Similar to the procedures above where the force history of Equation (5) is obtained, a step force function is used as input, and the creep indentation depth history function can be derived as (12) where F0 is the step force, The indentation force history has been obtained in Equation (5), where the elastic shear modulus G 1 as a combined elastic response of two springs shown in Figure 2(b) should be replaced by G 1s of one spring only. Then, the simulated curves for the two situations can be found in Figures 6c,d. It is concluded that the creep depth variation under different forces gets larger through creep while the indentation force variation under different depths

gets smaller through relaxation. Particularly, INCB028050 clinical trial in Figure 6d, the force finally decreases to negative values, which represent attractive forces. The attraction buy SN-38 cannot be found when G 1s and G 2s are very small. This phenomenon can be interpreted by the conformability of materials determined by the elastic modulus. When G 1s and G 2s get smaller, the materials are more conformable. Accordingly, in the final equilibrium state, the materials around the indenter tend to be more deformable to enclose the spherical indenter. This will result in a smaller attraction. In addition, the example of shear

dynamic experiment is simulated to obtain the storage and loss moduli of TMV/Ba2+ superlattice. The storage and loss shear moduli are calculated by [42] (13) (14) where G′ and G″ are storage and loss moduli, MK-4827 nmr respectively, ω is the angular velocity which is related to the frequency of the dynamic

system, and is the shear stress Sitaxentan relaxation modulus, determined by the ratio of shear stress and constant shear strain. Based on the relation between the transient and dynamic viscoelastic parameters in Equations (13) and (14), the storage and loss shear moduli are finally determined to be (15) (16) where G 2s  = E 2s / 2(1 + v 2s ). Figure 7 shows the curves of storage and loss shear moduli vs. the angular velocity. The storage shear modulus, G′, increases with the increase of angular velocity, while the increasing rate of G′ decreases and the angular velocity of ~2 rad/s is where the increasing rate changes most drastically. However, the loss shear modulus, G″, first increases and then decreases reaching the maximum value, ~3.9 MPa, at the angular velocity of ~0.7 rad/s. The storage and loss moduli in other cases as uniform tensile, compressive, and indentation experiments can also be obtained. Conclusions This paper presented a novel method to characterize the viscoelasticity of TMV/Ba2+ superlattice with the AFM-based transient indentation. In comparison with previous AFM-based dynamic methods for viscoelasticity measurement, the proposed experimental protocol is able to extract the viscosity and elasticity of the sample.