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Liquid crystals sit between a solid and a liquid: they flow, yet their molecules keep some order. For almost a century after their discovery, every known example was made of rod-shaped molecules. In 1977 a team at the Raman Research Institute in Bangalore showed that flat, disc-shaped molecules can do it too. The leader was Sivaramakrishna Chandrasekhar. This post covers his path, the discovery, a worked example using Bragg's law, and what students can learn from how he worked.
Who was S. Chandrasekhar?
He is not the astrophysicist Subrahmanyan Chandrasekhar of the Chandrasekhar limit. The Royal Society's biographical memoir of Sivaramakrishna Chandrasekhar gives his dates as 6 August 1930 to 8 March 2004, records that he died at his home in Bangalore aged 73, and says he had devoted himself to liquid crystals since the 1960s. A memoir in that series means he was a Fellow of the Royal Society.
John Goodby's obituary in Nature fills in the career. After postgraduate studies at the University of Cambridge, Chandrasekhar joined the University of Mysore with the task of creating a school of physics. There he decided to change his research from the solid state to liquid crystals, a field few scientists then knew. Goodby quotes him admitting that his knowledge of these phases was "limited to the brief accounts I had come across as a student more than ten years earlier in books published in the 1930s". After further time at Cambridge and University College London, he and a few of his students moved in 1971 to the Raman Research Institute, where he set up a liquid crystals laboratory.
What did the 1977 paper show?
The paper is Liquid crystals of disc-like molecules, by S. Chandrasekhar, B. K. Sadashiva and K. A. Suresh, received by the journal Pramana on 19 September 1977. Its abstract reports that pure compounds made of simple disc-like molecules, benzene-hexa-n-alkanoates, show thermotropic mesomorphism, meaning they form a liquid crystal phase over a range of temperature.
Thermodynamic, optical and X-ray studies led the team to propose a structure. The discs stack one on top of another in columns, and the columns pack in a hexagonal arrangement, but the spacing between discs inside each column is irregular. In the abstract's words, the structure has "translational periodicity in two dimensions and liquid-like disorder in the third".
Goodby's obituary describes the result as an entirely new class of liquid crystal, different from the classical ones made of rod-like molecules that had been known since Friedrich Reinitzer observed them in 1888.
How did the idea grow?
In a 1983 paper in the Philosophical Transactions of the Royal Society, Chandrasekhar described two structural types of liquid crystal formed by disc-like molecules: the columnar type and a nematic type, in which the discs point roughly the same way but have no long-range positional order. He also extended a standard mean-field theory to discs and studied fluctuations in the columnar phase.
He wrote the textbook Liquid Crystals, published by Cambridge University Press, and from 1991 he was director of the Centre for Liquid Crystal Research in Bangalore, according to Who Was Who.
Worked example: measuring the column spacing with X-rays
The team's structure came partly from X-ray diffraction. Bragg's law links the spacing d between rows of scatterers to the angle θ at which X-rays reflect strongly: nλ = 2d sin θ. The numbers below are sample values for a classroom example, not data from the 1977 paper.
Suppose copper X-rays (λ = 0.154 nm) give a strong first-order (n = 1) reflection at a scattering angle 2θ = 4.0°.
θ = 2.0°, so sin θ = 0.0349.
d = λ / (2 sin θ) = 0.154 / 0.0698 ≈ 2.21 nm.
In a hexagonal pattern of columns a distance a apart, the most widely spaced rows of columns are separated by d = (√3/2) a. So a = 2d/√3 = 4.41 / 1.732 ≈ 2.55 nm.
A column spacing of a few nanometres fits discs with long hydrocarbon chains sticking out from a central benzene ring. Small angles mean large spacings, which is why the column pattern shows up at low angle.
Common mistakes: using 2θ instead of θ in the formula, and treating d as the distance between columns. In a hexagonal pattern they differ by the factor √3/2. Our post on Lawrence Bragg and the X-ray law explains where 2d sin θ comes from.
What can a student take from how Chandrasekhar worked?
Change fields if the question is good enough. He moved into a subject he knew only from old textbooks.
Combine methods. The 1977 structure rested on heat measurements, optics and X-rays together, not on one test.
Build a group. The discovery was made with his students, in a laboratory he set up.
When a term like "mesophase" or "nematic" stops you, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can fill the gap before reading further.
Next step: rework the example for 2θ = 3.0° and check that the column spacing comes out larger.
