# How to explain the elasticity of polymers from the

2022-09-27
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How to explain the elasticity of polymers at the molecular level

to understand the elasticity of polymers at the molecular level, we must first see how the elasticity of a polymer chain (Gaussian chain) comes from. In order to make this answer more understandable, I decided to make an analogy first. If there is a non retractable rope, and the distance between the two ends of the rope can be changed, the shorter the distance between the ends of the rope, the higher the chaos of the rope (the more states may exist). There is only one state when the rope is completely stretched. For a microscopic polymer chain molecule, the straightening process is an entropy reduction process, which requires energy consumption, and the consumed energy is converted into elastic potential energy

at the microscopic level, we can use an entropy elasticity model to describe this phenomenon:

due to the conservation of energy, the elastic force of a polymer chain is equal to the first-order derivative of Helmholtz free energy to the end distance vector:

the internal energy of this polymer chain is composed of kinetic energy and potential energy. Kinetic energy is mainly determined by temperature and has little to do with conformation, The potential energy is mainly caused by the interaction between chain nodes (repulsion and attraction)

here, it is assumed that the internal energy of the Gaussian chain is independent of the end distance vector, so it can be obtained:

the magnitude of the elastic force can be derived from the Boltzmann relation and the end distribution function of the Gaussian chain (i.e. the number of microscopic states)

among them, the end distribution function can be derived from the random walk model:

a certain plastic strain will be produced locally.

substituting the two formulas into the elastic force will affect the braking performance solution to varying degrees, It can be concluded that for the projection on any axis, the elastic force has the following relationship with the end distance:

in the formula, and are the projection of the elastic force and the end distance on the Z axis respectively, K is the Boltzmann constant, t is the thermodynamic temperature, n is the number of chain links, L6, packaging and process performance experimental instruments (including packaging drop experimental instruments, packaging impact experimental instruments, friction and wear experimental instruments, bending experimental instruments, straightening machines, etc.); Is the Kuhn length. Because the elastic force of polymer chain mainly comes from the entropy change in the stretching process, it is called entropy elasticity. Entropy elasticity, as described above, conforms to Hooke's law

then, let me further explain the other questions of the subject. For the elasticity of rubber (cross-linked polymer), it is necessary to understand how to apply the elasticity of the above polymer chain in the polymer complex. In fact, a polymer complex can be understood as a structure composed of polymer chains between crosslinking points, that is, in the process of stretching rubber, the whole polymer complex structure changes macroscopically, and the polymer chains between crosslinking points change in compression or tension microscopically, so the rubber elasticity of the whole polymer complex is actually the vector sum of the elastic forces of the polymer chains between crosslinking points

the relationship between crosslinking degree and elastic force can be further understood. The increase of crosslinking degree leads to the decrease of the number of links between crosslinking points, that is, the elastic coefficient in the above formula increases, and the result is that the rubber hardens (the elastic modulus increases)

as for ignoring the interaction between links, it is not contradictory to the cross-linking of disulfide bonds, because the entropy elasticity model is applied to the chain segments between cross-linking points, without considering the cross-linking point itself

several factors are involved in the properties of polyethylene and nylon. First, the polymer without crosslinking will yield after deformation beyond a certain range, which is mainly caused by the slippage of the polymer chain. Secondly, HDPE is crystalline, so its elastic modulus is very large, and it is difficult to observe deformation. Because the modulus of LDPE is relatively low, it conforms to Hooke's law in a large range. In line, nylon is lower than the glass transition temperature at room temperature, so there is no long-range link movement, so the elastic modulus is also large

there are many types of polyethylene, including low density, linear low density, high density, ultra-high density, etc., so if you want to understand the specific force and thermal properties of a certain kind, you need to query individually. I have used g. R. Strobl's the physics of polymer Kunming Hengda science and Technology Co., Ltd. is composed of natural persons, Kunming University of science and technology, Hongta Innovation Investment Co., Ltd. and other shareholders. You can read it according to your own interests

for common linear polymers, the elastic modulus should decrease with the increase of temperature

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