Study of Thermal Internal Stresses in Certain Polymer Coatings

V. D. Filimonov, E. E. Sirotkina

(Presented by the scientific-methodological seminar of the Faculty of Chemical Technology)

Polymers possessing semiconductor properties have found application in electrophotography as photosensitive layers. These polymers are used in the form of thin films deposited on metal substrates.

In the course of the preparation and use of these films, internal stresses of various kinds arise in them, which can strongly affect the quality of the coating and its adhesion to the substrates. It is therefore clear that taking account of the influence of internal stresses is necessary when evaluating the quality of photosensitive coatings.

In addition, electrophotography very much requires elastic photosensitive coatings that could be applied to flexible substrates. Consequently, it was necessary to find parameters that would make it possible to evaluate the elasticity of photosemiconducting polymers synthesized in the Department of Technology of Basic Organic Synthesis.

The present work was devoted to the study of the internal stresses arising during the operation of photosensitive layers, and to the determination of certain mechanical characteristics of polymer coatings.

When polymer coatings are obtained on rigid substrates from a polymer solution, tensile internal stresses grow in the films as the solvent dries; the nature of their occurrence was established by V. A. Kargin [1]. In addition, considerable internal stresses in polymer coatings on metal may arise because of the large difference in the coefficient of thermal expansion (contraction) of polymers and metals; in polymers these coefficients are, as a rule, many times greater. Sufficiently high internal stresses in a coating can tear it away from the substrate and, if the adhesion to the substrate is greater than the cohesion of the film, destroy it.

There are several methods for measuring internal stresses in polymer coatings. In the works of V. A. Kargin and his coworkers [2], internal stresses were estimated from the radius of curvature of a metal foil bent by a polymer film applied to one side of the foil. A widely used method is the determination of internal stresses from the magnitude of the double refraction at the polymer–substrate boundary [3]. Both of these methods do not give quantitative values of internal stresses in coatings.

Internal stresses in polymer films can be determined by the method of deflection of the free end of a cantilevered plate [4] from the formula

\[ \sigma = \frac{hE_1t^3}{3l^2(t+\alpha t)\alpha t}+\frac{hE_2(t+\alpha t)}{l^2}, \tag{1} \]

where \(\sigma\) is the internal stress;
\(h\) is the deflection of the free end of the plate;
\(E_1\) and \(E_2\) are the moduli of normal elasticity of the substrate material and the coating, respectively;
\(l\) is the length of the plate;
\(t\) is the thickness of the substrate;
\(\alpha t\) is the thickness of the coating.

It has been shown [4] that the second term of equation (1) amounts to about 1% of the value of the first term. Therefore we determined the internal stresses from the considerably simpler equation

\[ \sigma = \frac{hE_1t^3}{3l^2(t+\Delta t)\Delta t}, \tag{2} \]

which does not include the value of the modulus of elasticity of the coating \(E_2\), unknown for most of the polymers studied.

It is of interest that equation (1) implies the possibility of determining, indirectly, the tensile modulus of elasticity \(E_2\) of a polymer coating. If two identical substrates are taken, differing only in thickness, with a polymer coating of identical thickness applied to them, then for each plate one may write:

\[ \begin{aligned} \sigma_{t_1} &= \frac{h_1E_1t_1^{\,2}}{3l^2(t+\alpha t)\alpha t} +\frac{h_1E_2(t_1+\Delta t)}{l^2} \\ \sigma_{t_2} &= \frac{h_2E_1t_2^{\,2}}{3l^2(t_1+\Delta t)\Delta t} +\frac{h_2E_2(t_2+\Delta t)}{l^2}. \end{aligned} \tag{3} \]

Solving the system of two equations with two unknowns with respect to \(E_2\), we obtained the following expression:

\[ E_2 = \frac{E_1\left[h_2(t_1+\Delta t)t_2^{\,3}-h_1(t_2+\Delta t)t_1^{\,3}\right]} {3l^2(t_1+\Delta t)\Delta t\,\Delta t\left[h_1(t_1+\Delta t)-h_2(t_1+\Delta t)\right]}. \tag{4} \]

Generally speaking, one may vary not only the thickness of the substrate, but also its length, as well as the thickness of the coating; in this case other expressions will be obtained, but the value of \(E_2\) should not change.

Using the calculated values of \(E_2\), we assessed the elasticity of the coatings obtained.

The obtained values of the moduli of elasticity for thin polymer coatings cannot be compared with the moduli of elasticity of bulk polymers, since it has been shown [5] that the structure of a polymer in thin films applied to different substrates differs from the structure of the polymer in bulk.

Experimental Part

Measurements of thermal internal stresses were carried out as follows: a polymer layer was applied to brass substrates 0.2, 0.15, and 0.09 mm thick, 9 cm long and 1.5 cm wide, by casting from solution and drying to constant weight. The dried plates with the polymer were cantilevered in a special clamp and, together with the clamp, placed in a drying cabinet with a glass door. The cabinet was heated to the softening temperature of the polymer film and the subst—

the plate with the film was cooled together with the chamber at a rate of about \(3^\circ\text{C}\) per minute down to room temperature. With a KM-6 cathetometer, at every \(5^\circ\) the height of rise of the free end of the plate was determined. Figures 1 and 2 show the graphical dependence of the increase in internal stresses in the coatings during their cooling. Table 1 gives

Table 1

Maximum internal stresses and moduli of elasticity

the values of the maximum thermal internal stresses and the moduli of elasticity of the polymers calculated by formula (4).

A series of polymers was studied, the characteristics of which are given in [6].

Discussion of Results

The moduli of elasticity (Table 1) obtained for the polymers studied are rather high (except for PVDFA and its copolymers with PVK) in comparison with the moduli of most thermoplastic polymers. Such high moduli of elasticity may occur in polymers possessing extremely rigid macromolecules incapable of highly elastic deformations. The polymers studied possess certain semiconducting properties, and such high moduli of elasticity agree well with the assumption that conjugation through carbazole radicals exists in their macromolecules, as a result of which the shape of the macromolecules becomes rigidly fixed. Hence also the poor elasticity of films of these polymers.

The method used for determining the moduli of elasticity has a number of advantages over ordinary mechanical methods. It is extremely simple in terms of instrumentation and makes it possible, in a single experiment, to determine the modulus of elasticity at any temperatures in a specified interval, i.e., to construct a graphical dependence of the modulus of elasticity on temperature, which can provide some data on the thermomechanical properties of the polymer.

On curves 3 and 4 of Fig. 1, showing the increase in thermal internal stresses during cooling of the films, an inflection is seen at temperatures of \(110—90^\circ\text{C}\); this inflection should correspond to the glass-transition temperatures of PVK and 3-Cl PVK, since a decrease in the mobility of segments of the macromolecular chains should reduce the ability of the macromolecular chains to relax internal stresses, as is shown by the increase in the steepness of the curves. Films of the PVK telomer (curve 5), on cooling, cracked at an internal-stress value of 50.2 kg/cm²; consequently, this value is the tensile strength limit of the telomer films. The drop in curve 5 shows the removal of internal stresses as a result of cracking of the film.

Fig. 1. Increase of thermal internal stresses: 1—PVC oligomer, 2—3-Cl PVC oligomer, 3—PVC suspension polymer, 4—3-Cl PVC polymerization product, 5—PVC telomer.

Fig. 2. Increase of thermal internal stresses: 1—PVDF, 2—PVDF + 5.2% PVC, 3—PVDF + 40% PVC.

Conclusions

1. By the method of deflection of the free end of a cantilever-fixed plate, the thermal internal stresses of certain photosensitive polymer coatings were determined.

2. An expression was obtained that makes it possible, by calculation from the change in internal stresses, to compute the elastic moduli of thin polymer coatings.

References

1. V. A. Kargin, M. N. Shteding. ZhFKh, 20, 7, 1946.

2. M. N. Koryakina, V. A. Kargin, T. N. Sogolova. Khim. promyshl., 1957, No. 5, 265.

3. S. A. Shraĭner, P. I. Zubov. Dokl. AN SSSR, 124, 1102, 5, 1959.

4. A. T. Sanzharovskii. Vysokomolekulyarn. soedin., 2, 1698, 1960.

5. Yu. M. Malinskii, I. V. Epelbaum, N. M. Titova, V. A. Kargin. Vysokomolekulyarn. soedin., 10, 786, 1968.

6. V. D. Filimonov, E. E. Sirotkina. Study of the adhesion of certain photosensitive polymers to metals (present collection).