The influence of water on the elastic modulus of paper. Part I: Extension of the H-bond theory

In Part I, the theory of hydrogen-bond-dominated solids is extended to explain phenomena concerning the elastic behavior of paper, based on the postulate that the number dencity of effective hydrogen bonds, normalized to on average bond stiffness, is higher for ultrasonic modulus measurements than for quasi-static measurements. This leads to the predictions: (I) The measured elastic modulus of a sheet of paper will depend upon whether the modulus is measured quasi-statically using load-elongation methods of ultrasonically using the time of flight method, and that the ultrasonic modulus, Es, will exceed the quasi-static modulus, Er, (Es > Er). (2) The rate of change of modulus with increasing moisture content, w, follows the rule: In[E] = A - (C.I.) w, where the negative slope of the curve In[E] vs. w is constant over a wide this of moisture contents. But again this slope will also differ whether measured quasi-statically or ultrasonically, with (C.I.)s > (C.I.)r. (3) Moreover, the extended theory predicts that the ratio of moduli at zero moisture content is related to the ratio of slopes by the expression: {[Es]r} / [Es]}3 =[(C.I.) + I] / [(C.I.) + I].