Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chain Collapse and Counterion Condensation in Dilute Polyelectrolyte
  Solutions   A new quantitative theory for polyelectrolytes in salt free dilute solutions
is developed. Depending on the electrostatic interaction strength,
polyelectrolytes in solutions can undergo strong stretching (with
polyelectrolyte dimension R_g\sim l_B^{1/3}N, where l_B is the Bjerrum length
and N is the number of the chain segments) or strong compression (with R_g\sim
l_B^{-1/2}N^{1/3}). A strong polymer collapse occurs as a first-order phase
transition due to accompanying counterion condensation.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph