## Molecular basis of polymer networks: proceedings of the 5th IFF-Ill Workshop, Jülich, Fed. Rep. of Germany, October 5-7, 1988The contributors to this volume appraise our knowledge of the molecular physics of polymer networks and pinpoint areas of research where significant advances can be made using new theories and techniques. They describe both theoretical approaches, based on new theoretical concepts and original network models, and recent experimental investigations using SANS, 2H NMR or QELS. These new techniques provide precise information about network behaviour at the molecular level. Reported results of the application of these and more traditional techniques include the microscopic conformation and properties of permanent networks or gels formed by specific interchain interactions, the behaviour of elastomer liquid crystals, and the static and dynamic properties of star-branched polymers. |

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Page 152

As a model system polybutadienes of narrow molecular weight

used as starting materials. These polymer chains are modified by introducing a

few 1,2,4-triazolidine-3,5-dione (urazole) groups U. These form defined dimeric

hydrogen bond complexes U + U -> U2. Introduction The study of polymers with

few strongly interacting groups along the polymer backbone has attracted

increasing attention during the past few years. Based on the work of Eisenberg

and others on ...

As a model system polybutadienes of narrow molecular weight

**distribution**areused as starting materials. These polymer chains are modified by introducing a

few 1,2,4-triazolidine-3,5-dione (urazole) groups U. These form defined dimeric

hydrogen bond complexes U + U -> U2. Introduction The study of polymers with

few strongly interacting groups along the polymer backbone has attracted

increasing attention during the past few years. Based on the work of Eisenberg

and others on ...

Page 178

Segment

Bjdrling and P. Linse Physical Chemistry 1 , University of Lund, Chemical Center,

Box 124, S-22100 Lund, Sweden 1. Introduction We summarize a coming

publication [1], which treats the equilibrium segment

attached poly(ethylene oxide) (PEO) chains. We give an alternate derivation to

that given by VAN LENT et al.[2], of the segment

in spherical and ...

Segment

**Distribution**for Terminally Attached Poly(ethylene oxide) Chains M.Bjdrling and P. Linse Physical Chemistry 1 , University of Lund, Chemical Center,

Box 124, S-22100 Lund, Sweden 1. Introduction We summarize a coming

publication [1], which treats the equilibrium segment

**distribution**for terminallyattached poly(ethylene oxide) (PEO) chains. We give an alternate derivation to

that given by VAN LENT et al.[2], of the segment

**distribution**for each rank, validin spherical and ...

Page 216

Introducing a Lagrange multiplier A for this constraint one finds that this problem

is equivalent to that of finding the unconstrained maximum of N £(r) = ln(Q(r))-A£*

7* (2.4) t=i Using Stirling's approximation (ln(x!) = x ln(x) — x) one thus obtains

from equating dC/dft equal to zero for all k 7l = i*hkgke-*k (2.5) for the equilibrium

size

following equation for A: N ]kutlikgte-kk = N (2.6) i=l Solving A from (2.6) at given

N, ...

Introducing a Lagrange multiplier A for this constraint one finds that this problem

is equivalent to that of finding the unconstrained maximum of N £(r) = ln(Q(r))-A£*

7* (2.4) t=i Using Stirling's approximation (ln(x!) = x ln(x) — x) one thus obtains

from equating dC/dft equal to zero for all k 7l = i*hkgke-*k (2.5) for the equilibrium

size

**distribution**. The requirement that V must satisfy the constraint (2.1) yields thefollowing equation for A: N ]kutlikgte-kk = N (2.6) i=l Solving A from (2.6) at given

N, ...

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### Contents

Remarks | 2 |

The BaumgartnerMuthukumar Effect in Networks | 11 |

Statistical Mechanics of dDimensional Polymer Networks and Exact | 17 |

Copyright | |

13 other sections not shown

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### Common terms and phrases

42 Molecular Basis anisotropy Basis of Polymer Bastide behaviour blends calculated carrageenan chain segments Chem chemical chemical potential configuration conformation constant constraints corresponding crosslinking curves deformation density dependence deswelling deuterated deviatoric distribution dynamics effect elastic free energy elementary strand elongation entanglements entropy equation equilibrium excluded volume experimental experiments exponent Flory Flory-Huggins Flory-Huggins theory fluctuations fractal dimension free chains free energy Gaussian gelation Gennes helix increases interaction parameter isotropic labelled paths layer length linear Macromolecules macroscopic measurements melt micronetworks modulus molecular weight monomers network chains neutron scattering observed obtained PDMS chains phantom network Phys polybutadiene polyelectrolyte Polymer Networks polymeric fractals polystyrene Proceedings in Physics properties radius of gyration ratio rod network Rouse model rubber elasticity S.F. Edwards sample scaling solution solvent Springer Proceedings star molecules star polymers swelling swollen temperature theory topological uniaxial values vector viscoelastic viscosity volume fraction