## INTRODUCTION

The experimental and theoretical understanding of polymers is vast but confined almost exclusively to situations where they are in liquid or solid environments. However the advent of some recent technological advances has expanded their domain to the other environments as well, such as in a vacuum or a gas. Here, we shall review recent studies of this unusual situation.1–8 We shall see how polymers in a vacuum are expected to be fundamentally different in their characteristics than in the more common liquid environment. This will also have the benefit of elucidating the role inertia plays even in a liquid phase. In the following, I will review some systems in the low density state and why we expect them to contain a wealth of new physics.

Theoretical treatments of polymer dynamics generally start with the same basic assumption, that motion at the smallest scale is heavily overdamped so that inertia can be neglected.9, 10 For analyzing many experiments this is an excellent approximation. However there are some experimental systems where this approximation does not work and these situations are becoming increasingly important.

Theoretical treatments of polymer dynamics in solution usually start with a Langevin equation or something more approximate,9 such as the Metropolis algorithm, often used in Monte Carlo simulations.11 The Langevin equation can include hydrodynamic interactions and forces between atoms, and random thermal forces. However inertial effects are almost always neglected. Such massless models lead to an enormous wealth of phenomena and the highly successful prediction of important physical quantities such as viscoelastic behavior for a wide variety systems. By utilizing many theoretical techniques devised to understand the basic equations, such as scaling and the renormalization group, one can often see universal behavior spanning decades in concentration and chain length. This has made polymer dynamics one of the best understood areas in condensed matter physics.

First, let us briefly review the justification for neglecting inertia in the description of polymeric systems. In order for this to be justified, we have to be considering dynamics on large enough timescales. Most polymeric systems are studied in solutions or melts, and properties of experimental interest, such as visco-elastic properties are normally probed at timescales greater than a picosecond and length scales greater than a nanometer. When considering the dynamics of a macromolecule of mass *m*, there are inertial effects giving a force *m* where **r** is the center of mass position, and the dots represent time derivatives. The local drag force can be written *b***ṙ**, with the Stokes drag coefficient *b* = 6πη*R*, with η denoting the viscosity and *R* an average linear dimension. Comparing these terms dimensionally, gives a cross over timescale τ_{c} = *m*/*b*. Let us first estimate this value for something the size of a typical monomer, using the drag on a sphere of radius 10 Å in water, and *m* = 100 Da. This gives τ_{1} of about 10^{−14} s. For timescales much greater than this, inertia can confidently neglected.

Now let us look at what happens on larger length scales, say for a linear polymer of *N* units. The mass *m* ∝ *N* and the size of the molecule *R* ∝ *N*^{ν}. Then the crossover time will be τ_{N} ∼ *N*^{1 − ν}. ν for a compact chain is 1/3 and ∼ 3/5 for a polymer in good solvent.10 Therefore the cross over time increases as a power of chain length. However the overall relaxation time including only damping increases with a larger exponent, τ_{rel} ∝ *N*^{3ν}, or greater if the system is dense. Therefore inertial effects, in this case are not important on the relaxation time scale for a chain. However internal modes for high enough wave number will overlap with this inertial timescale. This is a crude argument, but it suggests that inertia will contribute to motion on intermediate timescales and it has indeed been possible to measure inertial effects in polymer dynamics, as we will see later, by a more detailed analysis of this problem.

The above analysis shows that although inertial effects do not dominate polymer dynamics in solutions, it suggests that effects on internal modes should be measurable. To understand this better, a useful question to ask is if there are real systems where the mass term is dominant. Therefore, we will first turn our attention to situations where damping is small and inertial effects determine the systems behavior. We will see that this case is highly unusual and exhibits very interesting behavior. Then we explain the crucial role the nonlinearity plays in low dimensional systems in the absence of an interacting bath. With this understanding, we will explain how this manifests itself in the case of polymer chains and can shed light on the internal friction in situations such as mentioned earlier. The consideration of polymeric systems with inertia leads to a large number of interesting question, most of which are still quite unexplored. There are also unusual features of the equilibrium properties of isolated polymers which are brought about by additional conservation laws in this situation but will not be described here in detail. The interested reader can consult the relevant literature.2, 3, 6, 7