Alfred Saupe – 50 Years of Research

Abstract

In this commemorative article the major scientific achievements of Alfred Saupe are discussed. These comprise those which are clearly associated with his name and made him famous, and some important issues where his fundamental involvements are rather less apparent. Emphasis is put on his lasting impact on the liquid crystal field.

Keywords:

• Maier–Saupe theory
• liquid crystal NMR
• lyotropic liquid crystals
• biaxial nematics
• lasting impact
• Alfred Saupe

1. Introduction

Commemorating Alfred Saupe's scientific work one realizes immediately the enormous breadth and deepness of his research, which was maintained at very high levels for a very long time. Trained as a physicist, he did not specialize in experimental or theoretical physics, but rather did both. From his Diploma thesis work on polarized ultraviolet (UV) light absorption in the different phases of PAA (4,4'-dimethyoxyazoxybenzene) it became obvious that ordinary molecular forces are responsible for the nematic ordering, but there was no theory to explain that. So he devoted his Ph.D. work (with W. Maier as his supervisor) to the derivation of the molecular-field theory of orientational order due to van der Waals forces – a heavy quantum-mechanical second-order perturbation calculation of the angle-dependent potential of mean torque that led to the famous Maier–Saupe expression for the nematic order parameter. This theory made many predictions, which he started to test with several experimental methods. Among the former, the temperature dependence of the Frank elastic constants was investigated using the director reorientation by magnetic fields well above the well-known Frederiks instability threshold. Again, he supplied the missing parts of the theory for high fields on his own.

As a post-doc (in modern terms) he made contact with a more applied, electro-technical environment. There he grasped very new techniques, such as nuclear magnetic resonance (NMR), which were not commonly used at that time. He took the opportunity to apply these methods to nematic liquid crystals as well as to non-mesogenic organic molecules dissolved in them. Much experimental effort to make the methods work, together with theoretical work to make them meaningful and useful, followed and established in particular NMR as a valuable and indispensable standard tool for liquid crystal research. Nevertheless, he did not discard previously used methods, but rather combined them with new ones, such as infrared (IR) spectroscopy.

The third step in his scientific career led him, not quite by intention, to a macromolecular institute, where he was offered the possibility for Habilitation, a necessary prerequisite to make an academic career in Germany at that time. He added polymers and their investigation by NMR to his scientific portfolio – something that certainly played a role many years later, when he spent some time in Mainz as senior Humboldt fellow and when he was asked to head a Max Planck Research Group in Halle after the unification of Germany.

This experience of different scientific environments and the interaction with colleagues of different scientific backgrounds and expertise were an ideal preparation for his move to the LCI at Kent State, USA. Here, in a research focussed, multi-disciplined and liquid-crystal oriented place he was able to combine theory with experiment, add new techniques to the already standard ones, and look for new materials, new phases and their properties beyond simple uniaxial thermotropic nematics. And this he did to a large extent.

On the occasion of the 70th birthday of Alfred Saupe somewhat 14 years ago, a Festschrift was produced [1]. Among scientific papers from various colleagues it contains his personal CV (by P. Palffy-Muhoray), a list of his publications (until mid-1997), an English translation of his early papers on what is now called the Maier–Saupe theory originally published in German, and a laudatio ‘Alfred Saupe – 40 years of Research’. There [2] I have tried to discuss the scientific contents and merit of many of his papers, clustering them into topical groups, such as ‘structure and order’, ‘defects, dynamics and instabilities’, ‘new phases and phase transitions’ and ‘applied research’, which gives a glimpse of the broadness of Alfred Saupe's research. Of course, I will not repeat this here and, instead, will focus on the lasting scientific impact on the liquid crystal field that his achievements have made. As examples I will discuss the Maier–Saupe theory, NMR, tilted smectics, biaxial nematics, and other highlights that will persistently be connected with his name, and a few less known involvements in the early stages of important areas. A discussion of his last 12 research years will finish this homage to Alfred Saupe.

2. Maier–Saupe theory

Without any doubt, Alfred Saupe is best known, not only in the liquid crystal community, but also far beyond, for his share of the Maier–Saupe theory. Based on the assumption that only induced dipolar forces are relevant for orientational ordering, this theory is still applied to, or relevant for, quite different kinds of problems given the omnipresence of these van der Waals forces at the molecular level. The number of citations, almost 4000 up to now, for the three publications that developed the theory [3] is an impressive signature for its relevance. Furthermore, the rate of citation has been high over the years (apart from a slow start, probably due the language barrier) and does not yet show a decline. Even for the present decade the averaged rate is 30 citations per year for each of the three papers. The five years with the highest citation number are widely scattered between 1976 and 2001, indicating that the appreciation of the scientific community is a lasting and prevailing one.

Due to its general importance the Maier–Saupe theory is now included in most textbooks dealing with statistical and/or condensed matter physics, although often only in a very abbreviated way, for example in [4], or only the results for the self-consistent order parameter are presented and discussed, for example in [5]. A short exposition of the structure of this theory can be found in [2] and a more comprehensive treatment in [6], although the real beauty and profoundness of the theory can only be grasped by reading the original publication (or the English translation in [1]). With the assumption of induced dipolar forces many experimental results could be explained, for example the spectra of benzene π-electrons in PAA and the odd–even effect caused by alkyl chains. But this was not enough for Alfred Saupe. The theory made quantitative predictions regarding the jump of the order parameter at the weakly first-order isotropic-to-nematic transition, the temperature dependence of the order parameter including pretransitional effects, the density jump at the transition and various thermodynamic quantities such as the heat of transition, specific heat and compressibility. He successfully tested these predictions experimentally and could corroborate the applicability of the theory to the (thermotropic) liquid crystals known at that time. Clearly, permanent dipolar forces due to special chemical structures or steric forces due to the elongated form of the molecules are less important for the origin of nematic order. Repulsive steric forces play a role in lyotropics and are nowadays frequently used in computer simulations (even for thermotropics), since they take much less computation time than induced dipolar forces.

This early scientific achievement of Alfred Saupe already demonstrates his working style: to try to tackle a problem from all sides by different means and accept a result only after having obtained a comprehensive and coherent picture.

3. NMR and order

The use of NMR techniques to investigate liquid crystals is another area that is firmly associated with Alfred Saupe. His first, ground-breaking paper [7] on the application of NMR to nematics and its theoretical interpretation has drawn more than 400 citations, among them 75 in the 21st century. Again this shows the lasting impact his NMR research has had on the liquid crystal field. In the 10 years that followed the first publication, NMR was one of his favorite experimental techniques (more than 20 papers). However, also in later years he came back to it, in particular when new types of liquid crystals occurred, since NMR can be used for thermotropic and lyotropic liquid crystals as well as for side-chain and main-chain polymeric and elastomeric mesophases.

Basically, NMR probes the orientation of spins with respect to an applied magnetic field. Whether a system is disordered (powder or isotropic liquid) or ordered (liquid crystal or crystal) makes a difference to the NMR signal. Liquid crystals are thereby in between the solid case (order) and the liquid one (motional narrowing of the signals) and their NMR spectra need some special theoretical interpretation. Obviously, NMR is suitable for the extraction of information on orientations (e.g., of the director) and the strength of the molecular field creating the orientational order. Both aspects were exploited by Alfred Saupe from the beginning (for further developments of the method for use in liquid crystals, cf. [8]).

Having experimental access to the orientational order parameter, Alfred Saupe investigated several phase transitions, where often the strength of the order changes. In particular, first-order transitions and biphasic regions can be identified. The different orientations of prolate and oblate aggregates in a magnetic field allowed Alfred Saupe to detect a N_C-to-N_D phase transition in certain lyotropic systems leading ultimately to the discovery of a biaxial nematic phase (see later). NMR measurements on molecules dissolved in a nematic solvent were an important topic right from the beginning (with G. Englert) [9]. Due to the ordered environment that allows us to look at definite geometries, on the one hand, and due to the motional narrowing in the liquid phase resulting in sharp spectra, on the other, a host of valuable information on the dissolved molecules can be obtained. Of course, Alfred Saupe did not rely on just one technique, but combined NMR with other spectral methods (UV, IR) and with dielectric relaxation to obtain data on intermolecular forces, quadrupolar interactions, electronic structure, proton distances, anisotropic chemical shifts and more. Such information helps the chemical design of mesogens and the understanding of their liquid crystal phases.

4. Structure and phases

In Kent, Alfred Saupe started to carry out much theoretical and experimental work on new phases and their structure as well as on textures and defects that allowed for the identification of those new phases. The origin of these developments can be found in a short publication in 1969 [10], where several new ideas and speculations are laid out. This paper had an enormous and immediate impact on the liquid crystal community, although this is not adequately reflected by the relatively low number of 163 citations. In particular, the citations dropped considerably in the 1990s and thereafter. The reason might be that some of the discoveries are nowadays so obvious and well-known that the requirement for a citation is not seen, or the topics were amended afterwards by other researchers and are now not necessarily associated with Alfred Saupe.

The first point is his realization that the tilted smectic C phase has a nematic degree of freedom governed by an elastic free energy analogous to the Frank free energy for nematics. The difference comes from the smectic C phase being biaxial and having only one nematic degree of freedom. He formulated the appropriate nonlinear expression and deduced that Schlieren textures are possible and could be used to identify this phase experimentally. And that he did, too.

Secondly, he speculated on possible new smectic phases. Among them he proposed what is now called the smectic A₂ phase with antiferroelectric double layers. Somewhat later he developed a molecular-field theory of such a phase using the polar order parameter P₁ . After the experimental detection of such polar (and frustrated) smectic phases in 1979, this field of smectic polar polymorphism, and the phase transitions involved, increased immensely in the 1980s and 1990s.

He also predicted the chiral smectic C* phase (or an achiral smectic C phase with chiral dopants) to show a helical structure of the director similar to that in cholesterics, albeit tilted (conic helical). Of course, this phase is the prototype of ferroelectric liquid crystals, still today one of the major areas in liquid crystal research and applications (smectic devices). Unfortunately, Alfred Saupe did not realise at that time the ferroelectricity [11] (or, more precisely, helielectricity [12]) of that phase.

He was not only interested in static, structural questions. So the third topic of this paper dealt with the possibility of propagating bend/twist waves in nematics. He concluded that for the typical material parameters of nematic liquid crystals the (linear) director dynamics is always overdamped and relaxational. Again, this is common knowledge nowadays.

The fourth highlight concerns the structure of cholesteric blue phases. He gave the first reasonable model involving defect lines that could reconcile the microscopic (molecular) twist structure with the cubic crystalline structure on the mesoscopic length scale (optical wavelength). The field was further developed later and the models refined by others, and has seen a revival in recent years due to smectic blue phases, but Alfred Saupe was at the beginning of these developments.

Dealing with the nematic degree of freedom in smectic C liquid crystals, Alfred Saupe built a cell with different surface orientations demonstrating the existence of twist in that phase. At that time, J. Fergason co-invented (the other inventors are W. Helfrich and M. Schadt; for a more detailed discussion of the early development of twisted nematic displays, cf. [13], where Alfred Saupe's involvement is also mentioned), the nematic twist cell in Kent for use as a liquid crystal display. Thus, Alfred Saupe was involved in the early scientific considerations regarding this main application of liquid crystals, which still has a colossal commercial impact.

5. Lyotropics and biaxial nematics

In the mid-1970s Alfred Saupe's interest shifted to lyotropic liquid crystals. These mixtures of amphiphilic molecules (surfactants) and a suitable solvent are basically more complex than thermotropic low-molecular-weight liquid crystals, since the additional degree of freedom, the concentration of the amphiphiles (and that of the co-surfactant), governs the shape of the molecular aggregates. Rod-like and plate-like micelles, lamellar and bicontinuous double-layered structures are frequently found. They order macroscopically to (mostly) liquid crystalline phases. Therefore, they are like conventional liquid crystals with the additional possibility of changing the form and shape of the underlying structural entities making them very interesting at least at the basic scientific level.

NMR is a very versatile method for investigating lyotropic systems. Not only can the structure of the phase be obtained, but also the shape of the micelles. Alfred Saupe carried out many studies on nematic and cholesteric lyotropic phases. As a possibly unexpected result, it turned out that a nematic phase of calamitic micelles (N_L) has somewhat different physical properties than that made of discotic ones (N_C). In particular, the sign of the dielectric and diamagnetic susceptibility anisotropy differs in the two phases giving rise to a different orientation behaviour in external fields. He found a system, where both types of nematics occurred at different temperatures with a N_L-to-N_C transition in between. The chiralized system showed an appropriate cholesteric-to-cholesteric transition.

At least at that point, Alfred Saupe must have got the idea to look for a biaxial nematic phase. After a very delicate fine-tuning of temperature and concentrations of the surfactant and co-surfactant he finally succeeded (with L.J. Yu) in detecting the biaxial nematic phase [14] in a (small) temperature range between the two uniaxial phases. Using NMR structural studies, microscopic defects and texture observations and applying external fields, he was able to prove the biaxial nematic structure of that phase. Nevertheless, there were many doubts about this result to start with, because to that date all reports on detecting biaxial nematic phases in thermotropic systems had turned out to be premature. It took the scientific community a considerable amount of time before the experimental results could be corroborated in other laboratories. Lyotropic experiments are notoriously hampered by evaporation effects and a very precise fixing of concentrations is a non-trivial task.

Of course, he did not stop with the detection of the biaxial phase. He studied systematically the material properties of this and related lyotropic phases, such as the elastic constants, diffusion coefficients, resistivity, magnetic birefringence, diamagnetic susceptibilities, expansion coefficients, rotational viscosity, relaxation times, electric conductivity and more. While the publication of our manuscript on the hydrodynamics of the biaxial nematic phase [15] was severely hampered in the refereeing process, Alfred Saupe published almost simultaneously his well-known Leslie–Ericksen-type theory [16] on elasticity and flow (and its stability) of the biaxial nematic phase, which he needed for the interpretation of his measurements. The search for biaxial nematic phases outside the lyotropic branch has recently gained much momentum, which is demonstrated by the number of articles in this Volume devoted to that topic. Alfred Saupe will always be remembered as the first to demonstrate its existence experimentally.

6. The late period

In 1992 Alfred Saupe retired from the LCI and Kent State University and took over the duties as head of a Max Planck Research Group in Halle (amazingly, Alfred Saupe had many direct and indirect relations with Halle well before 1992 as is recounted in G. Pelzl's article in this issue). These and the final years were overshadowed by his progressing illness that severely reduced his scientific output. He was still a sought after discussion partner and informal advisor for many of his colleagues, scholars and friends. He managed to author seven additional publications (in addition to those 127 publications already listed in the Festschrift [1]) – shown here – involving 21 new co-authors (in addition to the 61 already listed in [1]), partly related to his duties in Halle (cf. Table 1).

Table 1. Additional co-authors after 1995

J. Bajc	X.-H. Chen	S. Diele	M. Giocondo
A. Hauser	G. Heppke	G. Hillig	D. Krüerke
I. Letho	Ch. Lischka	S. Markscheffel	S.-S. Pak
G.G. Peroli	G. Pelzl	M. Schadt	T. Scharf
G. Scherowski	M. Thieme	T. Tóth-Katona	E.G. Virga
W. Weissflog

• Surface-imaging of frozen blue phases in a discotic liquid crystal with atomic force microscopy [17],

• Uniform bookshelf alignment of chiral smectic C films with guided backflow [18],

• Orientational capillary pressure on a nematic point defect [19],

• Tilted smectic layers of a SmC* liquid crystal between homeotropically treated plates [20],

• Helical filamentary growth in liquid crystals consisting of banana-shaped molecules [21],

• Viscoelastic director rotation of a low molecular mass liquid crystal [22],

• Piezoelectricity of a ferroelectric liquid crystal with a glass transition [23].

As always during his whole scientific career, the diversity of topics and the variety of co-authors is remarkable. A new technique, atomic force microscopy (AFM), shows up and a new material, bent-core molecules, is used. As in his early days Alfred Saupe made use of new possibilities and opportunities at his new place in Halle. Again in the tradition of his kind of research, he came back to previous topics, such as defects, tilted smectics, nematic director dynamics and piezoelectricity.

Refusing for a long time to write a book he finally gave in, certainly to convey some of his knowledge to younger students entering the liquid crystal field, and he co-authored a book together with A. Jakli:

• One- and Two-dimensional Fluids: Properties of Smectic, Lamellar and Columnar Liquid Crystals [24].

7. Summary

It was not possible in this short article to discuss all areas of Alfred Saupe's research in detail. A few more will be mentioned here. His work on defects and textures, first in nematics and cholesterics and later in tilted smectics, aimed at understanding optical observations, comprises fan textures, focal conics, disclinations, spiral defects in free droplets, reflection bands of Grandjean textures and more. Instabilities, such as electro-hydrodynamic convection and undulational layer instability in smectic C liquid crystals, were investigated. Electric and/or optical problems played a role during the whole span of his scientific activities, from selective reflection and absorption in cholesteric fibres to electro-mechanical problems in smectic polymeric liquid crystals and solutions of polymers in low-molecular-weight liquid crystals. Again, the enormous breadth of his work is impressive.

Looking at the quantity of his output, one might be astonished by the rather modest number of 134 publications. However, this reflects his careful style of communicating results only when they are verified by different means and fully understood, and not publishing tiny bits of subcritical relevance. Even more significantly, he really did prefer talking to and discussing things with people, rather than writing papers. This is the place to apologize to all his many co-workers, whom I could not adequately mention and reference in this article, but who contributed directly and indirectly very much to his successful career.

Alfred Saupe is a striking example that there is scientific impact and influence beyond bibliometric numbers, the Hirsch index and the like. He was presented with several awards highlighting the respect he obtained from his peers, such as the Nernst Prize (of the German Bunsen Society), a senior Humboldt award (from the Alexander von Humboldt Foundation) that lead him to Mainz, an invitation as a fellow to the Wissenschaftskolleg Berlin, where he spent almost a year, the President's Medal of Kent State University, the Freedericksz Medal (of the Russian Liquid Crystal Society) and Honored Membership of the International Liquid Crystal Society. Recently, the Alfred Saupe Foundation has been established in his commemoration, which, starting in 2010, will award the annual Alfred Saupe Prize (through the German Liquid Crystal Society) with Helmut Ringsdorf as the first recipient.

Alfred Saupe will always be remembered for his outstanding achievement known as the Maier–Saupe theory and for his ground-breaking work and very early involvement in liquid crystal NMR, lyotropics and biaxial nematic liquid crystals, tilted smectic and ferroelectric liquid crystals, blue phases and smectic polar polymorphism and twist cell devices. Beyond being a great scientist he made a lasting impression on all who had the privilege of knowing him.