The dimer stage of nucleation may affect considerably the rate of the nucleation process at high supersaturation of the nucleating vapor. Assuming that the dimer formation limits the nucleation rate, the kinetics of the particle formation-growth process is studied starting with the definition of dimers as bound states of two associating molecules. The partition function of dimer states is calculated by summing the Boltzmann factor over all classical bound states, and the equilibrium population of dimers is found for two types of intermolecular forces: the Lennard-Jones ͑LJ͒ and rectangular wellϩhard core ͑RW͒ potentials. The principle of detailed balance is used for calculating the evaporation rate of dimers. The kinetics of the particle formationgrowth process is then investigated under the assumption that the trimers are stable with respect to evaporation and that the condensation rate is a power function of the particle mass. If the power exponent ϭn/(n ϩ1) (n is a non-negative integer͒, the kinetics of the process is described by a finite set of moments of particle mass distribution. When the characteristic time of the particle formation by nucleation is much shorter than that of the condensational growth, nϩ2 universal functions of a nondimensional time define the kinetic process. These functions are calculated for ϭ2/3 ͑gas-to-particle conversion in the free molecular regime͒ and ϭ1/2 ͑formation of islands on surfaces͒. ͓S1063-651X͑98͒06309-0͔
The formation of a gel in a disperse system wherein binary coagulation alone governs the temporal changes of particle mass spectra is studied under the assumption that the coagulation kernel is proportional to the product of masses of coalescing particles. This model is known to reveal the sol-gel transition, i.e., the formation of one giant cluster with the mass comparable to the total mass of the whole system. This paper reports on the exact solution of this model for a finite total mass of the coagulating system. The evolution equation for the generating functional defining all properties of coagulating systems is solved exactly for this particular kernel. The final output is the exact expression for the single-particle mass spectrum as a function of time. The analysis of the spectrum in the thermodynamic limit shows that after a critical time a giant single particle (the gel) appears. Although the concentration of this giant gel particle is zero in the thermodynamic limit, it actively interacts with smaller particles "eating" them and thus growing in mass. Special attention is given to the transition point, where the gel is appearing. It is demonstrated that the sol-gel transition reminds the second-order phase transition. The time dependencies of the gel mass, the number concentration, and the second moment of the particle mass spectrum are found.
An instrument has been developed to measure the complex dynamic shear modulus of 45 mg bitumen samples over a frequency range of 2-200 Hz and over a continuously variable temperature range. A moving coil vibrator applies a torque to the sample and a capacitance transducer measures the resulting rotation. A resolved component indicator is used to measure the amplitudes and relative phase of the voltages representing torque and rotation. The components of the complex modulus are then calculated directly by the use of simple equations.
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