Elasticity, plasticity and fine structure of plant cell walls

1. 1. The elementary process of elastic and plastic deformations in living tissues is closely related to their submicroscopic structure. Therefore, an attempt was made to arrive at a general picture of the submicroscopic structure of cylindrical plant tissues. 2. 2. Because cylindrical plant tissues have different elastic behavior longitudinally and transversely, an experimental device was constructed which permitted determination of two moduli of elasticity. Stretching horizontal cylindrical plant tissues gives three kinds of stress-strain curves and, therefore, Young's modulus also. These three stress-strain curves are parabolic, S-shaped and straight lines with tails. The S-shaped curves belong to rubber-like elastic plant tissues, the straight lines with tails belong to metal-like elastic plant tissues. By forcibly deflecting the cylindrical plant tissue at its center, force-deflection curves are obtained. The force-deflection curve for all cylindrical plant tissues consists of two parts, an ascending elasticity curve and a straight line plasticity curve. From these two curves we can compute the transverse modulus of elasticity, the coefficient of plasticity and the yield value for cylindrical plant tissues. 3. 3. Because all cylindrical plant tissues yield the same force-deflection curve, we may deduce the general law that in nature sideward breaking of plants always proceeds in the same way if a growing force is acting perpendicular to the plant. 4. 4. From the elastic and plastic quantities computed, the following new laws may be stated: 4.1. (a) Soft plant tissues are slightly elastic and very plastic, hard plant tissues are highly elastic and slightly plastic. 4.2. (b) The structure of cylindrical plant tissues is more solid longitudinally than transversely. The submicroscopic structure of the cell walls of cylindrical plant tissues is determined by linear molecules of cellulose which are more or less oriented parallel to the axis of these tissues. 5. 5. By using the elastic and plastic quantities computed, we find that plant tissues have two kinds of flexibility. Soft cylindrical plant tissues have the flexibility of wet paper. A second group of cylindrical plant tissues is flexible only in the plastic condition. 6. 6. By using the molecular network structure of rubber, the theoretical equation for the S-shaped stress-strain curve for rubber is found to be: f = G δ − 1δ2 where f = stress, α = 1 + strain, G is the modulus of rigidity. This theoretical curve coincides fairly well with the experimental curve for rubber. Hence, we find that there is a relationship between the molecular network structure and the elastic properties of vulcanized rubber. 7. 7. Because of similar elastic behavior of wool and vulcanized rubber we conclude that both substances have a similar molecular network structure. In addition there are thin micelles in wool. The network structure of wool is easily changed by heat. 8. 8. Because protoplasm has rubber-like elasticity, we postulate a rubber-like molecular network structure for protoplasm. The network structure of the very unstable protoplasm is easily changed, as is known to be true for wool. 9. 9. By using the theoretical equation for the S-shaped rubber curve in the case of the experimental S-shaped stress-strain curve for rhizomes of Equisetum fluviatile we conclude that there is a similarity of submicroscopic structure for vulcanized rubber and for cell walls of rhizomes of Equisetum fluviatile. In a similar way we find that there is a similarity of structure for raw catgut and vulcanized rubber. 10. 10. 10.1. (a) The submicroscopic structure of secondary cell walls of plant tissues of higher plants is composed of partly crystalline and partly amorphous cellulose. 10.2. (b) In the case of rubber-like elastic cylindrical plant tissues the amount of amorphous cellulose in secondary cell walls is greater than the amount of crystalline cellulose. For such a plant tissue we have the fact that the ratio between Young's modulus and the modulus of elasticitiy transversely is small. 10.3. (c) In the case of metal-like elastic cylindrical plant tissues the amount of crystalline cellulose in secondary cell walls is greater than the amount of amorphous cellulose. For such a plant tissue we have the fact that the ratio between Young's modulus and the modulus of elasticity transversely is great. 10.4. (d) The greater the ratio between the moduli of elasticity for a cylindrical plant tissue, the greater is the ratio between the amounts of crystalline and amorphous cellulose in the average secondary cell wall of the tissue, the greater the percentage of cellulose in this wall, and the greater the orientation of cellulose molecules parallel to the axis of the plant tissue in this wall. 11. 11. The submicroscopic structure of the highly plastic primary cell wall is given by a molecular network of cellulose. In this network there is no cross-linking, the chain molecules of cellulose are only entangled with each other. 12. 12. The physical part of growth of primary cell walls is explained by passage of glucose units from protoplasm to the meshes of the cellulose network in the primary wall. The plasticity of this wall is great because the meshes contain fat and wax and because the loose molecular chains of cellulose are easily moved. The pressure of turgor producing the motion of glucose to the primary wall must be greater than the yield value for this wall. In this case a plastic deformation of the wall is possible. 13. 13. The influences of humidity, temperature and tension on the value of Young's modulus in cylindrical plant tissues were investigated. The results are: 13.1. (a) Decrease in the amount of water in a cylindrical plant tissue increases the value of Young's modulus. 13.2. (b) Increase of temperature for a cylindrical plant tissue decreases the value of Young's modulus. 13.3. (c) Young's modulus for a cylindrical plant tissue increases with increasing tension. The foregoing three cases are to be expected if there is no change in the submicroscopic structure of the plant tissue generally. Thus, by increased tension macroscopic soft spots of a plant tissue are solidified and Young's modulus is increased. According to Meyer and Lotmar it is not possible to assume a change in the orientation of the cellulose molecules in cellulosic fibers by increased tension thus causing Young's modulus to become greater (17). From the work of Kratky the influence of deformation on the amount of orientation of cellulose molecules is known. But, in the case of influence of tension on cellulosic fibers, the elongations are only 2–3%. These small elongations do not produce observable orientation of cellulose molecules. Therefore, we must conclude that the submicroscopic structure of plant tissues generally is not changed by the influences of humidity, temperature or tension.