First-order scaling near a second-order phase transition: Tricritical polymer collapse

– The coil-globule transition of an isolated polymer has been well established to be a second-order phase transition described by a standard tricritical O(0) field theory. We provide compelling evidence from Monte Carlo simulations in four dimensions, where mean-field theory should apply, that the approach to this (tri)critical point is dominated by the build-up of first-order–like singularities masking the second-order nature of the coil-globule transition: the distribution of the internal energy having two clear peaks that become more distinct and sharp as the tricritical point is approached. However, the distance between the peaks slowly decays to zero. The evidence shows that the position of this (pseudo) first-order transition is shifted by an amount from the tricritical point that is asymptotically much larger than the width of the transition region. An isolated polymer in solution is usually argued to be in one of three states depending on the strength of the inter-monomer interactions which are mediated by the solvent molecules and can be controlled via the temperature T . Let us define the radius of gyration exponent ν as RN ∼ N as N → ∞, (1) where RN is the radius of gyration. Note that confluent logarithmic factors may also appear in this form. At high temperatures and in so-called “good solvents” a polymer chain is expected to be in a swollen phase (swollen coil) relative to a reference Gaussian state so that the average size of the polymer, as measured by the radius of gyration, scales with chain length faster than it would if it were behaving as a random walk. In dimensions 2 and 3 it is expected that the swollen value of ν = νs > 1/2. At low temperatures or in poor solvents the polymer is expected to be in a collapsed globular form with a macroscopic density inside the polymer: this implying an average size that scales slower [1] than a random walk, in particular (∗) E-mail: [email protected] (∗∗) E-mail: [email protected]