Statistical geometry of pores and statistics of porous nanofibrous assemblies

The application of theoretical models to describe the structure of the types of fibrous network produced by the electrospinning of polymers for use in tissue engineering and a number of other applications is presented. Emphasis is placed on formal analyses of the pore size distribution and porosities that one would encounter with such structures and the nature of their relationships with other structural characteristics likely to be important for the performance of nanofibrous materials. The theoretical structures considered result from interactions between randomly placed straight rods that represent fibres with nanoscale dimensions. The dominant role of fibre diameter in controlling the pore diameter of the networks is shown and we discuss the perhaps counter-intuitive finding that at a given network mass per unit area and porosity, increasing fibre diameter results in an increase in mean pore radius. Larger pores may be required for ingrowth of cells to nanofibrous networks, hence this study clarifies that simply making the diameters of the fibres smaller might not be the way to improve cell proliferation on such substrates. An extensive review of structural features of the network such as the distribution of mass, inter-fibre contacts and available surface for cell attachment, fibre contact distributions for integrity of the networks and the porosity and pore size distributions is given, with emphasis placed on nanofibre dimensions for the first time.