(70dk) Prediction of Vdw Force Interaction between Particles with Surface Roughness

Particle-particle interaction is of great importance in pharmaceutical manufacturing and formulation design. The cohesion/adhesion forces between individual particles of different physical and chemical properties may have great influences on bulk powder behavior such as the powder flowability and compatibility, and thus affect the process performance, e.g. the homogeneity and stability of the powder mixture in the blending process.

Generally the cohesion force between two particles consists of three force components, van der Waals force (vdW), capillary force and electrostatic force. Among them, vdW force is ubiquitous and is expected to be dominant under low relative humidity conditions. It is found that vdW force is very sensitive to the surface morphologies of particles. The nano-scale surface roughness of micron-sized particles may lead to several order of magnitude decreases in vdW force value compared to that of perfectly smooth particles of the same size.

A model is developed in our study to predict the interaction between two individual particles with rough surfaces. First of all, the surface roughness of sample particles was characterized by atomic force microscopy (AFM) measurement. Using the asperity features as primary parameters, the surface morphology of the real particle surfaces was simulated. A surface element integration method was applied on the generated surfaces subsequently to calculate the vdW force between two particles. Meanwhile, the actual vdW force interactions of five different particle materials including glass beads, polystyrene beads, spray-dried lactose, crystalline lactose and microcrystalline cellulose (MCC) were measured by AFM force volume mode. The experimental force data were found to agree well with the calculated force distribution.

In addition, a parametric analysis study was carried out based on our modeling work to quantify the relationship between particle characteristics and the vdW force interactions. It is found that the vdW force for rough particles is independent of the particle size at a certain particle size range. The key parameters which influence the vdW force are the asperity radius and height. The vdW force increases with the increase of asperity radius and decreases as the asperity height increases and/or the asperity height distribution gets wider. Meanwhile, it is also positively correlated with the asperity fractional coverage on the particle surface, the Hamaker constant and the contact area.