Single Molecule Visualizations of Polymer Partitioning within Model Pore Geometries Dmytro Nykypanchuk, † Helmut H. Strey, ‡ and David A. Hoagland* ,† Department of Polymer Science and Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003, and Department of Biomedical Engineering, Stony Brook University, Stony Brook, New York 11794 Received September 20, 2004; Revised Manuscript Received October 19, 2004 ABSTRACT: Probing the thermodynamics of polymer confinement in small pores, single DNA molecules were imaged by fluorescence microscopy as they partitioned within a pair of adjacent interconnected spherical cavities prepared by the colloidal templating method. This method produces pores of precisely known geometry and controlled level of confinement. As expected, a polymer weakly or moderately confined by cavities of unequal diameter was observed to maximize its configurational entropy by partitioning toward the larger cavity. The polymer’s cavity-to-cavity partition coefficient could be derived from the visualized bias in cavity occupation, and segmental excluded volume notably influences how this coefficient depends on chain length and two cavity sizes. A DNA molecule strongly confined within a pair of equal- sized cavities predominately adopts “bridging” configurations, splitting its segments between the two cavities. Segmental excluded-volume stabilizes such configurations; the stability reveals that a chain must overcome a doubly peaked energy barrier to move between cavities. Introduction Confining a flexible polymer in a small pore reduces the molecule’s configurational entropy. Confronted with a pore space offering different levels of confinement at different locations, such a polymer can maximize its entropy by partitioning to (preferentially occupying) the location or locations where the molecule is able to adopt the largest number of configurations. At equilibrium, partitioning eliminates inhomogeneities of chemical potential by creating inhomogeneites of polymer con- centration. Bigger polymers suffer more strongly from partitioning than smaller ones, a trend exploited in many methods that separate polymers by molecular size (gel permeation chromatography, gel electrophoresis). Although the importance of confinement-mediated par- titioning is widely appreciated, 1-4 molecular theories for the effect have not been experimentally tested in a systematic series of well-defined pore geometries, and the dynamic partitioning process has not been visual- ized. Here, we describe real-time, single-molecule imag- ing of flexible polymers (DNA molecules) partitioned within pore spaces prepared by the colloidal templating method. Our approach provides a quantitative, molec- ular-level assessment of polymer partitioning and af- fords many insights into the dynamics of heteroge- neously confined polymers. Equilibrium partitioning of solute between two re- gions of dissimilar free energy is quantified through the partition coefficient K, the ratio of the two solute concentrations. Porous materials that create spatial variations of free energy for polymeric solutes are usually chosen so that spatial variations of enthalpy are negligible. If so, by picking an unconfined region as the reference state, K ) exp(ΔS c /k), where ΔS c is the confinement entropy and k is the Boltzmann constant. Employing a Gaussian description for a confined chain and allowing the chain to sample equally all configura- tions not intersecting pore boundaries, Casassa 5 devel- oped the earliest theories of ΔS c germane to flexible polymers. Analytical results were reported for chains trapped within spherical, cylindrical, and slitlike pores. For a polymer of average end-to-end distance R parti- tioned into a pore of comparable or smaller size D,a Gaussian chain description leads to a scaling relation- ship, where N is the polymer’s number of Kuhn segments. Scaling relationships for ΔS c are extensively discussed in de Gennes. 3 Several features missing in a Gaussian chain descrip- tion can significantly influence ΔS c . In a good solvent, excluded volume effectively precludes overlap of chain segments, and an unconfined flexible polymer responds by swelling. Pore walls frustrate this swelling, thereby increasing |ΔS c | from its Gaussian chain value. For chains of finite stiffness/length, confinement models must replace Gaussian chain statistics with wormlike chain statistics. 6-9 Assessed at equal R, |ΔS c | for a wormlike chain is usually less than for a Gaussian chain (pore geometry affects the direction of the trend). Finally, nondilute chains in a good solvent feel each other even as they interact with pore walls, and the correlation length of the bulk solution supersedes R as the polymer length governing partitioning. Computa- tional methods, along with more sophisticated scaling approaches, address deficiencies of the Gaussian chain description, and detailed results have been reported for several idealized confinement geometries. 9-15 Sorption, size exclusion chromatography, and inter- ferometry experiments have all provided average K values for flexible polymers partitioned from solution into bulk materials possessing geometrically ill char- acterized and/or polydisperse pores. 16-19 For dilute polymer solutions, trends fall roughly in line with predictions derived using the Gaussian chain descrip- tion. Recently, a conductance method has been applied to the study of polymers partitioned within membrane- † University of Massachusetts Amherst. ‡ Stony Brook University. * To whom correspondence should be addressed. E-mail dah@ neurotica.pse.umass.edu. ΔS c ∼ N/D 2 (1) 145 Macromolecules 2005, 38, 145-150 10.1021/ma048062n CCC: $30.25 © 2005 American Chemical Society Published on Web 12/16/2004