Measurement of Thin Films in Shear by DMA

Thin films with a thickness of 50 to 200 μm are usually measured in tension in the DMA. They can, however, also be measured in shear if proper attention is paid to sample preparation and other factors. In this article, we present two examples to show how this is done.

Introduction

In the DMA, a sample undergoes periodic deformation. However, the force necessary to deform the sample acts not only on the sample but also on the sample holder. This means that the measured displacement amplitude is the sum of the deformation of the sample and the deformation of the sample holder. Ideally, the deformation of the sample holder should be negligible compared with the deformation of the sample.

When thin samples (thickness < 0.2 mm) are loaded in the shear sample holder, the danger is that the shear clamping plates tilt slightly and touch each other.

The results from a DMA measurement performed under these conditions are then completely wrong. To make sure the plates do not touch each other, one intuitively tends to measure thin samples with large diameters. The stiffness of such samples might then be greater than the stiffness of the sample holder. In such cases, the deformation of the sample holder contributes more to the total deformation than the deformation of the actual sample. When the modulus is calculated, the measured total deformation or stiffness must be corrected. This is done using the so-called stiffness correction.

The stiffness correction In general, the force applied to the sample deforms both the sample and the sample holder. The measured displacement amplitude, D_xm, therefore comprises the deformation of the sample, D_xs, and the deformation of the sample holder, D_xsh. The individual contributions to the deformation are given by the ratio of the applied force, F, and the stiffness according to eq (1):

Here S_m is the measured stiffness, S_s is the sample stiffness, S_sh is the sample holder stiffness, and F is the force amplitude. From eq (1) it follows that the measured stiffness is given by eq (2): 

If S_s << S_sh, the measured stiffness corresponds to the sample stiffness. If S_s >> S_sh, the measured stiffness corresponds to the sample holder stiffness. Solving eq (2) for the unknown sample stiffness, S_s, we obtain:

This means that to obtain the sample stiffness, S_s, the measured stiffness, Sm, must be corrected with the stiffness of the sample holder, S_sh. This correction is known as the stiffness correction. As a rule, the stiffness of the sample is orders of magnitude smaller than the stiffness of the sample holder. In this case, the stiffness correction is practically independent of the exact value of the sample holder stiffness, S_sh.

In the STAR^e software, eq (3) is used to correct the measure sample stiffness for all sample holders. Default values for the sample holder stiffness are stored in the database. In practice, the sample holder stiffness varies slightly from instrument to instrument and depends on how a sample is loaded in the sample holder in the DMA861^e . Investigations have shown that if the sample stiffness is smaller than 20% of the default value of the sample holder stiffness (i.e. Ss < 0.2·S_sh), the default value of the sample holder stiffness is sufficiently accurate to use for the stiffness correction. If the sample stiffness exceeds the stiffness of the sample holder (S_s > S_sh), the stiffness correction with the default values for the sample holder stiffness gives modulus values that are too low. In this case, there are two possibilities: 

^{Measurement of Thin Films in Shear by DMA | Thermal Analysis Application No. UC 293 | Application published in METTLER TOLEDO Thermal Analysis UserCom 29}