Mp. Taylor et Jeg. Lipson, COLLAPSE OF A POLYMER-CHAIN - A BORN-GREEN-YVON INTEGRAL-EQUATION STUDY, The Journal of chemical physics, 104(12), 1996, pp. 4835-4841
A Born-Green-Yvon (BGY) type integral equation is developed for the in
tramolecular distribution functions of an isolated flexible polymer ch
ain. The polymer is modeled as a linear array of n identical spherical
interaction sites connected by universal joints of bond length sigma.
In particular we study chains composed of up to n = 400 square-well s
pheres with hard-core diameters sigma and well diameters lambda sigma
(1 less than or equal to lambda less than or equal to 2). Intramolecul
ar distribution functions and the resulting average configurational an
d energetic properties are computed over a wide range of temperatures.
In the high temperature (good solvent) limit this model is identical
to the tangent hard-sphere chain. With decreasing temperature (worseni
ng solvent) the square-well chain undergoes a collapse transition iden
tified by a sudden reduction in chain dimensions and a peak in the sin
gle chain specific heat. Extensive comparison is made between the BGY
results and Monte Carlo results for square-well chains with lambda=1.5
. The BGY theory is extremely accurate for square-well 4-mers at all t
emperatures. For longer chains the theory yields reasonably accurate r
esults for reduced temperatures greater than Tapproximate to 1 (expan
ded and theta states) and qualitatively correct behavior for T<1 (col
lapsed state). Very accurate values for the theta temperatures for squ
are-well chains with 1.25 less than or equal to lambda less than or eq
ual to 2.0 are also obtained. (C) 1996 American Institute of Physics.