Elastomers and Rubber Elasticity - American Chemical Society


ELASTOMERS AND RUBBER ELASTICITY and their assumed relation to elongation. Similarly, elastic forces exerted by the chains in limiting the swelling of...
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13 Small Angle Neutron Scattering from Polymer Networks ROBERT U L L M A N

Downloaded by UNIV OF ARIZONA on October 2, 2015 | http://pubs.acs.org Publication Date: July 19, 1982 | doi: 10.1021/bk-1982-0193.ch013

Ford Motor Company, Engineering and Research Staff, Dearborn, MI

48121

The size and shape of polymer chains joined in a crosslinked matrix can be measured in a small angle neutron scattering (SANS) experiment. This is achieved by labelling a small fraction of the prepolymer with deuterium to contrast strongly with the ordinary hydrogenous substance. The deformation of the polymer chains upon swelling or stretching of the network can also be determined and the results compared with predictions from the theory of rubber elasticity. There are indications which fall short of definite proof, that a certain amount of chain rearrangement takes place, thus reducing the real chain expansion to values less than expected from elementary models. The theory of rubber e l a s t i c i t y has i t s origins i n the early work of Guth and Mark (1) who recognized that the reduction i n the number of statistical configurations of an uncoiled polymer molecule led to the e l a s t i c restoring force of rubber. This idea was pursued by many researchers. A major advance by James (2) and James and Guth (3) led to a model currently known as the phantom network. The ideas of James and Guth were strongly contested for many years, but recent analyses of Graessley (4,5) Ronca and Allegra (6), Flory (7) and Deam and Edwards (8), c l a r i f i e d the problem and established the l o g i c a l necessity of the James-Guth contribution. The phantom network model contains a c r u c i a l deficiency, well known to its originators, but necessary for simplifying the mathematical analysis. The model takes no direct account of the impenetrability of polymer chains, not i s the impossibility of two polymer segments occupying a common volume provided for i n this model. Different views have been presented to remedy these deficiencies, no consensus has been reached on models which are both physically r e a l i s t i c and mathematically tractable. When an e l a s t i c polymer network is stretched, the polymer chains are deformed. The v e r i f i c a t i o n of the theory has been largely based on measurements of the e l a s t i c restoring forces 0097-6156/82/0193-0257$06.25/0 © 1982

American Chemical Society

In Elastomers and Rubber Elasticity; Mark, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

Downloaded by UNIV OF ARIZONA on October 2, 2015 | http://pubs.acs.org Publication Date: July 19, 1982 | doi: 10.1021/bk-1982-0193.ch013

258

ELASTOMERS

AND

RUBBER

ELASTICITY

and their assumed r e l a t i o n to elongation. S i m i l a r l y , e l a s t i c forces exerted by the chains i n l i m i t i n g the swelling of the network i n a solvent has been widely used for assessing theoreti c a l results. In the phantom network model, the chain deformation i s i n simple one-to-one correspondence with the stresses induced by e l a s t i c deformation. If the phantom network model were known to be an accurate representation of the behavior of a real elastomer, an independent method of measuring chain deformation would only be of moderate interest. It has been clear that trapped entanglements contribute to the e l a s t i c modulus. Recently, Ferry and co-workers (9) i n a highly s i g n i f i c a n t set of investigations on networks crosslinked under s t r a i n have been able to show that the additional forces a r i s i n g from entanglements are quite large. I t i s not at a l l evident that the global expansion of polymer chains w i l l follow the e l a s t i c forces i n the simple relationship described i n a phantom network model i f contributions from entanglements are major. For this reason, the independent measurement of stresss t r a i n behavior together with determination of chain deformation is particularly significant. The molecular models of rubber e l a s t i c i t y relate chain s t a t i s t i c s and chain deformation to the deformation of the macroscopic material. The thermodynamic changes, including stress are derived from chain deformation. In this sense, the measurement of geometric changes i s fundamental to the theory, constitutes a direct check of the model, and i s an unambiguous measure of the mutual consistency of theory and experiment. Chain dimensions of polymer molecules i n bulk (10,11) or i n a concentrated medium (12) are measurable by small angle neutron scattering (SANS). The method i s based on the idea that molecular size and shape can be determined by labeling a small fraction of the chains by deuterium substitution. The scattering lengths of deuterium and ordinary hydrogen are very different, and a deuterated chain stands out i n strong contrast against a normal protonated matrix. I f the labeled chains are s u f f i c i e n t l y d i l u t e , the scattering method w i l l y i e l d molecular parameters. The SANS experiment i s applicable to polymeric networks containing some deuterium labeled chains. The chain geometry can be probed not only i n the unperturbed network, but changes i n chain shape and size can be measured as a function of s t r a i n or swelling. This enhances the a p p l i c a b i l i t y of SANS experiments for elastomeric systems. Neutron Scattering of Gaussian Chains The scattering of neutrons by any molecular system can be e l a s t i c or i n e l a s t i c , coherent or incoherent. The e l a s t i c coherent scattering of a labeled polymer i n a background matrix can be extracted from the data i n a properly designed experiment. The excess scattering from an ensemble of isolated chains (negligible intermolecular interactions i n the scattering In Elastomers and Rubber Elasticity; Mark, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1982.

13.

259

Small Angle Neutron Scattering

ULLMAN

function) may be written as 2

I(q) = A ( b b ) M c S(q) r

1

D

Downloaded by UNIV OF ARIZONA on October 2, 2015 | http://pubs.acs.org Publication Date: July 19, 1982 | doi: 10.1021/bk-1982-0193.ch013

2

I(q) i s the intensity at wave vector q, (b^b^) i s a con­ trast factor a r i s i n g from the difference i n scattering lengths of deuterated and protonated species, M i s molecular weight of the deuterated polymer, c i s concentration i n gm/ml, S(q) i s a p a r t i c l e scattering factor, and A contains machine constants, detector efficiency, and other fixed quantities. For the pur­ pose of the current study, S(q) i s the quantity of significance, and i t i s given by S(q)=i^