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forces - Matt Lang MIT Forces at the Molecular Level...

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Matt Lang, MIT Forces at the Molecular Level Covalent Interactions Here electrons are truly shared between atoms. To do this properly we need to know the wavefunctions describing the electron probability density around the atoms. Lets assume a model of a bond as a spring to make some approximations. Examples of typical energy of covalent bonds: Carbon Carbon single bond ~140kT Carbon Carbon double bond ~240kT Force on a spring ~ kx F spring := k stiff x integrate to get the energy, Mathcad does this for us Energy in a spring = F spring dx 1 k stiff x 2 2 E bond := 140 4. units of pN*nm A reasonable dissociation distance for this bond is 0.5 angstroms 0.5 set this value x := converted to nm 10 We can now estimate an approximate stiffness for the bond: E bond k stiff_estimate := 2 2 x k stiff_estimate = 4.592 × 10 5 units of pN/nm now generate a characteristic force required to rupture a covalent bond characteristic_force_covalent := k stiff_estimate x characteristic_force_covalent = 2.296 × 10 4 units of pN this = 23 nN or so These bonds are strong you couldn't break for example with an optical trap, need more force
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Matt Lang, MIT Ionic bonding/interactions develop using the physics of the coulombic interaction charge on an electron Thermal Energy "kT" distance separation, "r" q 1 1.60 10 19 × := kT 4.1 10 21
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