We study the process of charged polymer translocation, driven by an external electric potential, through a narrow pore in a membrane. We assume that the number of polymer segments, m, having passed the entrance pore mouth, is a slow variable governing the translocation process. Outside the pore the probability that there is an end segment at the entrance pore mouth, is taken as the relevant parameter. In particular we derive an expression for the free energy as a function of m, F(m). F(m) is used in the Smoluchowski equation in order to obtain the flux of polymers through the pore. In the low voltage regime we find a thresholdlike behavior and exponential dependence on voltage. Above this regime the flux depends linearly on the applied voltage. At very high voltages the process is diffusion limited and the flux saturates to a constant value. The model accounts for all features of the recent experiments by Henrickson et al. [Phys. Rev. Lett. 85, 3057 (2000)] for the flux of DNA molecules through an α-hemolysin pore as a function of applied voltage.

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The elution chromatography of flexible polymer molecules flowing through a microporous particle media is described by a combination of the Casassa model of flow segregation and the Di Marzio−Rubin lattice method for calculating the partition function of confined polymers. This combination of models allows for the treatment of polymer-surface interactions so that polymer chromatography in the exclusion and adsorption regimes can be described within a unified framework. The compensation point where repulsive polymer-surface excluded volume forces and short-range polymer-surface attractive forces counterbalance each other offers opportunities for separating complex molecules. For example, calculations for a diblock copolymer where one of the components is at the compensation point (“adsorption ϑ point”) indicate that only the remaining block influences the elution of the block copolymer as a whole. This theoretical result accords with experiments on block copolymers. This singular observation provides support for the Casassa viewpoint of molecular partitioning dominated polymer elution. The chromatography of triblock copolymers, stars, and combs is also examined to determine the selectivity of elution chromatography for separating these molecular architectures. The theoretical development in the present paper should lead to improved methods for the characterization of polymers with different molecular architectures. These developments also suggest new tools for studying polymer adsorption from dilute solution.

The problem of a polymer molecule whose two ends reside on opposite sides of a membrane or partition separating two solutions is solved exactly in the limit of no self-excluded volume. The monomers can go from one side of the membrane to the other only by threading serially through one hole in the membrane. The ends can be free, confined to run freely on the membrane surfaces, or be fixed to specific points on the membrane. It is found that the equilibrium thermodynamic phase transition is first order in all cases so that slight changes in pH, ionic strength, or temperature can move the polymer from being completely on one side of the membrane to being completely on the other side. Application to two biological problems are suggested: (1) the breaching of cell walls by the nuclear material of T2 bacteriophages, and (2) the transport of drugs that are affixed to these translocating polymers. The relation of this newly discovered transition to four other phase transitions that occur in isolated macromolecules (helix–random coil; equilibrium polymerization; polymer collapse; surface adsorption) is briefly discussed.

A mean-field treatment is given which enables us to solve for the dimensions of star molecules in both the expanded and collapsed states as well as all intermediate regimes. The scaling laws of Daoud and Cotton are recovered. For g" the ratio of the radius of gyration of a star of Farms to that of a linear chain, we obtain gs = 1.74F~4/5 which is smaller than computer generated data by about 6%.