles and rings or bentorganic nanofibers of various sizes are observed (Fig 1.7) AFM images revealthat these structures grow on a wetting layer of upright oriented moleculesand that the height to width ratio is different from that found for straightneedles [22] Typical rings have widths of around 100 nm, i.e., smaller thanthat of the straight needles at similar growth conditions (around 300 nm),but they are significantly higher (a few hundred nanometers) Especially thecircular rings show rather narrow size distributions Optical measurementsreveal that the molecules making up the rings are oriented radially, i.e., therings are truly bent nanofibers

Following achievement of a high degree of growth control, the nanofibersare used for investigating optical pecularities in the nanodomain In the fol-lowing, various applications are only briefly discussed For a more completedescription the reader is referred to the original literature

1.4 Selected Applications in Nano- and Microoptics

Light emitting nanofibers are an interesting model system for demonstratingthe resolution limit of optical microscopy at the interface between micro- andmacrocosmos In Fig 1.8 dark field and epifluorescence images of the samehexaphenyl nanofiber are shown Structures with characteristic dimensions of

Fig 1.8 Comparison of dark field (a) and epifluorescence (b) images of the same

in the nanofiber that gives rise to a bright luminescence spot

a few ten nanometers such as breaks in the nanofibers (exemplified by anAFM image in Fig 1.8b) are barely visible even in dark field images since thedifference in indices of refraction of nanofibers and underlying substrate issmall In dark field microscopy (Fig 1.8a) one illuminates the sample undernearly grazing incidence, thus enhancing the visibility for structures on thesurface that scatter light Consequently such structures appear bright on adark background Note that the structures seen in Fig 1.8 have heights ofless than 100 nm, i.e., much smaller than the wavelength of the light used forscattering

Much better contrast and visibility of subwavelength structures is obtained

in epi-fluorescence microscopy (Fig 1.8b) In such a set up UV light ates the nanofibers under normal incidence and the resulting luminescence

irradi-is observed under normal incidence, too Excitation and luminescence lightare separated with the help of a wavelength selective beam splitter and colorfilters At the breaks in the needles the internally generated luminescence isscattered into the far-field and thus submicron structures become easily visi-ble The true dimensions of the breaks, of course, cannot be determined viaoptical far field microscopy

The possibility to separate the nanofibers widely from each other (i.e., withdistances that are larger than the wavelength of the emitted light) as well astheir macroscopic long axes allow one to investigate in detail the influence ofmorphological changes in the nanometer-range on the optical properties As anexample we show in Fig 1.9 spectra obtained from a single nanofiber (circles)and from an ensemble of nanofibers (solid line) The spectrum from the singlenanofiber has been obtained by illuminating the nanofiber inside a microscopewith UV light and sampling the emitted light also inside the microscope with

an optical fiber, connected to a miniature spectrometer The relatively sharpspectral lines (given that the light is emitted from organic aggregates and thatthe samples are hold at room temperature) are due to a vibronic progression

Fig 1.9. Room temperature luminescence spectra obtained from an isolated

nanofiber (open circles) and an ensemble of nanofibers (solid line) The

equidis-tant lines on top of the graph represent the expected vibronic progression due tothe C-C stretching vibrations of all carbon atoms of the individual molecules in thenanofiber Due to reabsorption the highest energy (0-0) mode is relatively weak

It becomes stronger if one cools the sample [28]

of the exciton emission (perpendicular lines on top of the graph) In the case

of the single nanofiber spectrum the highest energy (0,0) band is not visibledue to a cut-off-filter in the microscope Nevertheless, comparison with thespectra from the needle ensembles reveals that the light emission becomesmore focussed to a narrow color range (namely 420± 5 nm) if an individ-

ual nanoaggregate is considered More extended spectroscopic measurementsalong a nanofiber show that the spectral width of this residual line depends onthe morphology of the aggregate and that it becomes narrower if the nanofiberwidth decreases, e.g., at the tip of the nanofiber [28]

If one increases the intensity of the excitation light, nonlinear optical effectscan be observed in the nanofibers The collective nonlinear optical response of

oriented arrays of para-hexaphenylene nanofibers has been studied using

fem-tosecond laser pulses [29] At excitation wavelengths between 770 and 786 nmcontributions to the two-photon signal intensity from both two-photon lumi-nescence (TPL) and second harmonic generation (SHG) have been observed,

where ISHG/ITPL≈ 0.015 More recent studies of SHG from nanofibers

trans-ferred onto glass substrates have shown that the SHG signal observed in [29]must have resulted from the wetting layer on the mica substrate If one modi-

fies para-quaterphenylene by adding electron donor and acceptor groups (e.g.,

methoxy- and amino-groups) and grows nanofibers from these functionalized

molecules, then the increased hyperpolarizability of the molecules results instrong SHG from the nanofibers [30].

The next logical step is to use the nonlinear optical signal to obtain tially resolved information on molecular properties of the nanoaggregates

spa-By use of a two-photon microscope the local polarized two-photon intensity along individual p-6P nanofibers could be determined [31] Figure 1.10 shows

polarized 10×10 µm2two-photon images of nanofibers on mica The nanofiberswere excited again with a femtosecond laser at 780 nm From a comparison ofthe intensity distributions at different polarization directions and employingthe tensorial nature of the respective optical response one can deduce localorientations of the hexaphenyl molecules along the nanofibers Essentially,just as in the linear case the absorption (and luminescence) is maximum ifthe electric field vector is parallel to the long molecular axis (which in turn isparallel to the optical transition dipole moment) and minimum if it is orientedperpendicular to it

Using the two-photon luminescence instead of the one-photon cence increases the spatial resolution and the signal-to-noise-ratio of themethod That way for all of the nanofibers shown in Fig 1.10 molecular ori-entations could be determined with a spatial resolution of less than 1µm [31].The results agree with possible molecular orientations predicted from bulk

lumines-growth of a para-hexaphenyl crystal.

Finally, organic nanofibers are also a nice testing ground for methods thataim to deduce directly properties of the near field such as scanning near fieldoptical microscopy (SNOM), Fig 1.11 [32] To obtain the images in Fig 1.11 an

inverted epifluorescence microscope was mounted on a (x,y,z)-movable table

and was used for focussed UV (360 nm) illumination of the sample outside

Fig 1.10. Polarized 10× 10 µm2 two-photon (400 nm) images of nanofibers onmica The nanofibers were excited with a femtosecond laser at 780 nm with a totalpower of 25 mW and with its electric field vector directed as shown with respect

to the nanofiber axes The detection was always polarized parallel to the individualmolecules [31]

Fig 1.11. Near field images (45× 45 µm2) of waveguiding nanofibers on mica.

(a) Topographical image, (b) optical image in the near field at contact with the

nanofibers The nanofibers have been excited with UV light on the left-hand sideoutside the viewing area shown in the plots They are not visible in the optical farfield [32]

the direct viewing area of the SNOM That way waveguiding through thenanofibers could be measured It is to be noted that the low transfer rate

of 425 nm photons from the luminescing nanofibers via the 160 nm diameterSNOM tip to the detector of less than 10−6 made rather dense needle arrays

and strong focussing of the exciting UV light necessary This, in turn, resulted

in photobleaching of the samples, which limited the possible data integrationtime and thus the signal-to-noise ratio

A 45× 45 µm2 scan along the sample at a constant distance of a fewnanometers maintained by shear force feedback is shown in Fig 1.11, both astopographic image (Fig 1.11a, from the shear force feedback) and as opticalimage (Fig 1.11b, from the measured counts in the photomultiplier) First ofall, it is interesting to note that the optical image shows some structures at

all since the observation point of the SNOM is outside the illumination area

by the excitation light This can only be explained by waveguiding of lightthrough the nanofibers, which then is transferred within the near field intothe SNOM Second, individual nanofibers show quite different brightnesses,although they look topographically very similar and the far field images revealindeed almost the same brightness (not shown here) Again, since the UVexcitation of the nanofibers occurs outside the viewing area of the SNOM onecould argue that some nanofibers are not visible in the SNOM since they donot guide blue light of 425 nm Measurements and calculations for waveguiding

in individual nanofibers indeed have shown that the critical minimum widthfor waveguiding is about 220 nm [33, 34] The waveguiding is damped mainly

by reabsorption in the nanofibers If one measures the scattered intensity as afunction of distance from the excitation point, then one obtains the imaginarypart of the dielectric function of an individual nanoaggregate, which is animportant quantity since it determines the light-matter interaction [33]

One should also recall that the SNOM images result from a coupling tween waveguiding modes in the nanofiber and waveguiding modes in theSNOM fiber The SNOM tip acts as a scatterer which transforms the wavevector of the nanofiber mode into different wave vectors of scattered waves.Some of those scattered waves can be coupled to the propagating fiber modes.This process is most effective if there is a phase matching between the waves.Therefore, it depends on the mutual position between nanofiber and theSNOM tip The nanofibers for which this condition accidentally is fulfilledare seen as more bright It is tempting to assume that both waveguiding ef-ficiency and phase matching are responsible for the strong selectivity of theSNOM.

be-1.5 Summary and Outlook: Future Devices

From Organic Nanofibers

In this chapter growth and growth control of quasi single crystalline, fiber-likeorganic nanoaggregates on specific template surfaces have been discussed Bynow it has thoroughly been demonstrated that organic molecular beam epi-taxy of polarizable, rod-like molecules with large delocalizedπ-electrons (viz.,

para-phenylenes) on single crystalline, flat substrate surfaces with large

elec-tric dipole domains (viz., muscovite mica) leads to the well organized growth oforganic nanofibers with remarkable optical properties These nanofibers havebeen used within the last five years for a series of benchmark experiments onstatic and dynamic, linear and nonlinear optics as well as morphology in themesoscopic size regime A few applications are detailed in this chapter

The fact that para-phenylenes plus muscovite mica constitute an unique

combination from a crystallographic and growth dynamic point of view hasresulted in unique nanoaggregates but obviously also limits the potential range

of applications of these nanofibers However, two recent developments haveopened the door to a much wider application potential of organic nanofibers:(1) the possibility to transfer the nanofibers from the original growth sub-strate to any other substrate or into liquids [35]; and (2) the possibility

to functionalize a para-quaterphenylene block with specific groups and the

generation of aligned nanofibers from these functionalized molecules [36]

In terms of implementation of nanoaggregates into working devices the formerdevelopment (1) has enabled electrical conductivity [37] as well as mechanicaldeformation measurements [38] on single nanofibers, whereas development (2)resulted in the growth of tailored nanoscaled frequency doubling elements [30].Further device development thus seems to be well in reach in the nearestfuture [39]

The author is indebted to the Danish Research Agencies FNU and FTPand to the TMR program FASTNet of the European Community as well asthe Danish National Advanced Technology Foundation for financial support

He would like to acknowledge Frank Balzer, Humboldt-University, Berlin as

the coinventor of the organic p-6P nanofibers Although many more people

are involved in various aspects of organic nanofiber research this article isbased primarily on work performed together with Jonas Beerman, JonathanBrewer, Vladimir G Bordo, Sergey I Bozhevolnyi, Manuela Schiek, andValentyn Volkov

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Titanium-Based Molecular Architectures

Formed by Self-Assembled Reactions

R Beckhaus

Summary. The design of highly ordered supramolecular structures has gained moreand more interest within the last few decades The concept of self-assembly chem-istry takes a key position in this field and a multitude of supramolecular com-pounds have been synthesized by combining simple building blocks to two- andthree-dimensional structures [1–3] Due to their electronic and steric versatility aro-

matic N -heterocycles play a prominent role as classical ligands in coordination

com-pounds, [4,5] as bridging ligands in binuclear derivatives [6–8] and as building blocksfor supramolecular compounds [9–17] Beyond their capability to connect metal cen-

and thereby may affect delocalization and transport of electrons [18] Comparedwith the highly developed late transition metal supramolecular chemistry, only afew attempts have been made to use the well defined coordination modes and thereducing properties of early transition metals [19, 20]

In recent years the research in the area of monometallic compounds has beenextended to polymetallic supramolecular systems, which may have a considerablepotential to design new materials for use in photochemical molecular devices Furthermore, several polynuclaer compounds have been created, which possess functionalitysuch as nonlinear optics, molecular magnetism, anion trapping, that means e.g., toact as molecular receptors, DNA photoprobe and other photophysical properties,successfully reflection potential advantages of multinuclear derivatives

In the course of our studies on the reactions of low-valent titanium compounds

and aromatic N -heterocycles we succeeded in the syntheses of various tetranuclear

complexes for which single crystal X-ray structure analyses confirmed structures ofmolecular squares and rectangles Here we wish to report on the syntheses of thesenovel self-assembled polynuclear titanium complexes and their properties [21, 24,

25, 31, 71, 83]

2.1 Introduction

The design of highly ordered supramolecular structures has gained more andmore interest within the last few decades The concept of self-assembly chem-istry takes a key position in this field and a multitude of supramolecular

Scheme 2.1.Binuclear low valent titanium complexes

compounds have been synthesized by combining simple building blocks totwo- and three-dimensional structures [1–3] Due to their electronic and stericversatility aromatic N-heterocycles play a prominent role as classical ligands

in coordination compounds [4, 5], as bridging ligands in binuclear tives [6–8], and as building blocks for supramolecular compounds [9–17].Beyond their capability to connect metal centers by forming ligand to metalbonds they provide the opportunity ofπ-backbonding and thereby may affectdelocalization and transport of electrons [18] Compared with the highly dev-eloped late transition metal supramolecular chemistry, only a few attemptshave been made to use the well-defined coordination modes and the reducingproperties of early transition metals [19, 20]

deriva-The formation of molecular squares and rectangles requires 90◦ angles at

the vertices, as typical for square planar or octahedral late transition metalspecies [1] Hence, only a few examples are known using distorted tetrahedralgeometries at the corners [21–23]

In the course of our studies on the reactions of low-valent titanium nitrogen

complexes (1) [24], which are characterized by strong magnetic coupling of both titanium centers leading to a diamagnetic properties of 1 [25], we are interested in the behavior of complexes of type 2 exhibiting bisazines as

bridging ligands between low valent titanium centers

Here we wish to report on the syntheses of these novel self-assembledpolynuclear titanium complexes and their properties, employing different

R R H

H R R

Ti

R R R R

Ti R R

Scheme 2.2. Low valent titanium “corners” in different oxidation states

N N

4,4'-bipyridine

N N

2-methylpyrazine

N N

plex 1 The titanium (d4) species can be prepared in form of the bisfulvene

complexes [27] and can be used in a direct manner [28]

2.1.1 Results and Discussion

It was found in our investigations that reactions of low valent early transitionmetal fragments with potentially bridging bisazines leads to formation of well-

defined molecular architectures (A), due to the strong reducing properties to accompanied radical induced C–C coupling reactions (B) and by primary

C–H bond activation reactions to multifold dehydrogenative C–C couplings

forming large surface aromatic systems (C).

Details are given in the next chapters

2.2 Formation of Molecular Architectures

We recently reported on the reaction of the excellent titanocene precursor[Cp2Ti{η2-C2(SiMe3)2}] (for Cp2Ti (3) [26]) with pyrazine (12) that leads to

the formation of the first structurally characterized molecular square with tanocene(II) corner units [Cp2Ti(µ-C4H4N2)]4(20) [21] Using different start- ing materials (5) for the metal compound as well as for the ligand (14, 15)

ti-further neutral molecular squares with titanocene corner units can be

synthe-sized Scheme 2.5 shows the formation of the molecular squares 18, 19, 20, and 21, that could be characterized by single crystal X-ray analysis, elemental

Ti L

L

N N H

N N

N N N

N

Ti

Ti Ti

H 3x

-3H2

N N

N N N

N

Ti

Ti Ti

N N H

H 3x

N N H

H

N N H

H N

H H

H H

A

B

C

Scheme 2.4. Reaction pathways of low valent titanium complexes with

N-Heterocyles (A formation of molecular architectures, B radical induced C–C coupling reactions, C dehydrogenative coupling)

analysis, and IR All compounds are intensely colored and highly sensitive toair and moisture

The reaction of [Cp2Ti{η2-C2(SiMe3)2}] with 4,4-bipyridine (15) in

toluene leads after a few minutes to a color change from yellow to dark blueand after 48 h at 60◦C dark blue crystals of 19 can be isolated in yields of

about 50% The tetrazine bridged complex 18 can be isolated from a dilute reaction solution of 3 and tetrazine (14) in toluene after 48 h as a crystalline

solid The dark blue crystals of both complexes show an intense metallic lustre.They are only sparingly soluble in aliphatic and aromatic solvents and ethersand do not melt below 250◦C In the mass spectra (EI 70 eV) no molecular

peaks could be observed Due to their low solubilities no recrystallizations arepossible Therefore, suitable single crystals for the X-ray analysis were grownfrom the reaction solutions

Single crystals of 19 can be obtained at 60◦C from toluene and in better

quality from tetraline at room temperature The molecular structure of 19, crystallized from tetraline (19a), is shown in Fig 2.1.

19a crystallizes in the space group P42/n with four solvent molecules per

tetramer The metal atoms are coordinated tetrahedrally by two Cp ligandsand two heterocycles As the titanium atoms are located in one plane the

N N

R = H

Ti N N R

Ti

N

N R

Ti

R Ti

N

N R R

R

R

R

Ti N N R Ti N

N R

N Ti N R

N Ti

N R R R

R

R

N N

R =t-Bu

N N

Scheme 2.5 Reactions of the titanocene complexes 3 and 5 with pyrazine (12), bipyridine (15), and tetrazine (14)

complex forms a nearly perfect square with the bent metallocene moieties ascorner units

Single crystals of the tetrazine bridged complex 18 can be grown from

dilute reaction mixtures in toluene Figure 2.2 shows the molecular structure

of 18.

18 crystallizes in the space group P421c and the crystal contains no solventmolecules In contrast to the analogue tetrameric pyrazine bridged complex[Cp2Ti(µ-C4H4N2)]4 (20) [21] the tetrazine complex 18 does not really form

a molecular square since the four titanium atoms do not lie in one planebut rather form a tetrahedron As it is mostly observed with tetrazine theheterocycle coordinates as a bismonodentate ligand similar to pyrazine andnot as a bisbidentate ligand [7]

In order to obtain analogue complexes with higher solubilities [(t-BuCp)2

Ti{η2-C2(SiMe3)2}] was used as a source for a titanocene fragment (4) with

bulky substituted Cp ligands The reactions of 4 with pyrazine and

bipyri-dine proceed more slowly but show the same color changes to violet and bluethat are observed when using [Cp2Ti{η2-C2(SiMe3)2}] If the reactions with

pyrazine and 4, 4  -bipyridine are carried out in n-hexane, crystals of 20 and

21 can be isolated from the reaction mixture in yields of 65% and 79%,

re-spectively Compared to the analogue complexes with unsubsituted Cp ligandsthey show a considerably increased solubility in aromatic solvents and THF

Furthermore they have lower melting points (20 197–200◦C; 21 203–206◦C),

but again no molecular peaks could be observed in the mass spectra (EI,

70 eV)

Ti1 N1 C1 C2 C3 C4 C5

C6

C7

C8 C9 C10 N2 Ti1a

Ct1

Ct2

Fig 2.1 Structure of 19a (50% probability, without H-atoms) Selected bond

2.086, Ti1–Ct2 2.092, N1–C1 1.358(3), N1–C1 1.374(3), N2–C6 1.363(3), N2–C101.370(3), C1–C2 1.366(3), C2–C3 1.418(3), C3–C4 1.418(3), C3–C8 1.424(3), C4–C5 1.366(3), C6–C7 1.368(3), C7–C8 1.424(3), C8–C9 1.423(3), C9–C10 1.364(3),N1–Ti–N2a 84.83(6), Ct1–Ti–Ct2 132.39, Ct1 = ring centroid of C11–C15, Ct2 =ring centroid of C16–C20, symmetry transformation for the generation of equivalent

atoms: a = −y + 1/2, x, −z + 1/2

Single crystals of 20 could be obtained from n-hexane, single crystals of

21 were grown by slow diffusion of n-hexane into a THF solution Figures 2.3

and 2.4 show the molecular structures of 20 and 21.

20 crystallizes in the space group P21/n and the crystal contains two

n-hexane molecules per molecular square 21 crystallizes in the space group

P-1 and contains 11 molecules THF per tetranuclear unit Both complexes

show a more or less square configuration The sterically demanding t-butyl

groups take nearly the same position in both complexes The Ti–N distances

in 19, 20, and 21 lie in the upper limit for Ti–N bonds and correspond to

values expected for titanium coordinated N-heterocycles [21] Bond lengthsand angles of the titanocene units correspond to known values for tetrahedralcoordination geometry

N2C2N3Ti1

C8

C12C11

C10

C9

C7C6

C5

C4

C3N3a

Fig 2.2 Structure of 18 in the crystal (50% probability, without H-atoms) Selected

2.086, Ti1–Ct2 2.075, N1–C1 1.377(7), N1–N2 1.420(5), N2–C2 1.305(7), N3–C21.337(7), N3–N4 1.412(7), N4–C1 1.298, N1–Ti1–N3a 88.84(19), Ct1–Ti–Ct2 130.24.Ct1 = ring centroid of C3–C7, Ct2 = ring centroid of C8–C12, symmetry transfor-

mation for the generation of equivalent atoms: a = −y + 1, x + 1, −z + 2

The successful syntheses of molecular squares with the different bridgingligands lead to the attempt to synthesize a mixed-bridged complex that con-tains bridging ligands of different lengths and exhibits the structure of a molec-ular rectangle Generally, only a few molecular rectangles are hitherto knownbecause most attempts to synthesize them in one step reactions resulted inthe preferred formation of the two homobridged molecular squares [3, 14].Therefore, a reaction with two subsequent steps was used to coordinate thetwo different ligands to the titanocene moiety Scheme 2.6 shows possible syn-thetic routes starting from a titanocene chlorine complex in the oxidation

state +III (11).

In the first reaction step the first bridging ligand is coordinated betweentwo [Cp2TiCl] units whose last coordination site is blocked by the chlorine

N5Ti4

Ti1

N7C88C87N8C86

C85

N1C22

C19

C21

C20N2

N3C41

C42C43

C44

N4

Ti2

Ct01Ct02

Ct05

Ct06Ct07

Ct03Ct04

Ti3Ct08

Fig 2.3 Structure of 20 in the crystal (50% probability, without H-atoms).

Ti1–Ct1 2.115, Ti1–Ct2 2.118, N1–C19 1.378(4), N1–C22 1.381(4), N2–C21 1.388(4),N2–C20 1.391(4), C19–C20 1.352(4), C21–C22 1.359(4), N8–Ti1–N1 84.30(10),Ct1–Ti1–Ct2 133,49, N2–Ti2–N3 85.08(10)

atom This reaction can be carried out successfully with pyrazine as well

as bipyridine and complexes 24 and 23 can be isolated as green crystals in

yields of 55% and 43%, respectively, and characterized by X-ray analysis, IR,

and elemental analysis [28] In the mass spectra of 24 and 23 only peaks of

the free ligands and [Cp2TiCl] are observed showing the low stability of thedimeric compounds For similar monomeric compounds [Cp2TiClL] with L =pyridine, PPhMe2 a complete dissociation into the ligand and 22 has been

observed at higher temperature (130◦C in vacuo for [Cp

2TiClPPhMe2]) [29]

In the second step an abstraction of the chloride ligand by reduction of the

titanocene(III)complexes 24 and 23 and a coordination of the second bridging

ligand has to take place Lithium naphthalenide is used as a soluble reducing

agent and the sparingly soluble rectangle 25 precipitates from the reaction mixture To inhibit dissociation of complexes 24 and 23 and avoid an exchange

of the ligands during the reduction the reaction was carried out at−78 ◦C.

Ti4

Ti1 Ti2

N8

C108 C109

C110 C111

C112

N1 C19

C23

C20 C21

C22

C26 C27 C28 N2 N3

C47

C48

C49 C50 C51

C54

C55 C56

N4 C52

N6 C84 C83 C82

N7 C103 C107

C104 C105

C106

Ct1

Ct2 Ct3

Fig 2.4 Structure of 21 in the crystal (50% probability, without H-atoms) Selected

Ti1–Ct2 2.104 Ti2–N2 2.19(4), N1–C23 1.37(5), N1–C19 1.37(5), N2–C24 1.38(6),N2–C28 1.38(5), C19–C20 1.36(6), C20–C21 1.42(6), C21–C26 1.42(6), C21–C221.43(6), C22–C23 1.37(6), C24–C25 1.36(7), C25–C26 1.43(6), C26–C27 1.43(6),C27–C28 1.35(7), N8–Ti1–N1 83.7(13), Ct1–Ti1–Ct2 134.18

If pathway (b) is used and 24 is reduced in the presence of pyrazine the reaction does not lead to the rectangular complex 25, instead the formation

of the molecular square 20 (R:H) is observed accompanied by a further

prod-uct (probably 19) However, if 23 is reduced in presence of 4, 4 -bipyridine

(pathway a) 25 can be isolated as needle-shaped blue violet crystals with an

intense metallic lustre The complex could be characterized by X-ray

anal-ysis, elemental analanal-ysis, and IR spectroscopy The synthesis of 25 can be

further simplified so that starting from [Cp2TiCl2] neither 22 nor 24 have

to be isolated and the molecular rectangle is easily accessible from simple,commercially available starting materials If titanocene dichloride is reduced

N N

Ti Ti

Ti

N N

N

N N

+2 C10H8

+2 LiC10H8+2 C10H8

Scheme 2.6 Possible synthetic routes to the molecular rectangle 25

in presence of pyrazine with one equivalent of lithium naphthalenide and then

a 4, 4 -bipyridine solution and the second equivalent of lithium naphthalenide

are added after cooling to −78 ◦C, 25 can be isolated in 45% yield

Crystal-lization from THF yields crystals of 25 that are suitable for X-ray diffraction The molecular structure of 25 is shown in Fig 2.5.

25 crystallizes from THF in the trigonal space group P3121 containing twosolvent molecules per tetrameric molecule in the crystal Each titanocene unit

is coordinated by a pyrazine molecule and a 4, 4 -bipyridine molecule and with

the planar configuration of the four titanium atoms a rectangular geometryresults for the complex

The efficient synthesis of 25 requires the absence of free pyrazine (12).

If 25 is reacted with 12, 20 is formed by ligand exchange Therefore only

pathway (a) is successful On the other hand no ligand exchange reactions

occur between 25 and 15 Disproportion reactions of 25 itself to 19 and 20

do apparently not take place

A similar but more soluble rectangular complex 26 can be obtained by

the same procedure using [(t-BuCp)2TiCl2] instead of [Cp2TiCl2] as startingmaterial After evaporating the reaction mixture and dissolving the residue in

toluene, 26 can be obtained by filtration from LiCl and subsequent addition

of n-hexane Again the blue-violet crystals show an intense metallic lustre.

Single crystals of 26 can be grown by recrystallisation from benzene from which 26 crystallizes in the space group P-1 The coordination geometry of 26

Ti1 C4

C21 C18 C22

C32

N4 C34 C33

N4a

Ti1a

Fig 2.5 Structure of 25 in the crystal (50% probability, without H-atoms).

Ti1–Ct1 2.111, Ti1–Ct2 2.068, Ti2–Ct3 2.095, Ti2–Ct4 2.094 Ti2–N2 2.128(4),Ti2–N3 2.220(4), N1–C13 1.375(6), N1–C11 1.385(6), N2–C14 1.379(6), N2–C121.396(6), N3–C29 1.353(6), N3–C25 1.359(6), N4–C30 1.352(7), N4–C34 1.356(6),C11–C12 1.359(7), C13–C14 1.351(7), C25–C26 1.371(7), C26–C27 1.426(7), C27–C28 1.425(7), C27–C32 1.432(7), C28–C29 1.359(7), C30–C31 1.347(7), C31–C321.427(7), C32–C33 1.411(7), C33–C34 1.363(7), N1–Ti1–N1a 83.68(15), N2–Ti2–N384.10(15), Ct1–Ti–Ct2 131.48, Ct3–Ti2–Ct4 131.00 Ct1 = ring centroid of C1–C5,Ct2 = ring centroid of C6–C10, Ct3 = ring centroid of C15–C19, Ct4 = ring cen-troid of C20–C24, symmetry transformation for the generation of equivalent atoms:

a = x − y + 1, −y + 2, −z + 2/3

shows no significant differences to the already discussed structures of the other

tetranuclear complexes The molecular structure of 26 is shown in Fig 2.6 The Ti–N distances to the pyrazine bridge in 25 and 26 are found shorter by

0.05–0.09 ˚A compared to the Ti–N distances of the titanium-bipyridine bond

In contrast to most of the known molecular rectangles with basically

differ-ent sides of the rectangle [3] the titanium-based compounds 25 and 26 contain

two bridging ligands of similar type Molecular rectangles with pyrazine and

4, 4 -bipyridine bridges has become available in the case of octahedrally

coor-dinated rhenium corners [30], exhibiting comparable, L-M-L angles (83.5 ◦, 25:

83.9 ◦ , 26: 83.8) and sizes of the cavities (7.21 ×11.44 ˚ A, 25: 7.20 ×11.52 ˚A, 26:

7.22 × 11.38 ˚A) However, in 25 and 26 the rectangular geometry is realized

by tetrahedrally coordinated corner atoms

Ti1

Ti2 Ti3

N3

N4

N5 N6

C48

C69 C70

C71

C72 C73 C76

C77 C78

C74 C75C97

C98 C99

Ct3 Ct4

Fig 2.6 Structure of 26 in the crystal (50% probability, without H-atoms) Selected

Ti1–Ct2 2.093, Ti2–N2 2.153(5), Ti2–N3 2.155(6), Ti2–Ct3 2.100, Ti2–Ct4 2.088,N1–C19 1.364(8), N1–C23 1.379(7), N2–C28 1.391(8), N2–C24 1.411(7), N3–C471.367(8), N3–C49 1.385(7), N4–C50 1.396(8), N4–C48 1.402(7), C19–C20 1.397(8),C20–C21 1.410(8), C21–C22 1.422(8), C21–C26 1.431(7), C22–C23 1.390(8), C24–C25 1.377(8), C25–C26 1.416(8), C26–C27 1.422(8), C27–C28 1.380(8), C47–C481.346(9), C49–C50 1.346(9), N8–Ti1–N1 84.82(18), Ct1–Ti1–Ct2 134.66, N2–Ti2–N3 82.51(19), Ct3–Ti2–Ct4 134.36

Except for 18 all complexes contain solvent molecules that can be removed

by drying the crystalline solid in vacuum In 19a the tetraline molecules are

located in canals that are formed by the molecular squares Figure 2.7 shows

a greater section of the structure of 19a including the solvent molecules.

The importance of the solvent molecules for the solid state structure andthe relatively great conformational freedom of the tetranuclear compounds is

shown by the structures of 19 obtained by crystallization from tetraline (19a) and toluene (19b) Figure 2.8 shows the configuration of the four titanium atoms in 19a and 19b in the side view onto the tetramers.

Whereas the configuration of the bicyclic bridged complexes 19a and 19b

is influenced by the solvents used for crystallization, the monocyclic bridged

complexes 18 and 20 exhibit different configurations as well (Fig 2.9) The

difference becomes visible in the arrangement of the titanium centers Whereas