Elongation and fluctuations of semi-flexible polymers in a nematic solventZ. Dogic,1J. Zhang,1A.W.C. Lau,1H. Aranda-Espinoza,2P. Dalhaimer,2D.E. Discher,2P.A. Janmey,2T.C. Lubensky,1and A.G. Yodh11Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 191042Institute for Medicine and Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104(Dated: Octob er 3, 2003)We directly visualize single p olymers with persistence lengths ranging from `p= 0.05 to 16 µm,dissolved in the nematic phase of rod-like fd virus. Polymers with sufficiently large persistencelength undergo a coil-rod transition at the isotropic-nematic transition of the background solvent.We quantitatively analyze the transverse fluctuations of semi-flexible polymers and show that atlong wavelengths they are driven by the fluctuating nematic background. We extract both theOdijk deflection length and the elastic constant of the background nematic phase from the data.PACS numbers: 61.30.-v, 64.70.Md, 82.35.PqPolymer coils in solution exhibit a variety of confor-mational and dynamical behaviors depending on manyfactors, including polymer concentration, polymer stiff-ness, solvent quality, solvent flow, and mechanical stress.Exciting recent experiments in this field have focused ondisentanglement of single biopolymers in isotropic solu-tions [1] as a result of externally applied forces and sol-vent flow, and on transport of single biopolymers throughnetworks of barriers [2] wherein conformational dynam-ics of the polymer play a critical role in affecting poly-mer separation. In this Letter, we explore the behaviorof polymer coils in anisotropic solutions. In particular,we present the first experimental investigation of isolatedsemi-flexible polymers dissolved in a background nematicphase composed of aligned rod-like macromolecules. Weshow by direct visualization that semi-flexible biopoly-mers in the nematic phase assume an elongated rod-likeconfiguration aligned with the background nematic di-rector. The coil-rod transition of the biopolymer canthus be tuned by varying the concentration of rods inthe background solvent so that the solvent undergoes anisotropic-nematic (I-N) phase transition. We quantita-tively explore the fluctuations of semi-flexible polymersand find they cannot be described by a theory whichtreats the nematic background as a fixed external field [3].Mixtures of semi-flexible polymers in lyotropic nematicsuspensions exemplify an emerging class of complex flu-ids – hyper-complex fluids, such as nematic elastomers [4]and nematic emulsions [5], wherein two or more distinctcomponents are combined to create systems that exhibitnovel physical properties and functions. Understand-ing the polymer-nematic system may lead to new ideasabout how to to achieve a high alignment of biopoly-mers, complementary, for instance, to existing methodsof DNA alignment [6]. Furthermore, since many biopoly-mers such as the actin filaments within the sarcomere andthe neurofilaments within the axon are in an anisotropic,nematic-like environment [7], our investigation may shedlight on the organization mechanisms within the cell.We have used fluorescence microscopy to study fourbiopolymers in isotropic and nematic colloidal suspen-TABLE I: The contour length L, the persistence length `p,and the diameter a of various polymers used in our experi-ments.Polymer L [µm] `p[µm] a [nm] Ref.λ-DNA 16 0.05 2 [18]neurofilament 2-10 0.2 10 [19]wormlike micelles 5-50 0.5 14 [17]F-actin 2-20 16 7 [20]fd virus 0.9 2.2 7 [13]sions. This approach yields new information about dy-namics and defects not readily accessible to traditionalprobes such as x-ray or neutron scattering [8]. In ad-dition, we have develop a rotationally-invariant free en-ergy for a single semiflexible p olymer in a nematic matrixwhich generalizes the work in [9, 10], and enables us toextract the Odijk length [11] and the elastic constant ofthe liquid crystal. These first direct measurements ofthe Odijk deflection length λ allow us to quantify thelength scale over which the polymer wanders before it isdeflected back by the nematic director.Our experiments employ an aqueous solution of rod-like fd viruses as a background nematic liquid crystal.This system has been studied extensively [12–14], andits phase behavior is well described by the Onsager the-ory for rods with hard core repulsion [15]. Another ad-vantage of this system is its compatibility with mostbiopolymers. We use four different semi-flexible poly-mers, whose diverse physical parameters are listed in Ta-ble I. To directly visualize the polymers dissolved inthe nematic background, we fluorescently labelled eachpolymer: DNA was labelled with YOYO-1 (MolecularProbes, Eugene OR), neurofilaments with succinimidylrhodamine B [16], F-actin filaments with rhodamine-phalloidin (Sigma, St. Louis MO), and wormlike micelleswith PKH26 dye (Sigma, St. Louis MO) which preferen-tially partitions into the hydrophobic core of the micelle.Since DNA, neurofilaments, and actin are all negativelycharged, we expect that they are stable in a suspension ofnegatively charged fd viruses. Wormlike micelles are ster-2ically stabilized with a neutral PEO brush layer, whichdoes not interact with fd virus or other proteins [13, 17].Bacteriophage fd was grown and dialyzed against aphosphate buffer as previously described (150 mM KCl,20 mM phosphate, 2 mM MgCl2, pH=7.0) [13]. Sampleswere prepared by mixing a small amount of polymer withfd solution at different concentrations and were placedbetween a coverslip and a glass slide. A chamber witha thickness of ∼ 50 µm was made by using a stretchedparafilm as a spacer. Samples sealed with optical glue(Norland Products, Cranbury, NJ) were allowed to equi-librate until no drift was visually detectable. To reducezbacdefisotropic nematicFIG. 1: Images of fluorescently labelled biopolymers in theisotropic (left) and nematic (right) phase of fd virus. Figures(a)-(d) are, respectively, the images of actin, wormlike mi-celles, neurofilaments, and DNA. The polymers in an isotropicsolution are confined by a thin chamber thus making the sam-ples quasi two dimensional. (e) A sequence of images illustrat-ing an actin filament escaping from a hairpin defect. The scalebar is 5 µm. (f) Schematic of a biopolymer in the backgroundnematic field; the conformation of the polymer is parameter-ized by R(z) = { rx(z), ry(z), z}. The nematic director pointsalong the