Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Persistence Length of Poly(vinyl amine): Quantitative Image Analysis versus Single Molecule Force Response Svilen Kozhuharov,† Milad Radiom,†,‡ Plinio Maroni,† and Michal Borkovec*,† †
Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, 30 Quai Ernest-Ansermet, 1205 Geneva, Switzerland ‡ School of Chemical Science and Engineering, KTH Royal Institute of Technology, Drottning Kristinas väg 51, Stockholm 10044, Sweden ABSTRACT: Single molecules of poly(vinyl amine) are analyzed in the adsorbed state by atomic force microscopy (AFM) in two different ways. First, high-resolution images of individual adsorbed polymers were recorded in monovalent electrolyte solutions. The backbone of the imaged polymers was digitized, and the directional correlation function and internal mean-square end-to-end distance were evaluated. These quantities were analyzed with the wormlike chain (WLC) model, and the persistence length was extracted. Second, individual polymer chains were picked up from the surface, and their force−extension behavior was recorded in the same electrolyte solutions. These force profiles were also interpreted in terms of the WLC model, whereby the elastic contribution was also considered. Both techniques yield the persistence length of the polymer. From imaging one obtains a persistence length of about 1.6 nm, while the force experiments yield a value around 0.51 nm. We suspect that the force experiments reflect the intrinsic part of the persistence length, while the imaging experiments yield the persistence length including the electrostatic part.
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INTRODUCTION The question of the persistence length of polyelectrolytes has been of substantial interest in the polymer science community. In their classical work, Odijk, Skolnik, and Fixman (OSF) suggested that this length has two contributions, namely the intrinsic part, which originates from the stiffness of the polymer backbone, and an electrostatic part, which is related to the electrostatic repulsion between the individual charged polymer segments.1,2 These authors have further proposed that the electrostatic part decreases very strongly with the salt concentration,1,2 while subsequent simulations and variational calculations suggest a weaker dependence.3−6 Because of the substantial interest in these questions, the persistence length was studied experimentally for DNA as well as for synthetic polyelectrolytes in detail. Most studies have relied on bulk techniques, which investigate properties of polymer solutions. These techniques include light, X-ray and neutron scattering, viscosity measurements, or birefringence.7−20 However, interpretation of such results is often complicated due to effects of polydispersity or interactions between the polymer chains. More recently, various techniques became available, which allow extracting the persistence length on the single molecule level. These modern tools comprise optical microscopy techniques based on fluorescence9 or various scanning probe techniques. In particular, the atomic force microscope (AFM) has been used to image individual DNA, polysaccharides, or polyelectrolytes.10−13,21−25 The stretching response of individ© XXXX American Chemical Society
ual DNA or protein molecule as well as polymer chains subject to external force can also be recorded with the AFM or by means of magnetic tweezers.26−33 Both types of experiments allow the determination of the persistence length on the single molecule level. A clear advantage of such single molecule techniques is that the respective results are independent of sample polydispersity. While the analysis of single molecules is promising, this approach is plagued by difficulties. The AFM imaging is commonly carried out in the dried state, which may induce uncontrolled drying artifacts.21−24 Analysis of the stretching response with the AFM did suffer from limited force resolution of the earlier generations of the AFMs.27−29 While magnetic tweezers offer superior force resolution, they only cover a relatively small force range and requite extremely long polymer molecules.30,31 Persistence lengths extracted from force profiles seem to be systematically smaller than the ones obtained by other techniques, even though definitive comparisons are lacking. The present study shows how to circumvent some of these difficulties with the recent generation of AFMs. These instruments use very small cantilevers with high resonance frequencies, which allow obtaining high-resolution images in liquids. Moreover, force profiles can be recorded with an improved accuracy, which results in a more straightforward data Received: April 19, 2018
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DOI: 10.1021/acs.macromol.8b00834 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
product of the tangent unit vector n evaluated at two different separations of the contour length s. Within the WLC model this correlation function decays exponentially, namely
interpretation. Here, we exploit these techniques to estimate the persistence length for single polyelectrolytes molecules in two independent ways, namely by imaging and from force extension profiles. With the same systems, we confirm that this quantity obtained from force experiments is indeed substantially smaller than the one from imaging. We deliberately focus on a well-studied polyelectrolyte, namely poly(vinyl amine) (PVA), in order to facilitate the comparison with previous work.
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⎛ s⎞ ⟨n(s)·n(0)⟩ = exp⎜ − ⎟ ⎝ 2l ⎠
(1)
The second approach relies on the internal end-to-end distance ρ, whose mean-square average can be evaluated by integrating eq 1. The respective expression reads
⎡ ⎛ s ⎞⎤ ⟨ρ2 (s)⟩ = 4ls − 8l 2⎢1 − exp⎜ − ⎟⎥ ⎝ 2l ⎠⎦ ⎣
EXPERIMENTAL SECTION
Materials. Poly(vinylamine) (PVA) was synthesized by the BASF (Ludwigshafen, Germany). The sample has a molecular mass of 520 kg/mol and a degree of hydrolysis of a 94.3% and was used as received. The same PVA sample was used in previous studies.22,28 For a similar PVA sample, the polydispersity index was estimated to be 1.66.22 To carry out the experiments, PVA was adsorbed to different substrates from solutions of appropriate concentrations in Milli-Q water. Solution pH was adjusted to 2.5 with dilute HCl and the ionic strength by KCl. PVA-free electrolyte solutions of the same pH and ionic strength were used for rinsing and to carry out the AFM experiments. The temperature during all experiments was 25.0 ± 0.2 °C. Imaging Experiments. A freshly cleaved mica sheet (Pelco Mica Sheets, Ted Pella, Inc., Cat. #53) was incubated for 1 min in a solution of PVA in the respective electrolyte of a concentration of 0.1 mg/L. Loosely bound molecules were removed by rinsing the mica sheet with the respective electrolyte solutions. Imaging was carried out in the same PVA-free electrolyte solution with the Cypher ES AFM (Asylum Research, Santa Barbara, CA) in an airtight fluid cell mounted in the environmental scanner (Asylum Research, Santa Barbara, CA). This cell also includes a hermetically sealed cantilever holder and thus avoids solvent evaporation during experiments. Biolever-mini cantilevers (BL-AC40TS-C2, Olympus, Japan) with silicon tips with a tip radius of
