What is the maximum theoretical size possible for a lighter-than-air
balloon, using ideal materials, before it loses its integrity?

Here's an article from a month ago, about sheets being made from the
famous nanotubes:


http://www.eurekalert.org/pub_releas...-utd081505.php

http://en.wikipedia.org/wiki/Nanotube

quote from Wikipedia:

"Ray Baughman's group from the NanoTech Institute at University of
Texas at Dallas produced the current toughest material known in
mid-2003 by spinning fibers of single wall carbon nanotubes with
polyvinyl alcohol. Beating the previous contender, spider silk, by a
factor of four, the fibers require 600J/g to break. In comparison, the
bullet-resistant fiber Kevlar is 27-33J/g. In mid-2005 Baughman and
co-workers from Australia's Commonwealth Scientific and Industrial
Research Organization developed a method for producing transparent
carbon nanotube sheets 1/1000th the thickness of a human hair capable
of supporting 50,000 times their own mass.

In August 2005, Ray Baughman's team managed to develop a fast method to
manufacture up to seven meters per minute of nanotube tape. Once washed
with ethanol, the ribbon is only 50 nanometers thick; a square
kilometer of the material would only weigh 30 kilograms."


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So if the limiting factor is tensile strength, and nanotube fibres are
the record-holder at 600J/g tensile strength (20x stronger than
kevlar??) while also having a mass of 30 kg per sq km, then how big can
one make a balloon held together by the nanotubes? And what kind of
displacement lift force would it exert?