Excluded Volume Effects on Polymer Cyclization - ACS Symposium

Chapter 6

Excluded Volume Effects on Polymer Cyclization Mitchell A. Winnik

Downloaded by UNIV OF SYDNEY on March 31, 2018 | https://pubs.acs.org Publication Date: November 30, 1987 | doi: 10.1021/bk-1987-0358.ch006

Department of Chemistry and Erindale College, University of Toronto, Toronto M5S 1A1, Canada

Recent theory suggests that cyclization phenomena (1) are much more sensitive to excluded volume effects than other properties of polymer chains. Intramolecular fluorescence quenching processes i n molecules contain ing appropriate end groups permit one to study both the dynamics and thermodynamics of end-to-end cycliza tion. As a consequence, the sensitivity of polymer cyclization to excluded volume can be examined. Excluded volume effects (2) i n polymers are defined as those e f f e c t s which come about through the s t e r i c interaction of monomer units which are remotely positioned along the chain contour. Each individual interaction has only a small e f f e c t , but, because there can be many such interactions i n a long polymer, excluded volume e f f e c t s become very large. One consequence of excluded volume i s to expand the polymer c o i l dimensions over that predicted from simple random walk models. The "unperturbed" values of the root-mean-squared end-to-end distance Rp° and radius of gyration R^ 0

for ideal (random walk) chains expand (to R„ and R~) i n the presence J?

b

of excluded volume. In solution, excluded volume e f f e c t s on a polymer can be suppressed by decreasing the q u a l i t y of the solvent f o r the polymer. Shrinkage o f the mean dimensions occur. At various individual 2 combinations of solvent and temperature, R., , as measured from l i g h t b

2 or neutron scattering, exactly equals (RQ°) · In these "theta-solvents," other properties o f polymers are expected to follow ideal behaviour. Recent theory suggests that c y c l i z a t i o n e q u i l i b r i a are doubly s e n s i t i v e to excluded volume e f f e c t s (3). Not only does chain expansion increase the mean chain end separation, but a second factor due to p a i r correlations also acts to decrease the p r o b a b i l i t y o f the chain ends being i n proximity: The two chain 0097-6156/87/0358-0057$06.00/0 © 1987 American Chemical Society

Hoyle and Torkelson; Photophysics of Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1987.


58

PHOTOPHYSICS OF POLYMERS

ends cannot, obviously, occupy the same space. In addition, the adjacent segments on the two chain ends also i n t e r f e r e with each other. Their positions are correlated with those of the chain ends. These e f f e c t s sum up i n such a way as to make i t very d i f f i c u l t f o r the chain ends even to get near one another. In poor solvents, unfavorable solvent-polymer interactions lead to net a t t r a c t i o n between the chain ends and t h e i r adjacent segments. This tends to overcome excluded volume repulsion. At the theta-point, these two factors should be exactly i n balance. The chain should recover ideal behaviour. Ideal behaviour f o r chain conformation i s represented by a Gaussian d i s t r i b u t i o n W(r) of end-to-end distances. Excluded volume e f f e c t s give a much d i f f e r e n t end distance d i s t r i b u t i o n function, Figure 1, with the biggest differences operating on chains which happen to have t h e i r chain ends i n proximity (4). C y c l i z a t i o n p r o b a b i l i t y depends upon the r a d i a l d i s t r i b u t i o n function 2

W(0) = lim 47ir W(r) =

4ΤΓΓ [3/2nR ] 2

2

3/2

(1)

r-K>

-3/2 For ideal chains W(0) should decrease as chain length Ν . For very long chains experiencing f u l l excluded volume, the exponent i s predicted to take the value -1.92. Measurements of c y c l i z a t i o n e q u i l i b r i a should allow these predictions to be tested. The theory of c y c l i z a t i o n dynamics i s less advanced. The prediction of the c l a s s i c treatment of Wilemski and Fixman (5) suggests that the D -1.5 d i f f u s i o n - c o n t r o l l e d c y c l i z a t i o n rate constant k^ ~ Ν i n the absence of excluded volume. The following sections of t h i s chapter examine experimental r e s u l t s about excluded volume e f f e c t s on experimental values of the c y c l i z a t i o n equilibrium constant Κ and cy the rate constant f o r end-to-end c y c l i z a t i o n k^ (6). The Polymer.

The focus here i s on the c y c l i z a t i o n behaviour of —6 polystyrene i n d i l u t e solution (ca. 2 χ 10 M) as studied through measurements of intramolecular excimer formation i n 1, (7) and exciplex formation i n 2 (8). (CH ) C0 CH CH -(CHCH ) (CHgCH)^-CHgCHgOgC(CHg), fFS^ '"2'3"2"2"2 T 2'm 2? 'n v

ο

2

3

2

2

2

V

2

m

v

o



WINNIK

Excluded

Volume Effects on Cyclization

Figure 1. A plot o f the end-distance d i s t r i b u t i o n function W(0) vs. the r a t i o of the end separation divided by R for a Q

Gaussian chain and for self-avoiding walk [SAW, f u l l excluded volume], following Ref. 4.



60

CH CH- (- C H Ç H - ) - C H C H 0 C (C H ) 3

2

οι

X

Ζι

ο

2

2

2

2

3
—I

0

L_

50

ι

100

TEMPERATURE

ι

150 C ° C )

Figure 3. The c y c l i z a t i o n exponent from the expression —Ύ = aN as a function o f temperature f o r samples of 2 i n cyclopentane.

Figure 4.

Fluorescence spectra o f Py-PS-Py ( M = 4500) i n R

cyclopentane [1], acetone [2], and a 1:1 mixture [3] of these solvents.




Figure 6.

The c y c l i z a t i o n equilibrium constant K

solvent composition f o r Py-PS-Py cyclopentane-acetone mixtures.

(M = 4 5 0 0 )

c y

vs.

in


β. WINNIK

Excluded Volume Effects on Cyclization

67

Acknowledgment. We are grateful f o r the support of NSERC Canada and the donors of the Petroleum Research Fund, administered by the American Chemical Society. The real credit f o r the results described here belongs to Dr. A. S i n c l a i r and Dr. J.M.G. Martinho, who carried out the experiments described here. They are, of course, c i t e d i n the references.

REFERENCES


1. 2.

Cyclization Dynamics of Polymers 23. Flory, P.J. In Statistical Mechanics of Chain Molecules; Wiley-Interscience: New York, 1969. 3. deGennes, P.G. In Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, New York, 1979. 4. Oono, Y.; Freed, K. J . Phys. A Math. Gen. 1982, 15, 1931. 5. (a) Wilemski, G.; Fixman, M. J. Chem. Phys. 1964, 60, 866, 878. (b) Doi, M. Chem. Phys. 1975, 9, 455; Sunagawa, S.; Doi, M. Polym. J. 1975, 7, 604; 1976, 8, 239. 6. Cuniberti, C.; Perico, A. Prog. Polym. Sci., 1984, 10, 271. 7. (a) Winnik, M.A. Accounts Chem. Res. 1985, 18, 73. (b) Winnik, M.A. In Cyclic Polymers; Semlyen, A . J . , Ed.; Applied Science Publishers: London, U.K., 1986. 8. (a) Beinert, G.; Winnik, M.A. Can. J. Chem. 1986, 64, 1743. (b) Winnik, M.A.; Sinclair, A.M.; Beinert, G. Macromolecules 1985, 18, 1517. (c) Sinclair, A.M.; Winnik, M.A.; Beinert, G. J. Am. Chem. Soc. 1985, 107, 5798. 9. Winnik, M.A.; Redpath, A.E.C.; Paton, K.; Danhelka, J. Polymer 1984, 25, 91. 10. Sinclair, A.M. Ph.D. Thesis, University of Toronto, 1986. 11. Saeki, S.; Kuwahara, N; Konno, S.; Kaneko, M. Macromolecules 1973, 6, 246, 589. 12. (a) Palit, S.R.; Colombo, G.; Mark, H. J. Polym. Sci. 1951, 6, 295. (b) Ishikawa, K.; Kawai, T. J. Chem. Soc. Jpn. Ind. Chem. Sec. 1952, 55, 173. 13. Maillols, H.; Bardet, L; Grombo, S. Eur. Polym. J. 1978, 14, 1015. 14. Martinho, J.M.G.; Winnik, M.A. Macromolecules 1986, 19, 2281. RECEIVED May 22, 1987


Excluded Volume Effects on Polymer Cyclization - ACS Symposium

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