Your understanding of reduced units in molecular dynamics simulations is on the right track. Reduced units are a way to scale the physical properties of a system so that certain parameters are set to unity, which can simplify calculations and make the simulation more general. Here’s a clearer explanation of reduced units and how they apply to your polymer in water simulation:

Reduced Units:

In reduced units, the following parameters are often set to 1:

• Length (σ): The length unit is typically set to the size of a particle, which could be the van der Waals radius or another relevant length scale.
• Energy (ε): The energy unit is often set to the strength of the pairwise Lennard-Jones interaction between particles.
• Mass (m): The mass unit is set to the mass of a particle in the system.

These units are defined relative to the system you are studying. For example, in a Lennard-Jones fluid, σ might be the distance at which the interparticle potential is zero, and ε might be the depth of the potential well.

Are All Parameters Equal to One?

No, not all parameters are equal to one. Only the base units (length, energy, and mass) are set to one. Other parameters, such as bond lengths, angles, charges, and force constants, are scaled relative to these base units. Here’s how it works for your polymer in water system:

• Bond lengths and angles: These are scaled relative to the length unit (σ). For example, if a bond length in your polymer is 0.2 nm, and σ is defined as 0.1 nm, then the bond length in reduced units would be 2σ.
• Charges: These are scaled relative to the square root of the energy unit (ε) divided by the length unit (σ). This ensures that the electrostatic interaction energy has the correct dimensions.
• Force constants: For bonded interactions like harmonic bonds and angles, the force constants are scaled relative to the energy unit (ε) and the length or angle unit.

Simulating a Real Model:

When you perform a simulation in reduced units, you are still simulating a real model. The advantage is that the simulation becomes more general and can be applied to a wide range of systems with similar interactions. The parameters you use (like σ, ε, and m) are chosen to reflect the physical properties of the actual system you are studying.

Polymer in Water:

For a polymer in water, you would typically define your reduced units based on the properties of the solvent (water) and the polymer. For example:

• Length (σ): Could be set to the oxygen-oxygen van der Waals distance in water.
• Energy (ε): Could be set to the strength of the Lennard-Jones interaction between water molecules.
• Mass (m): Could be set to the mass of a water molecule.

Then, the polymer’s properties would be scaled accordingly. This does not mean you are simulating a ball and spring model; rather, it’s a way to abstract the physical properties to a set of units that makes the simulation more manageable and computationally efficient.

In summary, using reduced units does not mean you are simulating a non-real model. It is a way to standardize the system so that the simulation can be applied broadly while still reflecting the physical properties of the real system. The choice of what parameters to set to one and how to scale the others depends on the specifics of the system you are simulating.

In reduced units, parameters like sigma, epsilon, and mass are set relative to a reference, simplifying comparisons across systems. For polymers, different atoms may have different reduced parameters depending on scaling choices, but the approach still generalizes interactions.

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