3 ms·

Onsager was a bastard with omitting details. He has a 1949 paper on packing of hard rods (and other anisometric particles), which is 4 pages long, but a colleag

Onsager was a bastard with omitting details. He has a 1949 paper on packing of hard rods (and other anisometric particles), which is 4 pages long, but a colleague who went through the details of the derivation spent half a year and filled a ring binder with intermediate calculations.

spekcular 5y ago
Damn. I never actually learned this stuff. Is there a good textbook account of this isotropic-to-nematic transition that includes full details? Or is there still a gaping hole in the published literature? In other words, did your colleague do this as a kind of history project, or because the details weren't available anywhere else?
- semi-extrinsic 5y ago
  I don't think there are textbooks on this stuff, it is too much of a niche, you probably need to read journal papers. A place to start might be the classic "What is liquid?" review paper by Barker and Henderson: https://link.aps.org/pdf/10.1103/RevModPhys.48.587?casa_token=-genrs8MUOYAAAAA:Fb81hNeEqpW7KS5WbVPd5NWQ5iPF_fXWyZwCcDpabL1kIcKR6HUwRiK9HeIvQaUeSBNAGt1vRn2gPE4 https://link.aps.org/pdf/10.1103/RevModPhys.48.587?casa_toke... ... and then the classic review paper on liquid crystals by Stephen and Straley: https://link.aps.org/pdf/10.1103/RevModPhys.46.617?casa_token=56_7AuMCfT0AAAAA:P_3CXKuVC_1MGFqsA-SX2dYcVqZiV1SxQ7FxFmukH73GHaLcjUMvpwffTwepIrkjzoGfmilcospc7Ic https://link.aps.org/pdf/10.1103/RevModPhys.46.617?casa_toke... But I believe the "gaping hole" as you call it has been mostly filled by the recent work. You probably still need to spend some weeks to follow along though. The motivation for my colleague was to develop the Onsager theory further, since Onsager only went to the second virial coefficient. They were able to go to higher-body contributions and get nice algebraic results for the equation of state, IIRC. I can probably dig up the DOI if you want to read it.
  - spekcular 5y ago
    Yes, I'd love to read it, if you have time to find the DOI. Thanks!
    - semi-extrinsic 5y ago
      Here you go: http://doi.org/10.1080/00268970801926958 http://doi.org/10.1080/00268970801926958
      - spekcular 5y ago
        Thanks!
sva_ 5y ago
I wonder if this is a consequence of people demanding more "rigor" nowadays?
- stjohnswarts 5y ago
  Well with electronic form it is now quite trivial to include the derivation, so no real reason not to publish it or at least a detail set of steps so demanding more rigor seems fair.

spekcular 5y ago

Damn. I never actually learned this stuff. Is there a good textbook account of this isotropic-to-nematic transition that includes full details? Or is there still a gaping hole in the published literature? In other words, did your colleague do this as a kind of history project, or because the details weren't available anywhere else?

semi-extrinsic 5y ago
I don't think there are textbooks on this stuff, it is too much of a niche, you probably need to read journal papers. A place to start might be the classic "What is liquid?" review paper by Barker and Henderson: https://link.aps.org/pdf/10.1103/RevModPhys.48.587?casa_token=-genrs8MUOYAAAAA:Fb81hNeEqpW7KS5WbVPd5NWQ5iPF_fXWyZwCcDpabL1kIcKR6HUwRiK9HeIvQaUeSBNAGt1vRn2gPE4 https://link.aps.org/pdf/10.1103/RevModPhys.48.587?casa_toke... ... and then the classic review paper on liquid crystals by Stephen and Straley: https://link.aps.org/pdf/10.1103/RevModPhys.46.617?casa_token=56_7AuMCfT0AAAAA:P_3CXKuVC_1MGFqsA-SX2dYcVqZiV1SxQ7FxFmukH73GHaLcjUMvpwffTwepIrkjzoGfmilcospc7Ic https://link.aps.org/pdf/10.1103/RevModPhys.46.617?casa_toke... But I believe the "gaping hole" as you call it has been mostly filled by the recent work. You probably still need to spend some weeks to follow along though. The motivation for my colleague was to develop the Onsager theory further, since Onsager only went to the second virial coefficient. They were able to go to higher-body contributions and get nice algebraic results for the equation of state, IIRC. I can probably dig up the DOI if you want to read it.
- spekcular 5y ago
  Yes, I'd love to read it, if you have time to find the DOI. Thanks!
  - semi-extrinsic 5y ago
    Here you go: http://doi.org/10.1080/00268970801926958 http://doi.org/10.1080/00268970801926958
    - spekcular 5y ago
      Thanks!

sva_ 5y ago

I wonder if this is a consequence of people demanding more "rigor" nowadays?

stjohnswarts 5y ago
Well with electronic form it is now quite trivial to include the derivation, so no real reason not to publish it or at least a detail set of steps so demanding more rigor seems fair.