Intramolecular Interactions in a Flexible Polymer Molecule

Miyakawa, Harumitsu; Saitô, Nobuhiko

doi:10.1295/polymj.10.27

Cited by 6 publications

(4 citation statements)

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“…we find after integrating that P k becomes pk = k (~/ R )~g ( k / r , R / (R2)01/2) (9) where g is a dimensionless function of k/r and R (R2);l2. and replace g(k/r,l) by its mean value g:…”

Section: Theorymentioning

confidence: 93%

Phase Transition Behavior of the Isolated Polymer Chain

1979

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I , , " I 271 (1976).R. Guillard and A. Englert, Biopolymers, 15, 1301 (1976). V. V. Zelinski, V. P. Kolobkov, and L. G. Pikulik, Opt. Spektrosk., 1, 560 (1956). (38) As to the active sphere radius r, ' for intermolecular electron transfer, there are some arguments. If one assumes a uniform distribution of energy acceptors around an energy donor, the condition that the total transfer efficiency calculated by the active sphere model is the same as that for the exact case, yields, ro6 Jrd4*r2 dr = 4*r2 drwhere r, denotes the Forster distance. Integration gives r, ' = 1.16rp The above equation means the radius of the active sphere should be a little larger than the Forster distance. Jabionski (A. Jabronski, Bull. Acad. Pol. Sci., Ser. Sci. Math., Astron. Phys., 6,663 (1958)) reported a similar calculation and suggested r, ' = 1.33r0. On the other hand, in the intramolecular case, the distribution of acceptors cannot be uniform and,. strictly speaking, there can be no simple way to define r,'. In fact, a comparison of static transfer efficiency for the active sphere model (broken line in Figure 3) with that for the exact case (solid line, ro = 24 A) indicates that r, ' should be smaller than ro for n < 12 but larger than ro for n < 12. However, since the difference between the two lines is not significant, it is sufficient to use the Forster distance as an active sphere radius in our approximate analysis. A small change in the active sphere radius did not change any conclusions in the text. The authors wish to thank the referee for informine us of this Doint.ABSTRACT: A mean field theory of chain dimensions is formulated which is very similar to the van der Waals theory of a simple fluid. In the limit of infinite chain length, the chain undergoes a Landau-type second-order phase transition. For finite chains, the transition is pseudo-second-order. At low temperatures, the chain is in a condensed or globular state, and the mean square gyration radius (S2) varies as r2/3 where r is proportional to chain length. At high temperatures, the chain is in a gaslike or coil state where (p) varies as r6/5. In the globular state, fluctuations in (S2) are very small, whereas they are very large in the coiled state. A characteristic feature of the theory is that ternary and higher order intramolecular interactions are approximated. At high temperatures, only binary interactions are important, but a t low temperatures, many of the higher order terms contribute. An important conclusion of this study is that a polymer chain does not obey ideal chain statistics a t the 8 temperature. Although the second virial coefficient vanishes at 8, the third virial coefficient does not; its presence is responsible for the perturbation of the chain statistics.For an infinite chain, 8 and the second-order phase-transition temperature are identical. For finite chains, the pseudo-second-order transition temperature is less than 8. When generalized to d dimensions, the theory yields at low temperatures ( S 2 ) d / 2r for all d and at high temperatur...

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“…we find after integrating that P k becomes pk = k (~/ R )~g ( k / r , R / (R2)01/2) (9) where g is a dimensionless function of k/r and R (R2);l2. and replace g(k/r,l) by its mean value g:…”

Section: Theorymentioning

confidence: 93%

Phase Transition Behavior of the Isolated Polymer Chain

1979

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“…This prior work is summarized in Professor Saitô’s exceptional textbook on polymer physics [15], which provides some information concerning his research into protein conformations. In the 1970s, his research interests expanded to include the statistics of random coil chains, the stability of α -helical polymer structures, and the widths of polymer chains [16–22]. These studies were followed by investigations of intramolecular α -helix- β -structure-random coil transitions in polypeptides [23,24].…”

Section: Genesis Of the Island Model: From Polymers To Proteinsmentioning

confidence: 99%

Statistical mechanics of protein structural transitions: Insights from the island model

Kobayashi

2016

BIOPHYSICS

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The so-called island model of protein structural transition holds that hydrophobic interactions are the key to both the folding and function of proteins. Herein, the genesis and statistical mechanical basis of the island model of transitions are reviewed, by presenting the results of simulations of such transitions. Elucidating the physicochemical mechanism of protein structural formation is the foundation for understanding the hierarchical structure of life at the microscopic level. Based on the results obtained to date using the island model, remaining problems and future work in the field of protein structures are discussed, referencing Professor Saitô’s views on the hierarchic structure of science.

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“…It may be unnecessary to say that studies of the surface morphology of block polymers are of academic and practical importance in connection with biomedical science and applications such as in throm-boresistance15 and cell separation. 16 A polystyrene-polyisoprene diblock polymer designated was synthesized by living anionic polymerization at -78 °C using sec-butyllithium as the initiator and tetrahydrofuran as the solvent. The number-average molecular weight of the block polymer determined by osmometry was 5.24 X 10s and the weight fraction of the polystyrene component determined by elemental analysis was 52%.…”

mentioning

confidence: 99%