# What formula should I use to calculate the total energy of a linear polymer chain?

I am using the Bead-spring model to model a polymer chain.

Suppose, the polymer has 3 monomers in its chain:
$$\ce{A1-A2-A3}$$

And,

I can use the following formula to calculate the total Lennard-Jones potential: $$U_{LJ}(r) = U_{12}(r_{12}) + U_{23}(r_{23}) + U_{31}(r_{31})$$

Where,

$$U_{ij}(r_{ij}) = 4 \cdot \epsilon \cdot \left[ \left(\frac{\sigma}{r_{ij}}\right)^{12} -\left(\frac{\sigma}{r_{ij}}\right)^{6} \right]$$

Since we also have two springs here, we have to use the following formula to model the total spring potential:

$$U_{spring}=U_{1, 2}(r_{1,2}) + U_{2, 3}(r_{2,3})$$

where,

$$U_{i, i+1}=k(r_{i, i+1} - 3.8)^2$$

So, the total potential of the polymer chain would be:

$$U_{total} = U_{ij}(r_{ij})+U_{spring}$$

Now, as far as I know, total potential and total energy are two different things in the case of a polymer.

What formula should I use to calculate the total energy of a linear polymer chain?

• You need to understand what a force field is and how it works. The total potential energy of a system is a sum of different contributions, not only two.
– Camps
Apr 26, 2022 at 20:32

The difference between total potential energy and total energy is just the kinetic energy, which is the sum of the kinetic energies of your particles, $$E_K = \frac{1}{2}\sum_{i=1}^3 m_i v_i^2$$
where $$m_i$$ are masses and $$v_i$$ are velocities.