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

Suppose, the polymer has 3 monomers in its chain:


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


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

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

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


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

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?

  • 2
    $\begingroup$ 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. $\endgroup$
    – Camps
    Apr 26, 2022 at 20:32

1 Answer 1


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.

  • $\begingroup$ Please, kindly, either describe these terms or refer to a citation where they are already described. $\endgroup$
    – user366312
    Apr 26, 2022 at 22:54
  • $\begingroup$ Perhaps you could start here: en.m.wikipedia.org/wiki/Kinetic_energy $\endgroup$
    – Hayden S
    Apr 26, 2022 at 22:55

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