Hysteretic Conformational Transition of Single Flexible Polyelectrolyte under Resonant AC Electric Polarization

There is growing interest in modifying the conformational structures of polyelectrolytes, whose repeating monomers bear ionizable groups in aqueous media. Effective and reversible structural manipulation of polyelectrolytes, including proteins and DNAs, is important not only to fundamentally understand many biomacromolecular processes, such as protein folding and DNA packaging into chromosomes, but also to broad applications from emerging bionanotechnology to energy conversion. As these conformations are realizable in nature, their free energies and the energy barriers between them are often of the order of thermal energy, kBT. Because the adopted conformations of polyelectrolytes are highly sensitive to the local electrostatic environment, dc or low-frequency ac electric fields have been used to manipulate polyelectrolyte chains in aqueous solutions by redistributing counterions surrounding the polyelectrolyte backbones. However, the large forces of dc mean fields, with corresponding energies larger than thermal noise, often remove the possibility of multiple free energy minima with different molecular conformations, thus preventing reversible and hysteretic transitions between different molecular conformation states;although hydrodynamic or field screening effects can produce hysteretic changes in the molecular dimension or hydrodynamic radius. Moreover, dc or low-frequency ac electric fields produce net electro-osmotic flow and electrode redox reactions, which can camouflage the direct effect of the electric field on the polyelectrolyte conformation. In this work, we employ spatially uniform ac fields of high frequency to induce the conformational changes in single flexible polyelectrolyte chains, such that ac-electrokinetic-induced flow and Faradaic reactions are eliminated to preserve thermal noise-driven conformational transitions. Recent polarization experiments with ac frequencies beyond the inverse charge relaxation timeof themolecules, that is, theRC (resistance-capacitance) time required for the molecules to neutralize any field-induced charge polarization, suggest that high-frequency ac field is more effective in depleting or concentrating the counterions around nanocolloids and molecules with capacitive charging ion currents. As such dynamic polarization is transient, the hysteretic molecular conformation transitions should be retained but converted to that with respect to frequency variation. We augment this strong high-frequency ac polarization of counterions to induce charge density changes along the polyelectrolyte. The charge polarization of polyelectrolytes under dc or low-frequency ac fields has been theoretically studied and reviewed. Yet prior work hasmainly focused on “strong” polyelectrolytes whose charges are fixed and neutralized by the localized counterions, known as “condensed counterions”. The effect of ac electric fields is thus limited tomobile counterions in the diffusive double layer and not the condensed ones in the Stern layer, resulting in simply modifying the screening ion cloud near a polyelectrolyte without fundamentally changing its charge density. However, for the large class of “weak” polyelectrolytes, whose charges are mobile and highly tunable by the local counterion concentration, their polarization and resulting conformational dynamics under an ac field could be drastically different and yet remains poorly understood. Field-induced counterion dissociation and condensation are expected to sensitively produce nonuniform charge density variation (to the extent of inverting the charge) along the backbones of such polyelectrolytes and can hence readily induce reversible thermal noise-drivenpolyelectrolyte conformational transitions;not just changes in the radius of gyration. The coil-to-globule transition (CGT) of polyelectrolytes is considered to be a complicated process governed by charge fraction, molecular architecture, and intermolecular interactions. In contrast to a gradual CGT process for flexible neutral polymers, an abrupt first-order CGT has been predicted by theory and computer simulation but is only confirmed until recently in single-molecule experiments by using AFM and fluorescence correlation spectroscopy (FCS). The CGT of polyelectrolytes can be realized by varying the pH or ionic strength or adding condensing agents, which inevitably modify the solution chemistry to make the transition highly irreversible. In this Communication, we report a reversible and gradual ac-fieldinduced CGT of a synthetic weak polyelectrolyte, poly(2-vinylpyridine) (P2VP), in dilute aqueous solutions at varied ac frequency, ω, and strength, Epp, by using FCS at a single molecule resolution (see Supporting Information for experimental details). Briefly, the experimental setup of one-photon FCS is based on an inverted microscope (Zeiss Axio A1) equipped with an oil-immersion objective lens (100 , NA=1.4). The tiny fluctuations, I(t), in fluorescence intensity, due to the motion of fluorescent molecules in and out of the laser excitation volume, with an Ar laser (Melles Griot, λ=488 nm) are measured by two singlephoton counting modules (Hamamatsu) independently in a confocal detection geometry at a sampling frequency of 100 kHz in this work. The autocorrelation function, G(τ), of measured I(t) as GðτÞ 1⁄4 AEδIðtÞδIðtþ τÞae=AEIðtÞae ð1Þ