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Lecture 13 Steric Interactions and Entropic repulsion

Lecture 13 Steric Interactions and Entropic repulsion. What did we cover in the last lecture?. The pressure exerted between charged surfaces in an electrolyte is the sum of osmotic pressure and dispersive terms. In this lecture…. 1) Steric (Entropic) stabilisation of particles and surfaces

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Lecture 13 Steric Interactions and Entropic repulsion

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  1. Lecture 13 Steric Interactions and Entropic repulsion

  2. What did we cover in the last lecture? The pressure exerted between charged surfaces in an electrolyte is the sum of osmotic pressure and dispersive terms

  3. In this lecture… 1) Steric (Entropic) stabilisation of particles and surfaces 2) Surfaces with grafted molecules 3) Boltzmann form of entropy 4) Free Energy of grafted molecules 5) Entropic forces between sterically stabilised surfaces Further Reading Gases, Liquids and Solids, 3rd Edition, D. Tabor, Cambridge University Press, p326-321, 1993 Intermolecular and Surface forces, J. Israelachvili, chapter 14

  4. Colloidal stability It is sometimes not possible to use charges to keep particles and surfaces apart in solution This is true when using organic solvents as the suspending medium (e.g. in ferrofluids), as ionic solids (electrolytes) are often poorly soluble in these solvents An alternative route to stabilisation is to use Steric (or entropic) repulsion effects between surfaces

  5. Entropic (Steric) Forces Surfaces can be decorated with long molecules (e.g. polymers) Molecules are tethered to a surface by one end and can wave around freely in solution. As a result they have a large number of configurations (directions in which they can point) When two surfaces come close together, the number of configurations that the molecules can adopt is reduced. This reduces the entropy (or measure of disorder). The system resists this reduction in entropy by generating a repulsive force…

  6. Boltzmann form of Entropy Boltzmann derived a statistical form of the entropy of a system, S, such that where W is the number of available (micro) states corresponding to a given macrostate and kB is Boltzmann’s constant (JK-1 ). In this case… Macrostate → molecule tethered to the surface Microstate → a single orientation of the molecule

  7. The entropy of a tethered rod Suppose we treat the molecule as a rigid rod with length, l, and area, a, at each of its ends (See OHP) If we allow the rod to point in any direction it can sweep out half a sphere with a total area, A1 The number of different possible microstates (orientations of the rod), W, is then given by dividing ratio of A1 to a So the entropy (S1) of the tethered rod becomes

  8. Confinement of tethered molecules When a solid surface approaches the tethered rod, its motion becomes restricted and it can sweep out a much reduced area At a separation D between the surfaces, the total area that can be swept out is A2 where The entropy of these ‘confined’ molecules is therefore

  9. How do we extract a force? We can extract a force if we know how the entropic contribution to the interaction energy , U, depends upon separation D The change in the Gibbs free energy of the system at constant temperature is given by Where DH and DS are the change in enthalpy (energy of interaction) and entropy caused by bringing the surfaces together

  10. Entropic repulsion Force per molecule If we consider only the entropy contribution (for now) the force per molecule is where So the force F is

  11. Pressure due to entropic forces The force between the surfaces is positive and therefore repulsive If the separation between tethering points is, d, then the effective area occupied by one molecule is d2 The force per unit area (Pressure) is P, where

  12. Problem • Two perfectly flat surfaces are brought into close proximity such that dispersion forces attract them towards one another. One of the surfaces is coated with a layer of rod-like molecules of length 3nm with the highest possible surface grafting density that allows the free end of the molecules to rotate freely • Calculate the magnitude of the pressure exerted on the surfaces due to repulsive steric (entropic) forces, at room temperature, if the surfaces are separated by a distance of 2.5nm • Calculate the equilibrium separation of the surfaces at room temperature if the Hamaker constant is 1x10-20 J

  13. Summary of key concepts When the motion of molecules near a surface is confined it reduces the entropy of the system This gives rise to repulsive force which acts to push surfaces apart and increase the entropy again For rod like molecules on a surface which occupy an area d2, the pressure between surfaces at a separation, D, is given by

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