0f983fd8-0eb5-4b1b-9a0b-aee10a6098ff-160428114548.pptx

rubber

1. RUBBER ELASTICITY

2. ELASTOMERS OR RUBBER? Long chain molecules with some crosslinks Material which have the ability to regain its energy or rebound nature Steel more elastic than rubber- 10 times more extensible

3. Undergo large deformation (extension and compression) even under small load. Exhibit 100% complete recoverable deformation Rubber-like Elasticity Requirements

4. High coiled molecule or polymer Above Tg – High local segmental mobility Amorphous material(Stable state) High Molecular weight polymer Absence of bulky groups Infinite possibility of conformation Absence of polar groups Cross-linkable MOLECULAR REQUIREMENTS

5. (1) (2) 1 2 Modulus (E) Low High Recoverable Not Yes Elastic behaviour Less High

6. For the rubber bands, it is the crosslinks which determine the properties. Crosslinks provide a 'memory'. When the network is stretched, entropic forces come into play which favour retraction, returning the network to its original unstretched /equilibrium state.

7. According to 1 st law, change in internal energy dE of an isolated system is equal to the difference between heat added to the system dQ and work done by the system. According to 2 nd law, incremental heat is equal to product of entropy change dS and absolute temperature

8. 1 st Law – Total energy of a body is const . ie , E= Q – W or dE = dQ – dW (A) 2 nd Law – Change in entropy can never be negative. dQ = TdS (B) When a piece of rubber is stretched with force F to get change in length dL , the work done is dW = pdV – FdL (C) Substitute (B) and (C) in in (A) dE = TdS – pdV + FdL (D) Thermodynamics of rubber elasticity

9. Rubber – considered as an incompressible material; change in volume on deformation is negligible ie , dV = 0 Hence, FdL = dE – TdS (E) Taking partial derivative w.r.t length at const temp and Volume F = (∂E/ ∂V)V,T - T(∂S/∂L)V,T (F)

10. Ideal rubber Case: Under elastic force only uncoiling and loosening of molecules occur. These conformations don’t have much effect on internal energy of the system. On other hand, changes in entropy are considerable. ie , (∂E/∂L) V,T = 0

11. Due to decrease in entropy on extension. Entropy elasticity Stretched Undeformed rubber Deformed rubber

12. Undeformed State Deformed State Randomly coiled molecules Orderly arranged Amorphous Crystalline High S Low S Large no. of configurations of equal potential energy Reduction in no. of configurations

13. Cross-link points Mobile segments

14. S = k ln Z where k = Boltzmann const , Z = no. of configuration possibilities

15. Where N → number of chain segments between cross linking points Constant at const temperature Equation Of State For a Rubbery material

16. Deformation Heat Metals – Energy derived elasticity Thermoelastic experiment

17. Deformation Heat Rubbers – Entropy derived elasticity

18. On stretching rubber, it contracts or shrinks upon heating. Sharp contrast to the familiar response of expansion shown by other solids and liquids. This behavior first reported by Gough and then studied in detail by Joule – called Gough-Joule Effect Thermoelasticity is the basis of this experiment. GOUGH JOULE EFFECT

19. To derive stress-strain relationship for cross linked rubber network. 1) Statistical theory formulated by Meyer and his associates 2) Phenomenological approach – Mooney, Rivlin , Saunders Meyer first to confirm experimentally the entropic mechanism of rubber like elasticity which is now generally accepted. Basic Approaches

20. Relates the properties of a rubber to its basic molecular structure. Least probable form – extended form of long molecule, since thermal motion disturbs the ordered arrangement of chain. Apply tensile stress to the ends of such chain, it can be made to uncoil; which results in its orientation. Decrease in entropy takes place must be accompanied by evolution of heat. STATISTICAL THEORY

21. Entropy contribution Internal Energy Contribution Tg Temp Intercept- Internal Energy contribution Slope – Entropy contribution F v/s Temp @ const STRESS Retractive force (F)

22. Internal energy change is too small in comparison with entropic term (from graph). Rubber deformation is totally due to thermal motion, and there is a direct proportionality between isothermal elastic modulus and absolute temperature . Entropy change Calculation – from no. of conformations available to a chain with free rotation at C-C linkages and Gaussian distribution of distances b/w chain ends .

23. ie , (∂ S /∂ L ) T < 0, and thus (∂ f /∂ T ) L > 0. Temp tension - to maintain a given length, i.e., a given extent of molecular-strand alignment. Temp thermal motion tending to produce randomness (entropy) Assume polymer chains are freely joined i.e., there is no barrier to rotations about the CH2—CH2 single bonds, and the distance between the termini of a given polymer chain is characterized by a random, or Gaussian, distribution, it is possible to derive an expression for the entropy.

24. From this, the stress r can be related to the fractional elongation, σ = L / L : r = ρ RT/ zM ( σ – 1/ σ² ) = Y’ ( σ – 1/ σ² ) –(1) where ρ = density of the (unstrained) polymer having a monomer molecular weight M , and z = average number of monomer units between cross-links, R = gas constant, T = absolute temperature. By comparing r = f/a = Y s (Y=modulus and s=strain) and eq (1), coefficient ( ρ RT/ zM ) is an effective Young's modulus, Y' , that can be obtained by plotting r v/s ( σ – 1/ σ² ).

25. In this way, z can be determined, and an important characteristic of the elastomer can be obtained because z can be related to the more immediate (and practical) concept of the fraction of monomers that are cross-linked in the polymer, F cl . If a polymer chain consisting of N monomer units contains n cross-links, the average number of monomer units between cross-link nodes is z = N/n , and the fraction of cross-links is F cl ~ n/N . Typically, F cl is a few percent; its value depends on the particular vulcanization process used.

26. To understand the molecular properties and theoretical concepts that characterize rubber elasticity. Elasticity of NR – 3 major molecular properties :- a) Poly (isoprene) subunits can freely rotate, b) forces b/w the polymer chains are weak (as in a liquid), and c) the chains are linked together in a certain way at various points along the polymer. Latter property is especially important for reversible elasticity. Also eliminates the phenomenon called creep in which an elastomer, once deformed, will remember and "relax" back to the deformed shape. Conclusion