Estimating organic chain length through sound velocity measurements

The ability to measure the length of polymers while monitoring their production is evidently extremely valuable, but is also a useful tool for chemical identification purposes at other times, e.g. the analysis of waste water. A study of the relationship between velocity of sound and chain length has been carried out. Initial studies were performed on two model systems; a series of pure liquid n-alkanes (pentane to hexadecane) and 1-alcohols (methanol to 1-dodecanol). This study was extended to look at an industrially significant system of dimethylsiloxanes 200 fluid (L2, 0.65 cSt) to 200 fluid (5000 cSt). Corresponding density data have been taken from the literature and the adiabatic compressibility determined. The measured adiabatic compressibility has been compared with two molecular models of wound velocity, the Schaaffs model and a development of the Urick equation. The Urick equation approach is based on a determination of the compressibility of the methylene or siloxane repeat units which make up the chains in these linear molecules. We show that the Urick equation approach accurately predicts sound velocity and compressibility for the higher members of each series, whilst the Schaaffs approach fails for the 1-alcohols. We suggest that this is because of the influence of the hydroxyl end group through hydrogen bonding with methylene groups within the chain. This interaction modifies the derived compressibility of the methylene groups, so reducing their compressibility relative to that of the n-alkanes. The technique described provides valuable new insights into end-group, intermolecular and intra-molecular interactions in liquid linear-chain molecules. From this detailed analysis of the mechanisms involved, a model is derived. This model can give very precise estimations of the composition of a pure liquid. In the case of mixtures of polymers, it is necessary to use the modified Urick equation and then, in addition, the concentration dependence of both the velocity of sound and the density must be measured.