Macromolecular Dynamics and Rouse Model

A measure of how easily a polymer chain can move through a narrow space, like a tube. It's determined by the chain's velocity in response to a force along the tube's direction.

The friction force acting on a polymer chain inside a tube. It's directly proportional to the length of the chain, meaning longer chains experience more friction.

A measure of how quickly a polymer chain diffuses in a tube. It's related to the tube mobility and temperature.

The average time it takes for a polymer chain to move its entire length in a tube. It's proportional to the cube of the chain length, meaning very long chains take much longer to move.

A measure of the polymer's ability to relax its shape, like the stress it experiences, after a deformation. It's affected by factors like the polymer's chain length and temperature.

A simplified model representing a polymer chain as a series of beads (subunits) connected by springs, where the springs obey Hooke's law and act as universal joints. This model considers frictional forces, inter-subunit forces, and random collisions with the surrounding medium.

The behavior of a polymer chain moving through a network of fixed obstacles, like a worm wriggling through a tube. It involves the chain leaving parts of its path and creating new ones, leading to a gradual renewal of its trajectory.

The region or path within a network of obstacles where a polymer chain is confined by the obstacles. It is a space in the network through which the chain can move.

The characteristic time it takes for a polymer chain undergoing reptation to completely renew its tube (path) through a network of obstacles. It is a measure of how long it takes for the chain to reorient itself within the network.

In the Rouse model, the viscosity (resistance to flow) of a polymer melt (molten plastic) is directly proportional to the number of repeat units (monomers) in the polymer chain. This relationship holds for low molar masses.

Entanglements are physical interconnections between polymer chains in a melt, where the chains cannot move freely past each other. These entanglements significantly impact the viscosity of the melt.

At high molar masses, the viscosity of a polymer melt does not simply scale linearly with the chain length (M), but instead shows a much stronger dependence, typically proportional to M raised to the power of 3.5. This behaviour arises due to chain entanglements.

The critical molar mass (Mcr) is a threshold value where polymer chains begin to exhibit entanglement effects. Below Mcr, the Rouse model accurately predicts viscosity. Above Mcr, entanglement effects dominate, and the viscosity increases significantly with molar mass.