LOG-NORMAL DISTRIBUTION OF ELECTROSPUN NANOFIBRE DIAMETERS: DERIVATION FROM MULTIPLICATIVE JET SPLITTING AND EXPERIMENTAL VERIFICATION AS A PROCESS-STABILITY CRITERION

Abstract

The distribution law of electrospun nanofibre diameters is usually selected empirically, by fitting whichever function best matches the histogram, which prevents the result from being transferred between systems. This work derives the distribution from the physics of the process and then verifies it experimentally. Successive splitting of the electrospun jet is represented as a multiplicative random process, so that the logarithm of the fibre diameter is a sum of independent random contributions; by the central limit theorem the diameter is then log-normally distributed, in agreement with Kolmogorov's theory of stationary fragmentation. Two materials were examined by scanning electron microscopy at 1000× and 15000×: a composite web containing silk fibroin and a reference web spun from a 16% poly(vinyl alcohol) solution. The mean fibre diameters are 306.24 nm and 249.89 nm respectively, both within the range reported for regenerated silk fibroin. Pearson's goodness-of-fit test at a confidence level of 0.99 does not reject the log-normal hypothesis for either material (χ² = 4.31 < 20.1 with p = 0.82, and χ² = 8.32 < 13.3 with p = 0.081). Because conformity to the log-normal law follows from the stationarity of the splitting process, its experimental confirmation constitutes indirect evidence that the process is stable; conversely, departure from the law indicates the onset of instability. Use of the distribution test as an equipment-free criterion for statistical process control is therefore proposed, together with a discussion of the sampling and projection biases that affect diameter measurement from electron micrographs.