Development of minimal models of the elastic properties of flexible and stiff polymer networks with permanent and thermoreversible cross-links.

We review the elasticity of flexible and stiff polymer networks with permanent cross-links and synthesize these results into a unifying polymer chain network model. This framework is then used to address how the network elasticity becomes modified when the network cross-linking is thermoreversible in nature, changes in the stability of the network with deformation, and the effect of a variable rate of network deformation on the non-linear elastic response. Comparisons are made between this class of simplified network models with elasticity measurements performed on flexible chain and stiff fiber networks, both with permanent and associative cross-links. Although these network models are highly idealized, they are apparently able to capture many aspects of the elastic properties of diverse real networks.

[1]  H. Pelzer.  Zur kinetischen Theorie der Kautschuk-elastizität , 1937 .

[2]  R. Gaylord,et al.  Rubber elasticity: a scaling approach , 1987 .

[3]  G. Heinrich,et al.  Rubber elasticity of polymer networks: Theories , 1988 .

[4]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[5]  P Bongrand,et al.  Cell adhesion. Competition between nonspecific repulsion and specific bonding. , 1984, Biophysical journal.

[6]  J. Dudowicz,et al.  Lattice model of equilibrium polymerization. VII. Understanding the role of "cooperativity" in self-assembly. , 2008, The Journal of chemical physics.

[7]  Entanglement coupling in linear polymers demonstrated by networks crosslinked in States of strain. , 1972, Proceedings of the National Academy of Sciences of the United States of America.

[8]  G. McKenna,et al.  Mechanical and Swelling Behaviors of Rubber: A Comparison of Some Molecular Models with Experiment , 1999 .

[9]  Paul J. Flory,et al.  Statistical Thermodynamics of Rubber Elasticity , 1951 .

[10]  C. Tanford.  Macromolecules , 1994, Nature.

[11]  S F Edwards,et al.  The statistical mechanics of polymerized material , 1967 .

[12]  N. R. Langley.  Elastically Effective Strand Density in Polymer Networks , 1968 .

[13]  K. Freed,et al.  Multistep relaxation in equilibrium polymer solutions: a minimal model of relaxation in "complex" fluids. , 2008, The Journal of chemical physics.

[14]  Ligand-receptor interactions , 1999, 0809.1926.

[15]  Ghassan S Kassab,et al.  Biaxial elastic material properties of porcine coronary media and adventitia. , 2005, American journal of physiology. Heart and circulatory physiology.

[16]  H. Rehage,et al.  Two‐Dimensional Model Networks , 1990 .

[17]  The Thermodynamics of a Strained Elastomer. I. General Analysis , 1948 .

[18]  S. S. Sternstein,et al.  Reinforcement Mechanism of Nanofilled Polymer Melts As Elucidated by Nonlinear Viscoelastic Behavior , 2002 .

[19]  Y. Fung.  Elasticity of soft tissues in simple elongation. , 1967, The American journal of physiology.

[20]  Rheological constitutive equation for a model of soft glassy materials , 1997, cond-mat/9712001.

[21]  M. Djabourov,et al.  All Gelatin Networks: 2. The Master Curve for Elasticity† , 2002 .

[22]  Linhong Deng,et al.  Universal physical responses to stretch in the living cell , 2007, Nature.

[23]  T. Witten,et al.  Connection between polymer molecular weight, density, chain dimensions, and melt viscoelastic properties , 1994 .

[24]  P. Janmey,et al.  Strain hardening of fibrin gels and plasma clots , 1997 .

[25]  R. Rivlin.  Torsion of a Rubber Cylinder , 1947 .

[26]  J. E. Mark,et al.  Elastomeric polymer networks , 1992 .

[27]  M. Peleg.  Mathematical characterization of the plasticizing and antiplasticizing effects of fructose on amylopectin , 1996 .

[28]  F. Horkay,et al.  Studies on the mechanical and swelling behavior of polymer networks based on the scaling concept. 4. Extension of the scaling approach to gels swollen to equilibrium in a diluent of arbitrary activity , 1982 .

[29]  G. Allen,et al.  Thermodynamics of rubber elasticity at constant volume , 1971 .

[30]  D A Weitz,et al.  Prestressed F-actin networks cross-linked by hinged filamins replicate mechanical properties of cells. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[31]  Micha Peleg,et al.  A mathematical model of crunchiness/crispness loss in breakfast cereals , 1994 .

[32]  S. Kawata,et al.  Size dependence of transition temperature in polymer nanowires. , 2008, The journal of physical chemistry. B.

[33]  J. Kalfus,et al.  Viscoelastic response of nanocomposite poly(vinyl acetate)‐hydroxyapatite with varying particle shape—Dynamic strain softening and modulus recovery , 2007 .

[34]  Sam F. Edwards,et al.  The theory of rubber elasticity , 1976, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[35]  R. D. Groot,et al.  Molecular theory of strain hardening of a polymer gel: Application to gelatin , 1996 .

[36]  C. Horgan,et al.  A description of arterial wall mechanics using limiting chain extensibility constitutive models , 2003, Biomechanics and modeling in mechanobiology.

[37]  A. Yodh,et al.  Local and global deformations in a strain-stiffening fibrin gel , 2007 .

[38]  P. G. de Gennes,et al.  Remarks on entanglements and rubber elasticity , 1974 .

[39]  Robert A. Riggleman,et al.  Antiplasticization and the elastic properties of glass-forming polymer liquids , 2010 .

[40]  K. Shull,et al.  Strain stiffening in synthetic and biopolymer networks. , 2010, Biomacromolecules.

[41]  D. Mooney,et al.  Independent Control of Rigidity and Toughness of Polymeric Hydrogels , 2003 .

[42]  Richard S. Graham,et al.  Neutron-Mapping Polymer Flow: Scattering, Flow Visualization, and Molecular Theory , 2003, Science.

[43]  Elasticity of swollen polyvinyl alcohol and poly(vinyl acetate) networks , 1980 .

[44]  R. Landel,et al.  The Strain‐Energy Function of a Hyperelastic Material in Terms of the Extension Ratios , 1967 .

[45]  M. Peleg.  Mapping the stiffness-temperature-moisture relationship of solid biomaterials at and around their glass transition , 1993 .

[46]  Y C Fung,et al.  The degree of nonlinearity and anisotropy of blood vessel elasticity. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[47]  C. Broedersz,et al.  Origins of elasticity in intermediate filament networks. , 2010, Physical review letters.

[48]  P. Flory.  Molecular Theory of Rubber Elasticity , 1979 .

[49]  J. Berret,et al.  Evidence of shear-induced fluid fracture in telechelic polymer networks. , 2001, Physical review letters.

[50]  J. Ferry.  Applications of a two-network model for crosslinks and trapped entanglements , 1979 .

[51]  J. Barbera,et al.  Contact mechanics , 1999 .

[52]  C. Price.  Thermodynamics of rubber elasticity , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[53]  Feng,et al.  Effective-medium theory of percolation on central-force elastic networks. , 1985, Physical review. B, Condensed matter.

[54]  J. Hubbard,et al.  Semiempirical theory of relaxation: concentrated polymer solution dynamics , 1991 .

[55]  T. McLeish.  Tube theory of entangled polymer dynamics , 2002 .

[56]  Michael Thorpe,et al.  Rigidity percolation in glassy structures , 1985 .

[57]  N. Stergiopulos,et al.  Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. , 1996, Journal of biomechanics.

[58]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[59]  Goldenfeld,et al.  Dynamic scaling and spontaneous symmetry breaking at the gel point. , 1992, Physical Review A. Atomic, Molecular, and Optical Physics.

[60]  W. Graessley,et al.  Rubber Elasticity of Well-Characterized Polybutadiene Networks , 1979 .

[61]  J. Douglas,et al.  Gelation in Physically Associating Polymer Solutions , 2001 .

[62]  Daniel A. Fletcher,et al.  Reversible stress softening of actin networks , 2007, Nature.

[63]  P. Janmey,et al.  Nonlinear elasticity in biological gels , 2004, Nature.

[64]  C. Hui,et al.  Fracture and large strain behavior of self-assembled triblock copolymer gels , 2009 .

[65]  R. Rivlin,et al.  Departures of the Elastic Behaviour of Rubbers in Simple Extension from the Kinetic Theory , 1953 .

[66]  Michael Rubinstein,et al.  Nonaffine Deformation and Elasticity of Polymer Networks , 1997 .

[67]  P. Flory,et al.  Statistical thermodynamics of random networks , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[68]  Peter Regitnig,et al.  Mechanics of the human femoral adventitia including the high-pressure response. , 2002, American journal of physiology. Heart and circulatory physiology.

[69]  T. McLeish,et al.  LOZENGE CONTOUR PLOTS IN SCATTERING FROM POLYMER NETWORKS , 1997 .

[70]  D. W. Saunders,et al.  Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[71]  R. Gaylord,et al.  The localisation model of rubber elasticity. II , 1990 .

[72]  Burak Erman,et al.  Theory of elasticity of polymer networks. 3 , 1982 .

[73]  Peter Sollich,et al.  Rheology of Soft Glassy Materials , 1996, cond-mat/9611228.

[74]  Yihong Chen,et al.  The ‘localization model’ of rubber elasticity: comparison with torsional data for natural rubber networks in the dry state , 1991 .

[75]  Y. Fung,et al.  Pseudoelasticity of arteries and the choice of its mathematical expression. , 1979, The American journal of physiology.

[76]  Hubert M. James,et al.  Theory of the Elastic Properties of Rubber , 1943 .