Criteria ruling particle agglomeration

Most of the technically important properties of nanomaterials, such as superparamagnetism or luminescence, depend on the particle size. During synthesis and handling of nanoparticles, agglomeration may occur. Agglomeration of nanoparticles may be controlled by different mechanisms. During synthesis one observes agglomeration controlled by the geometry and electrical charges of the particles. Additionally, one may find agglomeration controlled by thermodynamic interaction of the particles in the direction of a minimum of the free enthalpy. In this context, one may observe mechanisms leading to a reduction of the surface energy or controlled by the van der Waals interaction. Additionally, the ensemble may arrange in the direction of a maximum of the entropy. Simulations based on Monte Carlo methods teach that, in case of any energetic interaction of the particles, the influence of the entropy is minor or even negligible. Complementary to the simulations, the extremum of the entropy was determined using the Lagrange method. Both approaches yielded identical result for the particle size distribution of an agglomerated ensemble, that is, an exponential function characterized by two parameters. In this context, it is important to realize that one has to take care of fluctuations of the entropy.

Significance of thermodynamic interaction parameters in guiding the optimization of polymer:nonfullerene solar cells

Recent advances in analysing the morphology of nonfullerene polymer solar cells are discussed with an effective thermodynamic interaction parameter.

THERMODYNAMIC INTERACTION COEFFICIENTS IN LOW-CONCENTRATED LIQUID BINARY ALLOYS

The article considers basic expansion of thermodynamics and thermodynamic interaction coefficients of the first, second and third orders of low-concentrated binary alloys. The values of interaction coefficients of the first and second orders in 37 such systems were estimated according to experimental thermodynamic data on the concentration dependence of excess chemical potential of an impurity in liquid alloys of binary systems. Estimates were obtained by the numerical differentiation method. This method is based on Newton first interpolation formula. Calculation formulas for the corresponding estimates are given. A simple theory is proposed that relates the thermodynamic interaction coefficient of the second order with the first-order one in the liquid alloy of certain system. The theory is based on the lattice model of a solution and the principles of statistical mechanics. The FCC lattice is adopted as a model lattice. The model of pair interaction between metal atoms in the alloy was used. The radius of this interaction corresponds to radius of the nearest atomic shell. Using the proposed theory, thermodynamic interaction coefficients of the second-order for all 37 systems considered in this work, as well as the values of the third order interaction coefficients for 23 systems out of 37 mentioned above, were calculated. For these 23 systems, theoretical estimates of the second-order interaction coefficients are in agreement with experimental ones both by sign and by order of magnitude. This circumstance can be considered as evidence of applicability of the numerical differentiation method for estimation of thermodynamic interaction coefficients of the first and second orders in liquid binary alloys. The accuracy of estimating the values of the third derivative by numerical differentiation is insufficient. That makes it impossible to compare the calculated values of the interaction coefficients of the third order with the experimental ones, obtained by this method. It can be assumed that the theoretical calculations just give an idea of the magnitudes’ order of these coefficients.