Download Cyclic Polymers PDF

TitleCyclic Polymers
Author
LanguageEnglish
File Size4.3 MB
Total Pages397
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

Similer Documents