##### Document Text Contents

Page 1

CYCLIC POLYMERS

Page 2

CYCLIC POLYMERS

Edited by

J. A. SEMLYEN

Department of Chemistry, University of York, UK

ELSEVIER APPLIED SCIENCE PUBLISHERS

LONDON and NEW YORK

Page 198

NEUTRON SCATTERING FROM CYCLIC POLYMERS 193

D = Dmeasured(~slT) (298 K/~toluene)) to account for measurements made in

different solvents and at different temperatures. This allows direct

comparison between the sets of data. The absolute precision of the neutron

scattering data is no better than 3 neV, which typically corresponds to an

error of ± 10 % on a value of D(c) of the order of 3 x 10- 6 cm2 s -1, whilst

data obtained using light scattering give values of D with an experimental

error of the order of ± 5 %, and the precision of the data obtained by

boundary spreading is estimated to be about ± O' 5 %. 14 The ratio

Dlinear/Dcyclic is found to be 0·84 ± 0'016, which compares favourably with

the predicted value of8/3n = 0·85 for cyclic and linear polymers of the same

molecular weight and in the absence of free draining and excluded volume

effects. 19 •23 Knowing the diffusion coefficients for all of the samples, it is

possible to calculate the hydrodynamic radius and compare this with data

from other sources.

(a) The hydrodynamic radius, RH , may be calculated directly from D via

the Stokes-Einstein equation 14.19

kBT

D = (31)

6n~sRH

where all symbols carry their usual meanings.

(b) For both cyclic and linear polymers, R*, which defines overall

molecular dimensions, and is thus comparable with <S2)1/2, is defined by

Q*, the crossover from Q2 tOQ3 behaviour. For 8-solvent conditions,

Akcasu's curve shows this crossover to be defined by Q* R*:~ 1. Thus a

crude experimental value of R* may be obtained directly from the data

plotted in Fig. 9 by taking R* = I/Q*. These values are quoted in Table 3

and are of the same order of magnitude as the molecular dimensions

meoasured using the methods described in the section 'Small Angle Neutron

Scattering' .

Table 3 includes the values of <S2);/2 obtained by small angle scattering,

so that the ratio <S2);/2/RH may be compared with theoretical predictions.

For the linear samples, it may be shown that in the Gaussian limit23 the

radius of gyration is expected to be related to the hydrodynamic radius via

<S2)1/2 = 3n81/2 RH = 1·505RH (32)

However, recent experimental determinations of the relationship60

<S2);/2/RH suggest a somewhat lower value than this of 1·27 ± 0·06. The

experimental values presented here have an average of 1·21. For the cyclic

samples the theoretical ratio of <S2);/2/RH' again in the Gaussian limit, is

Page 199

194 KEITH DODGSON AND JULIA S. HIGGINS

TABLE 3

Dimensions of Cyclic and Linear Poly(dimethylsiloxanes)

(All dimensions are in A)

Un nn Rg R* Rg RiRH RH

(SANS) ( =1IQ*) (QENS) (boundary

spreading

or QELS)

(a) Linear samples (T = 293 K)

1100 24 7 6 6-4 1·1 6·7

2100 54 10·2 7·6 1·34

2700 74 12-4 12 12·1 1·02

6400 172 21·2 18 19·6 1·1

15100 408 40·0 26·4 1·5 26·4

(b) Cyclic samples (T = 293 K)

800 20 5 5·1

2000 54 7·8 6·8 1·15

2700 73 9·5 II 10·7 0·89 9·9

6300 170 14·3 16 14·7 0·97

15400 415 29 22 18·9 1·5

Rg = <S2)1/2.

predicted to be (2In) -1/2 = 1.2533. 14•35 The values presented in section (b)

of Table 3 suggest again that the experimentally determined value appears

to be somewhat lower than that predicted, with an average of 1·15.

REFERENCES

1. Willis, B. T. M. (Ed.), Chemical Applications of Thermal Neutron Scattering,

Oxford University Press, Oxford, 1973.

2. Kostorz, G. (Ed.), Treatise on Materials Science and Technology, Vol. 15,

Neutron Scattering, Academic Press, London, 1979.

3. Maconnachie, A. and Richards, R. W., Polymer, 19 (1978) 739.

4. Higgins, J. S., In: Developments in Polymer Characterisation-4 (ed. J. V.

Dawkins), Elsevier Applied Science Publishers Ltd, London, 1983, pp. 131-76.

5. Van Hove, L., Phys. Rev., 95 (1954) 249.

6. Casassa, E. F., J. Polym. Sci., A, 3 (1965) 605.

7. Ibel, K. J., J. Appl. Cryst., 9 (1976) 296.

8. Neutron Beam Facilities Available to Users, Scientific Secretariat, Institut

Laue-Langevin, 156X Centre de Tri, 38042, Grenoble Cedex, France.

9. Jacrot, B., Rep. Prog. Physics, 39 (1976) 911.

10. Higgins, J. S., Dodgson, K. and Semlyen, J. A., Polymer, 20 (1979) 553.

Page 396

INDEX 393

Sol-gel transition, 368-70

Solvent effects

cyclization kinetics, 295

cyclization studies, 330-3

dimethylsiloxane ring-chain

equilibrium, 98-100

Sommer-Ansul synthesis method,

126, 127

Space-time correlation functions,

74-7

neutron scattering, 170

Spectroscopic methods, 285-345

advantages of, 285-6

sample size required, 293

Spring-and-bead models, 187, 188,

299,300

Star-shaped molecules, 56, 58

Staudinger macromolecular

hypothesis, I

Step reactions, examples quoted, 199

Stereoisomers, phenylmethylsiloxane

oligomers, 102-3

Stokes-Einstein diffusion radius, 159

Stokes-Einstein equation, 193

Styragel (G PC) column packing, II,

119

Styrene--ethyldimethacrylate system,

gel point studies, 352-3

Styrene polymers

block polymers with

dimethylsiloxane, 129-30,

214-16

concentrated solution studies,

341-4

cyclization studies, 321-33

dilute solution properties, 216-18

polymers, 214-18, 219

small angle neutron scattering data,

181,218,219

Substituents, effect on siloxane cyclics

formation, 93-7

Sulphamide bond formation, 288, 311

Sulphides, cyclic oligomers, 208-9,

212

Sulphonamides, fluorescence, 311

Sulphur

cyclic octamer, 33

Sulphur-contd.

cyclic polymer concentration, 12-13

liquid

freezing point data, 33

molecular constitution of, 33-4

ring-chain polymer equilibrium

calculations, 35-7

rotational isomeric state model

for, 34-5

Supercoiled DNA rings, 235-6

effects on interaction with other

molecules, 246-7

effects on shape, 247-8

effects on structure, 241-7

energetics, 237-41

Synthesis. See Preparation methods

Temperature effects, cyclization

studies, 316

Tetrahedrane system, 197

Tetrahydrofuran, cyclic oligomers,

209-10

2,2,7,7-Tetramethyl-I-oxa-2, 7-

disilacycloheptane, ring-chain

polymer equilibrates, 126-9

Thermodynamic considerations,

ring-chain equilibrium, 97-100

Theta( O)-so Ivents

siloxane polymers, 98, 115, 150,

154

styrene polymers, 325-9, 343, 344

Theta( O)-tem pera tures

cyclohexane, 325, 341

dimethylsiloxane ring-chain

equilibrium, 98

Thorpe-Ziegler reaction, 7

Toluene, as solvent for

dimethylsiloxane polymers, 16,97,

98,99, III, 117, 118, 150, 151,

159-61

styrene polymers, 343, 344

Toluene-dB' 218, 219

Topoisomers, DNA closed-duplex

rings, 234-5

Toroidal supercoil structure, DNA

rings, 241, 242, 243, 248

Page 397

394 INDEX

Translational diffusion coefficients

concentration dependence, 154-7

dimethylsiloxane polymers, 152--4

exact solution, 66

Kirkwood's approximation, 46, 65

Tree structure, polymers near gel

point, 351, 360, 368, 370, 377

Trifiuoromethanesulphonic acid, 87,

88,89,90

Trifiuoropropylmethylsiloxane,

cyclics, 92, 93, 94, 95

Trimethylene succinate, ring--chain

polymer equilibrates, 19, 20

1,3,6-Trioxocane, cyclic oligomers,

210, 211

Triplet quenching, 289, 311

Triplet-triplet (TT) annihilation, 289,

323-5,327

Twist number, DNA rings, 236-7

Twisted rings

configurational distributions for,

49-51

shrinking factors affected by

number of twisting points,

55-6

Universal calibration (GPC) curves,

polystyrenes, 216, 217

Urethanes

cyclic oligomers, 213-14

gelation formation, 365-6

networks, 375-6

Valinomycin, 198

Vinyl acetate polymers

concentrated solution studies,

340-1

spectroscopic studies, 333--4

Vinyl monomers, crosslinking in

loops, 44, 45

Viscoelastic properties, 79

Viscosities: see Bulk viscosity;

Intrinsic viscosity

Wang-Uhlenbeck procedure, 48-9,

60,80

Watson-Crick structure for DNA,

234

Weight average molecular weights,

siloxanes, 116

Weight concentration calculations,

siloxane ring--chain equilibrate,

116-17

Weight fraction, siloxane rings, 91, 92

Weight-average functionalities, 352

Wilemski-Fixman (WF) model, 297,

299, 302

experimental results, 325

Writhing number, DNA rings, 236-7

X-ray diffraction analysis, cyclic

peptides, 274, 275

Xylene, as solvent in dimethylsiloxane

ring--chain equilibrium, 97, 100

Zimm hydrodynamic correction, 187

Zimm hydrodynamics, 81

Zimm (non-draining) model, 300

Zimm plot slope, 172

CYCLIC POLYMERS

Page 2

CYCLIC POLYMERS

Edited by

J. A. SEMLYEN

Department of Chemistry, University of York, UK

ELSEVIER APPLIED SCIENCE PUBLISHERS

LONDON and NEW YORK

Page 198

NEUTRON SCATTERING FROM CYCLIC POLYMERS 193

D = Dmeasured(~slT) (298 K/~toluene)) to account for measurements made in

different solvents and at different temperatures. This allows direct

comparison between the sets of data. The absolute precision of the neutron

scattering data is no better than 3 neV, which typically corresponds to an

error of ± 10 % on a value of D(c) of the order of 3 x 10- 6 cm2 s -1, whilst

data obtained using light scattering give values of D with an experimental

error of the order of ± 5 %, and the precision of the data obtained by

boundary spreading is estimated to be about ± O' 5 %. 14 The ratio

Dlinear/Dcyclic is found to be 0·84 ± 0'016, which compares favourably with

the predicted value of8/3n = 0·85 for cyclic and linear polymers of the same

molecular weight and in the absence of free draining and excluded volume

effects. 19 •23 Knowing the diffusion coefficients for all of the samples, it is

possible to calculate the hydrodynamic radius and compare this with data

from other sources.

(a) The hydrodynamic radius, RH , may be calculated directly from D via

the Stokes-Einstein equation 14.19

kBT

D = (31)

6n~sRH

where all symbols carry their usual meanings.

(b) For both cyclic and linear polymers, R*, which defines overall

molecular dimensions, and is thus comparable with <S2)1/2, is defined by

Q*, the crossover from Q2 tOQ3 behaviour. For 8-solvent conditions,

Akcasu's curve shows this crossover to be defined by Q* R*:~ 1. Thus a

crude experimental value of R* may be obtained directly from the data

plotted in Fig. 9 by taking R* = I/Q*. These values are quoted in Table 3

and are of the same order of magnitude as the molecular dimensions

meoasured using the methods described in the section 'Small Angle Neutron

Scattering' .

Table 3 includes the values of <S2);/2 obtained by small angle scattering,

so that the ratio <S2);/2/RH may be compared with theoretical predictions.

For the linear samples, it may be shown that in the Gaussian limit23 the

radius of gyration is expected to be related to the hydrodynamic radius via

<S2)1/2 = 3n81/2 RH = 1·505RH (32)

However, recent experimental determinations of the relationship60

<S2);/2/RH suggest a somewhat lower value than this of 1·27 ± 0·06. The

experimental values presented here have an average of 1·21. For the cyclic

samples the theoretical ratio of <S2);/2/RH' again in the Gaussian limit, is

Page 199

194 KEITH DODGSON AND JULIA S. HIGGINS

TABLE 3

Dimensions of Cyclic and Linear Poly(dimethylsiloxanes)

(All dimensions are in A)

Un nn Rg R* Rg RiRH RH

(SANS) ( =1IQ*) (QENS) (boundary

spreading

or QELS)

(a) Linear samples (T = 293 K)

1100 24 7 6 6-4 1·1 6·7

2100 54 10·2 7·6 1·34

2700 74 12-4 12 12·1 1·02

6400 172 21·2 18 19·6 1·1

15100 408 40·0 26·4 1·5 26·4

(b) Cyclic samples (T = 293 K)

800 20 5 5·1

2000 54 7·8 6·8 1·15

2700 73 9·5 II 10·7 0·89 9·9

6300 170 14·3 16 14·7 0·97

15400 415 29 22 18·9 1·5

Rg = <S2)1/2.

predicted to be (2In) -1/2 = 1.2533. 14•35 The values presented in section (b)

of Table 3 suggest again that the experimentally determined value appears

to be somewhat lower than that predicted, with an average of 1·15.

REFERENCES

1. Willis, B. T. M. (Ed.), Chemical Applications of Thermal Neutron Scattering,

Oxford University Press, Oxford, 1973.

2. Kostorz, G. (Ed.), Treatise on Materials Science and Technology, Vol. 15,

Neutron Scattering, Academic Press, London, 1979.

3. Maconnachie, A. and Richards, R. W., Polymer, 19 (1978) 739.

4. Higgins, J. S., In: Developments in Polymer Characterisation-4 (ed. J. V.

Dawkins), Elsevier Applied Science Publishers Ltd, London, 1983, pp. 131-76.

5. Van Hove, L., Phys. Rev., 95 (1954) 249.

6. Casassa, E. F., J. Polym. Sci., A, 3 (1965) 605.

7. Ibel, K. J., J. Appl. Cryst., 9 (1976) 296.

8. Neutron Beam Facilities Available to Users, Scientific Secretariat, Institut

Laue-Langevin, 156X Centre de Tri, 38042, Grenoble Cedex, France.

9. Jacrot, B., Rep. Prog. Physics, 39 (1976) 911.

10. Higgins, J. S., Dodgson, K. and Semlyen, J. A., Polymer, 20 (1979) 553.

Page 396

INDEX 393

Sol-gel transition, 368-70

Solvent effects

cyclization kinetics, 295

cyclization studies, 330-3

dimethylsiloxane ring-chain

equilibrium, 98-100

Sommer-Ansul synthesis method,

126, 127

Space-time correlation functions,

74-7

neutron scattering, 170

Spectroscopic methods, 285-345

advantages of, 285-6

sample size required, 293

Spring-and-bead models, 187, 188,

299,300

Star-shaped molecules, 56, 58

Staudinger macromolecular

hypothesis, I

Step reactions, examples quoted, 199

Stereoisomers, phenylmethylsiloxane

oligomers, 102-3

Stokes-Einstein diffusion radius, 159

Stokes-Einstein equation, 193

Styragel (G PC) column packing, II,

119

Styrene--ethyldimethacrylate system,

gel point studies, 352-3

Styrene polymers

block polymers with

dimethylsiloxane, 129-30,

214-16

concentrated solution studies,

341-4

cyclization studies, 321-33

dilute solution properties, 216-18

polymers, 214-18, 219

small angle neutron scattering data,

181,218,219

Substituents, effect on siloxane cyclics

formation, 93-7

Sulphamide bond formation, 288, 311

Sulphides, cyclic oligomers, 208-9,

212

Sulphonamides, fluorescence, 311

Sulphur

cyclic octamer, 33

Sulphur-contd.

cyclic polymer concentration, 12-13

liquid

freezing point data, 33

molecular constitution of, 33-4

ring-chain polymer equilibrium

calculations, 35-7

rotational isomeric state model

for, 34-5

Supercoiled DNA rings, 235-6

effects on interaction with other

molecules, 246-7

effects on shape, 247-8

effects on structure, 241-7

energetics, 237-41

Synthesis. See Preparation methods

Temperature effects, cyclization

studies, 316

Tetrahedrane system, 197

Tetrahydrofuran, cyclic oligomers,

209-10

2,2,7,7-Tetramethyl-I-oxa-2, 7-

disilacycloheptane, ring-chain

polymer equilibrates, 126-9

Thermodynamic considerations,

ring-chain equilibrium, 97-100

Theta( O)-so Ivents

siloxane polymers, 98, 115, 150,

154

styrene polymers, 325-9, 343, 344

Theta( O)-tem pera tures

cyclohexane, 325, 341

dimethylsiloxane ring-chain

equilibrium, 98

Thorpe-Ziegler reaction, 7

Toluene, as solvent for

dimethylsiloxane polymers, 16,97,

98,99, III, 117, 118, 150, 151,

159-61

styrene polymers, 343, 344

Toluene-dB' 218, 219

Topoisomers, DNA closed-duplex

rings, 234-5

Toroidal supercoil structure, DNA

rings, 241, 242, 243, 248

Page 397

394 INDEX

Translational diffusion coefficients

concentration dependence, 154-7

dimethylsiloxane polymers, 152--4

exact solution, 66

Kirkwood's approximation, 46, 65

Tree structure, polymers near gel

point, 351, 360, 368, 370, 377

Trifiuoromethanesulphonic acid, 87,

88,89,90

Trifiuoropropylmethylsiloxane,

cyclics, 92, 93, 94, 95

Trimethylene succinate, ring--chain

polymer equilibrates, 19, 20

1,3,6-Trioxocane, cyclic oligomers,

210, 211

Triplet quenching, 289, 311

Triplet-triplet (TT) annihilation, 289,

323-5,327

Twist number, DNA rings, 236-7

Twisted rings

configurational distributions for,

49-51

shrinking factors affected by

number of twisting points,

55-6

Universal calibration (GPC) curves,

polystyrenes, 216, 217

Urethanes

cyclic oligomers, 213-14

gelation formation, 365-6

networks, 375-6

Valinomycin, 198

Vinyl acetate polymers

concentrated solution studies,

340-1

spectroscopic studies, 333--4

Vinyl monomers, crosslinking in

loops, 44, 45

Viscoelastic properties, 79

Viscosities: see Bulk viscosity;

Intrinsic viscosity

Wang-Uhlenbeck procedure, 48-9,

60,80

Watson-Crick structure for DNA,

234

Weight average molecular weights,

siloxanes, 116

Weight concentration calculations,

siloxane ring--chain equilibrate,

116-17

Weight fraction, siloxane rings, 91, 92

Weight-average functionalities, 352

Wilemski-Fixman (WF) model, 297,

299, 302

experimental results, 325

Writhing number, DNA rings, 236-7

X-ray diffraction analysis, cyclic

peptides, 274, 275

Xylene, as solvent in dimethylsiloxane

ring--chain equilibrium, 97, 100

Zimm hydrodynamic correction, 187

Zimm hydrodynamics, 81

Zimm (non-draining) model, 300

Zimm plot slope, 172