Coagulation threshold energy

D, Dm, Ds Diffusion, inter diffusion and self diffusion coefficient, respectively Dp Particle diffusion coefficient E Threshold energy of coagulation Edk Macroscopic bulk breaking energy... 

Tensile relaxation modulus Tensile stress relaxation modulus Threshold energy of coagulation Activation energy Exchange energy of i-j contact Helmholtz free energy (F = E—TS)... 

The experiments in the first series were conducted with methylated surfaces immersed in aqueous solutions of alkylbenzenesulfonates. The free energy of interaction between methylated glass and quartz spherical surfaces having radii of about 1 mm was studied as described in Section 1.2. Parallel to these studies, the colloid stability of 10 mn particles of methylated Aerosil (i.e., hydrophobized nanoparticles of quartz) suspensions was monitored via turbidity measurements. A characteristic sharp increase in turbidity was observed at the coagulation threshold. This behavior was reversible an increase in the surfactant concentration resulted in a decrease in turbidity, while dilution of the solutions caused the turbidity to increase. 

In the case of energy barriers, the previous theory is not applicable anymore, since besides diffusion, the coagulation depends on the barrier threshold, too. The coagulation rate is expected to be less, and so it is called slow coagulation. The probability for the particles to overcome the barrier depends on the energy barrier ( ) and the temperature according to the Boltzmann distribution. 

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