Measuring the Elastic Modulus of Thin Polymer Sheets by Elastocapillary Bending

We describe bending by liquid/liquid or liquid/air interfaces as a simple and broadly applicable technique for measuring the elastic modulus of thin elastic sheets. The balance between bending and surface energies allows for the characterization of a wide range of materials with moduli ranging from kilopascals to gigapascals in both vapor and liquid environments, as demonstrated here by measurements of both soft hydrogel layers and stiff glassy polymer films. Compared to existing approaches, this method is especially useful for characterizing soft materials (<megapascals in modulus), thin sheets with sub-millimeter in-plane dimensions, and samples immersed in a variety of liquid media. The measurement is independent of the three-phase (liquid/solid/medium) contact angle for appropriately chosen wetting conditions, therefore requiring only knowledge of the liquid/medium surface tension and the sheet thickness to characterize sheets with specified shapes. Using the method, we characterize photo-cross-linkable polyelectrolyte hydrogel sheets swelled to equilibrium in an aqueous medium and demonstrate good agreement with predicted scalings of the modulus and swelling ratio with cross-link density.