This spreadsheet and the associated read-me file can be used to estimate the molar mass between crosslinks in rubbery and rubber-like materials. This will take data from either a rheometer or dynamic mechanical analysis (DMA) instrument. You will need to identify a clear rubbery plateau ideally in frequency sweep, but also can be identified from temperature sweep experiments. Depending on your instrument (rheometer for G’ or DMA for E’) use the appropriate tab. If your primary chain molecular weight (Mp or uncross linked polymers) is known, say from size exclusion chromatography, you can use the tabs where Mp is known, otherwise use the alternative tab where Mp is unknown.
All that is needed to use this spreadsheet is Microsoft Excel.
Original Equations taken from: Treloar, L. R. G. “The elasticity and related properties of rubbers.” Reports on progress in physics 36.7 (1973): 755. (Equations 2.17 and 2.17a) and assuming incompressibility E’=3G’.
Implementation of spreadsheet include: S. V. Wanasinghe, E. M. Schreiber, A. M. Thompson, J. L. Sparks, D. Konkolewicz, ‘Dynamic covalent chemistry for architecture changing interpenetrated and single networks’ Polymer Chemistry 2021, 12, 1975-1982, DOI: 10.1039/D1PY00198A, P. Chakma, Z. A. Digby, J. Via, M. P. Shulman, J. L. Sparks and D. Konkolewicz, ‘Tuning Thermoresponsive Network Materials through Macromolecular Architecture and Dynamic Thiol-Michael Chemistry’, Polymer Chemistry 2018, 9, 4744-4756, DOI:10.1039/C8PY00947C.
If using this molar mass between crosslinks template in your research resulting in publication, MACRO asks that you acknowledge the template as follows. “We acknowledge the molar mass between crosslinks calculator from the Konkolewicz group and Hubbard provided by the Macromolecular Alliance for Community Resources and Outreach.”