Odijk skolnick fixman Analysis of the salt dependence of this regime indicates that the polymer’s Kuhn length is proportional to the NaCl and confirmed a good agreement with the theory of Odijk, Skolnick and Fixman (Odijk, 1977, 1978; Odijk & Houwaart, 1978; Skolnick & Fixman, 1977), i. Indeed, Fouissac, Milas, Rinaudo, and Borsali (1992) studied the dependence of the radius of gyration (R g) on the concentration of NaCl and confirmed a good agreement with the theory of Odijk, Skolnick and Fixman (Odijk, 1977, Odijk, 1978, Odijk and Houwaart, 1978, Skolnick and Fixman, 1977), i. 19,22 This result agrees with only one of the two prevailing models for polyelectrolyte structure: it disagrees with the Odijk-Skolnick-Fixman (OSF) prediction ( ℓ ∼ r D 2 ) 53,54 but agrees This stiffness follows Odijk–Skolnick–Fixman theory (17, 18) (l p ∼ l p,0 + I −1), where l p,0 is the persistence length excluding electrostatic considerations, which governs the average dimension of a DNA random coil, explicitly described by the radius of gyration: (R G ∼ l p 1 / 5 (λ D + λ D log λ D). 1 Intrinsically stiff chains: The Odijk-Skolnick-Fixman theory Odijk 2 and, independently, Skolnick and Fixman 3 were the first to develop a theory for persistence length of polyelectrolyte. Conformation of single polyelectrolytes in tetravalent salt solutions is investigated under the framework of a We provide experimental evidence for the electrostatically related excluded‐volume effects on the colligative properties and the single chain behavior of polyelectrolyte solutions in the dilute regime. 39, 41,42 Initially, Odijk 43 and Skolnick and Fixman (OSF) 44 proposed that the persistence length of a rodlike highly charged polyelectrolyte such as DNA should depend on Debye screening length In the pioneering work of Odijk, 1 Skolnick and Fixman 2 (OSF), a Debye–Hückel based approach to modeling electrostatic interactions was used to define an electrostatic persistence length of semiflexible polyelectrolytes proportional to the square of the Debye screening length. by the Odijk-Skolnick-Fixman (OSF) theory, applicable to rigid and semi-flexible chains [19, 20]. The ionic strength dependence of persistence length was similar in all segments, indicating that the residual differences in the elasticity of the segments derive from nonelectrostatic mechanisms. We argue that the observed features of the kHz range relaxation are due to much weaker electrostatic interactions that lead to the absence of Manning condensation as well as a rather high flexibility of HA as compared to DNA. There is currently no consensus that the classical perspective of electrostatic persistence length (the so-called Odijk–Skolnick–Fixman, or OSF, formulation), derived by equating changes in OSF - Odijk-Skolnick-Fixman. This effect introduces a new length scale, known as the Skolnick–Fixman–Odijk length. An induced attraction between monomers is due to thermal fluctuations and correlations We observe no significant deviations from the prediction l e∝κ-2 by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity using the Odijk-Skolnick-Fixman (OSF) electrostatic-sti ening model, in which salt-dependent Debye-Huc kel (DH) screening modulates intra-chain repulsion. Article Google Scholar Our results are in qualitative agreement with the classical Odijk−Skolnick−Fixman (OSF) theory, 52,53 which predicts that persistence length should be proportional to κ −2 , where κ −1 A detailed discussion of the κ dependence of the persistence length by far exceeds the focus of the current paper, but we would like to point out that recent simulations and scaling considerations for long flexible polyelectrolytes [146–148, 162] are in agreement with the original prediction l ~ κ –2 by Odijk and Skolnick and Fixman for theories of the Odijk-Skolnick-Fixman (OSF) type (23–25). For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations We found a large discrepancy between the Odijk, Skolnick and Fixman theory and our measurements. The essence of the Odijk and Skolnick-Fixman argument is that bending a charged rod will bring charges into closer proximity, which will cost more energy if there are fewer screening counterions and, therefore, the stiffness will be increased at low salt. thesis, “Investigations on a Rod Like Polyelectrolyte Model”, focused on polymer statistical mechanics with Dr. The viscosities of aqueous sodium alginate solutions were measured in different NaCl concentrations (Cs) at 298 K. IOP Publishing (opens in a new tab) Save. The effective potentials between ions are systematically parametrized using a relative entropy coarse-graining approach [Carmichael, S. The obtained results represent a new insight into the conformation and mechanical characteristics of HA molecules and complement the characterization of this biopolymer by bulk methods. e. Semidilute solutions 6. In order to shed additional light on the behavior of ds-DNA in solutions of polyvalent salts we thus embark on a systematic study of the dielectric response of DNA solutions in multivalent salt bathing solutions. We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. We show that there are strong local turian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. Marshall Fixman. 02 M were roughly 70% larger than predlcted by the Le Bret theory and the Odijk-Skolnick-Fixman theory. theoretical studies [17, 18] and very recent sim ulations [9, 10]. A Gaussian variational method is employed, taking $\\ell_{\\rm e}$ as the only variational parameter. Google Scholar [2] Skolnick J and Fixman M 1977 Macromolecules 10 944. In this paper we revisited the problem of persistence length of polyelectrolytes. As a point of departure we choose the Elements of Odijk-Skolnick-Fixman and Yamakawa-Fujii polymer solution theories have been modified to create a new model that correlates flexible coil polyion intrinsic viscosity behavior with solvent and polymer properties. The latter approach is adopted in the present paper. Finally, we show that the low-force elasticity becomes linear (γ = 1) at ≈ 3 M salt, and interpret this as a Θ point of the polymer. The results are in agreement with the picture outlined in the Odijk-Skolnick-Fixman theory, in which the behavior of charged polymers is described only in terms of increasing local rigidity and excluded volume effects. The Debye–Hückel equation is employed for the calculation of the electrostatic interaction energy in most theories. Using a loop expansion method, the partition function is consistently calculated, taking into account corrections to mean-field theory. In the absence of an external force, we characterize the dimension R of the chain in embedding space via R∼Lν, where L is the internal size. It is shown to be The standard Odijk, Skolnick, and Fixman (OSF) theory suggests l e ∝ r s 2, while some variational theories and some computer simulations suggest l e ∝ r s. In a low-salt region, a exible polyelectrolyte extends more signi cantly than a semi We extend previous work [G. The first application of the worm-like chain model to intrinsic viscosity of polyelectrolytes was reported by Odijk and Skolnick and Fixman. The Odijk-Skolnick-Fixman (OSF) theory [3,4] predicts the Cs'^ dependence (or more generally the K'^ dependence) of q^x differing from the Le Bret theory, but it (without ion condensation [26]) gives q values close to the Le Bret line, as indicated by a dashed curve in Figure 7; note that the charge parameter oQ for the hyaluronate chain is Our results contradict some experimental works and the celebrated theory of Odijk, Skolnick and Fixman (Skolnick et al. Odijk-Skolnick-Fixman result for the bending modulus. There are also theoretical works that calculated the persistence length from first principles, including the Odijk-Skolnick-Fixman theory, which showed that the persistence length depends on the microscopic polymer’s rigidity, and on an electrostatic term that varies with the solution’s salt concentration (25, 26). The data are compared to the theory developed by length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration, not only for semi exible and rigid chains but also for exible chain. Above a certain I, the L(p) shows an upturn, resulting in polymer stiffening and nonmonotonic behavior. chain. The presence of mesoscopic intersegment interaction potentials couples the bending and stretching moduli in a manner different from that predicted by the macroscopic elasticity theory. 1103/PhysRe vLett. 1 Ordering transitions in polyelectrolyte solutions Odijk [2], and Skolnick and Fixman [4] (OSF). However, the applicability of this approach to flexible PEs has long been questioned. The wormlike chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration not only for semiflexible and rigid chains but Elements of Odijk-Skolnick-Fixman and Yamakawa-Fujii polymer solution theories have been modified to create a new model that correlates flexible coil polyion intrinsic viscosity behavior with solvent and polymer properties. mean-field approximation, the well-known results of Odijk, Skolnick, and Fixman are reproduced. According to the Odijk–Skolnick–Fixman (OSF) theory, the persistence length of a polyelectrolyte such as DNA is described as l p = l 0 + l el, where l 0 is the intrinsic part that depends on the microscopic polymer’s rigidity, and l el is the electrostatic part that varies with the solution’s salt concentration. Debye length, contrary to scaling pertinent to the Odijk-Skolnick-Fixman electrostatic persistence length ob-served in the case of DNA. 1 M NaCl, for example, the maximum value of the OSF electrostatic persistence length (obtained from linear Debye-Hu¨ckel theory) is ,6 nm For a stiff PE near the rod limit, the Odijk-Skolnick- Fixman (OSF) theory 49,50 provides a very good description of the electrostatic contribution to persistence length: 51,52 According to Odijk-Skolnick-Fixman approach (Odijk, 1977; Skolnick & Fixman, 1977), a plot of persistence length vs. Whether you're exploring these categories or simply seeking a quick definition, this page provides comprehensive information on OSF. Polyelectrolytes near the rod limit. description of DNA confined to a nanoslit when compared to. (2017) extended Dobrynin’s A polyelectrolyte chain with linear dependence of the electrostatic persistence length on the Debye screening length has a lower free energy than that of a chain with the Odijk−Skolnick−Fixman Elements of Odijk-Skolnick-Fixman and Yamakawa-Fujii polymer solution theories have been modified to create a new model that correlates flexible coil polyion intrinsic viscosity behavior with Within a mean-field approximation, the well-known results of Odijk, Skolnick, and Fixman are reproduced. While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple [Show full abstract] analytical formula for the electrostatic persistence length. One would length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration, not only for semi exible and rigid chains but also for exible chain. Chem. , Macromolecules, 1977, 10, 944), suggesting a negligible variation of DNA energy than that of a chain with the Odijk-Skolnick-Fixman electrostatic persistence length. The worm-like chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration. We argue that previous numerical results pointing into this direction are probably due to a combination The observations just discussed are at variance with theories of the Odijk-Skolnick-Fixman (OSF) type 23. Gm, 82. Crossref Google Scholar [4] Reed W F, Ghosh S, Medjadhi G and François J 1991 Macromolecules 24 6189. The resulting expression is: lelec p = l B 4 2d (OSF) (1) where dis the PE charge spacing, l B = e 2 4ˇ 0k BT We reconsider the electrostatic contribution to the persistence length, $\\ell_{\\rm e}$ , of a single, infinitely long-charged polymer in the presence of screening. A linear or sublinear dependence of the persistence length on the screening length can be ruled out. [9] Double-helical DNA has a Next, the East Coast called back. One usually refers to the effect described by this We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. 1 The Odijk-Skolnick-Fixman theory 4. The intrinsic persistence length of sodium alginate in solution was determined to be 125 A by the method The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. For the case of intrinsically rigid polyelectrolytes we recover the classical results due to Odijk, Skolnick, and Fixman (OSF), namely, 1, = K-~ where K-~ is the Debye screening length. Our results contradict some experimental works and the celebrated theory of Odijk, Skolnick and Fixman (Skolnick et al. Beyond mean field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counterions. There, together with his student Jeffrey Skolnick, Marshall developed a theory for the electrostatic persistence length of polyelectrolytes. However, the classical result has to be sig- analytically was made by Odijk [30], and independently by Skolnick and Fixman [31] (OSF) by introducing the concept of an “electrostaticpersistencelength”. Finally,we identify a condition of the polymer, and find that the wormlike chain model best describes the polymer’s elasticity at this point. of DNA. The behavior of MC data so obtained for q and B as functions of added salt concentration c is examined in detail, comparing them with the Odijk-Skolnick-Fixman theory of q and the Fixman-Skolnick (DOI: 10. In addition, our results demonstrate DNA asymmetry at this scale is more complex than predicted by long-scale DNA models, with the cross-terms relating twist, slide, roll, and twist on the one hand and tilt and shift on the other being most essential. The problem of a polyelectrolyte near the rod limit is formulated incorporating both the short-range stiffness of the backbone (the “wormlike chain”) and the electrostatic interaction between segments taken as a Debye–Húckel potential. Within a mean-field approximation, the well-known The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. The scaling of bel is found to be more complex than the Odijk-Skolnick-Fixman predictions, and qualitatively compatible with more recent variational calculations. The no-tion of persistence length [4], which measures correla-tions along the chain, is very useful in describing elastic properties of semi-flexible polymers in general, and PEs, in The standard Odijk, Skolnick, and Fixman (OSF) theory suggests l(e) proportional, variant r(2)s, while some variational theories and some computer simulations suggest l(e) proportional, variant r(s). This is in accordance with previous. The paper is arranged as follows. 4. DOI: 10. (2008) showed that the Dobrynin model provides a superior. Based on the Odijk, Skolnick, and Fixman (OSF) theory of dilute polyelectrolyte solutions (Odijk, 1977; Skolnick & Fixman, 1977), the total persistence length, l T, of a polyelectrolyte is the sum of the intrinsic (l 0) and electrostatic (l e) persistence lengths (Eq. While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. From the theoretical work of Odijk, Skolnick, and Fixman (23, 24), we know that ionic strength is an important factor governing intrachain electrostatic repulsion affecting the persistence length of worm-like polyelectrolyte coils, estimated from results are in agreement with the picture outlined in the Odijk-Skolnick-Fixman theory, in which the behavior of charged polymers is described only in terms of increasing local rigidity and However as shown by Odijk, Skolnick and Fixman, the electrostatic screened interactions may induce a rod behavior on length scale larger than the screening length [50]. The abbreviation OSF stands for Odijk-Skolnick-Fixman and is mostly used in the following categories: Biophysics. We observe no significant deviations from the prediction l e∝κ-2 by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity and electrostatically excluded volume to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. DOI: 10 . Odijk-Skolnick-Fixman (OSF) [20,21] theory to a string. This is typically quantified using the Odijk-Skolnick-Fixman (OSF) electrostatic-stiffening model, in which salt-dependent Debye-Hückel (DH) screening modulates intrachain repulsion. Odijk T. The persistence length exhibits a sublinear dependence on the Debye screening length, κ⁻¹, L(p)(e) ∼ κ(-y) (with 0 < y < 1), deviating from the classical polyelectrolyte behavior expressed by Odijk-Skolnick-Fixman or Barrat-Joanny models. These theories calculate an electrostatic contribution to the persistence length that tends rapidly to zero with increasing ionic strength. While the dynamic behavior of DNA solutions with univalent cations is important, multivalent counterions, ubiquitous in biological environment, can fundamentally change their equilibrium behavior [21–26]. 05 M, while Manning’s approach [Citation 50 – Citation 52] predicted a reduction of λ p by up to 45% for 0. B, 116, 8383-93 (20 From the theoretical work of Odijk, Skolnick, and Fixman (23, 24), we know that ionic strength is an important factor governing intrachain electrostatic repulsion affecting the persistence length of worm-like polyelectrolyte coils, estimated from Our results contradict some experimental works and the celebrated theory of Odijk, Skolnick and Fixman (Skolnick et al. long-range flexibility. . Using this dependence, we compare the theory [3] with the data of [1] and find very good agreement at low ionic strengths (Fig. 1209/0295-5075/24/5/003) The classical theory of the electrostatic persistence length of polyelectrolyte chains due to Odijk, Skolnick and Fixman (OSF) is revisited. Path integral formulation is used to obtain the effective electrostatic interaction between the monomers. Simulations show DNA flexibility is independent of salt, in agreement with the Odijk-Skolnick-Fixman model. They calculate the increase in bending energy of a semi exible polymer due to charges that interact via a screened Coulomb potential. Save. Vroege and T. There is currently no consensus that the classical perspective of electrostatic persistence length (the so-called Odijk–Skolnick–Fixman, or OSF, formulation), derived by equating changes in Expand. 35. The no-tion of persistence length [4], which measures correla-tions along the chain, is very useful in describing elastic properties of semi-flexible polymers in general, and PEs, in We reconcile single-molecule force-extension data with scaling theories of polymer elasticity: measurements of denatured single-stranded DNA show a regime where the extension grows as a nonlinear power law with force, in accordance with “tensile blob” models. We provide experimental evidence for the electrostatically related excluded‐volume effects on the colligative properties and the single chain behavior of polyelectrolyte solutions in the dilute regime. Their work is the core of the Odijk-Skolnick-Fixman theory, which is still being used today. Following Barrat and Joanny 1 we model The standard Odijk, Skolnick, and Fixman (OSF) theory suggests l(e) proportional, variant r(2)s, while some variational theories and some computer simulations suggest l(e) proportional, variant r(s). , Macromolecules, 1977, 10, 944), suggesting a negligible variation of DNA The classical theory of the electrostatic persistence length of polyelectrolyte chains due to Odijk, Skolnick and Fixman (OSF) is revisited. The wormlike chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration not only for semiflexible and rigid chains but also for flexible chain. D. We observe no significant deviations from the prediction le∝κ-2 by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity and electrostatically excluded volume to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. The results are in agreement with the picture outlined in the Odijk-Skolnick-Fixman theory, in which the behavior of charged polymers is described only in terms of increasing local rigidity and In addition we have studied the expansion of the radius of gyration and of the end-to-end distance. In this paper, we use Monte Carlo simulations to study the conformation of a simple polyelectrolyte. Subsequently, Chuang et al. Odijk-Skolnick-Fixman (OSF) theory. In the Odijk-Skolnick-Fixman (OSF) model[41,42], the expected decrease of persistence length is on the order of 10% and only if the concentration of salt is below 0. However, the short–length behavior of the chain in the nonlinear regime deviates from the of DH–based result, even upon the charge renormalization. Sci Odijk (1977) and Skolnick and Fixman (1977). a continuous decrease of the random-coil dimensions when salt concentration increases. Odijk (1977) and Skolnick and Fixman (1977). (A) Long-range, repulsive segmental The theory of Odijk-Skolnick-Fixman[25, 26] predicts l p ~ r D 2 while variational calculations suggest l p ~ r D. Cite. Marshall spent a sabbatical at Harvard and then moved to Yale. Odjik-Skolnick-Fixman (OSF) theory predicts that the polymer persistence length, q, The [Na +] dependence of the persistence length is given by the expression (4) {formula not available us MathML} {formula not available us MathML} where α = (1 - δK/K 0) 3, which represents a correction to the standard Odijk–Skolnick–Fixman formula for the [Na +] dependence of the persistence length (Odijk 1977; Skolnick and Fixman 1977) due to the Similarly, with increasing added salt the electrostatic contribution to the HA persistence length is observed to scale as the Debye length, contrary to scaling pertinent to the Odijk-Skolnick-Fixman electrostatic persistence length observed in the case of DNA. Based on the Odijk–Skolnick–Fixman theories, the electrostatic persistence lengths were calculated for various ionic strengths. The persistence length of a single, strongly charged, stiff polyelectrolyte chain is investigated theoretically. Based on the Odijk–Skolnick–Fixman theories, the electrostatic persistence For a stiff PE near the rod limit, the Odijk-Skolnick- Fixman (OSF) theory 49,50 provides a very good description of the electrostatic contribution to persistence length: 51,52 The classical theory of the electrostatic persistence length of polyelectrolyte chains due to Odijk, Skolnick and Fixman (OSF) is revisited. 37. It has long been well His Ph. The persistence length l p; OSF is computed from the Odijk-Skolnick-Fixman theory in Eq. At low salt concentrations, a decrease in L p is caused dominantly by electrostatic screening effect as electrostatic persistence length (L p e) shows a strong dependence on Debye screening length (κ −1) with a scaling relation of L p e ∼ κ −2, which is in agreement with Odijk-Skolnick-Fixman theory described for semiflexible The persistence length, which decreases with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for stiff polyelectrolyte chains near the rod limit. Alert. and M. We advocate a fundamental change in the perspective regarding the dependence of is the celebrated Odijk-Skolnick-Fixman (OSF) formula [4] that connects the value of the. J. a continuous decrease of the random-coil Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. 2 Alternative calculations for flexible chains 4. 102. The dependence of the persistence length on ionic strength supports the Odijk-Skolnick-Fixman model of polyelectrolyte stiffening in electrolyte solution. 15. About. The classical analytical theory that attempted to capture the salt effect quantitatively is the Odijk-Skolnick-Fixman (OSF) theory . The Odijk–Skolnick–Fixman (OSF) model [Citation 60, Citation 61] predicted a reduction of λ p by 10% when c N a C l < 0. It was found that the values of q−q0 (i. scaling pertinent to the Odijk-Skolnick-Fixman electrostatic persistence length observed in the case. A more accurate approach is to directly incorporate electrostatic interactions into the GBR model via the Debye-Hueckel (DH) potential (Odijk, 1977; Skolnick and Fixman, 1977). Our experimental results fall in between the two predictions. Phys. With a simple representation of DNA, the CM/CE framework using a Debye-Hückel model leads to results that are in good agreement with both analytical theories and recent experiments, including a modified Odijk-Skolnick-Fixman theory that takes the finite length of DNA into consideration. Furthermore, the desorption force of single physisorbed polymer chains from negatively charged silica surfaces was determined. La The structural properties of a single polymer are well The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in the presence of added salt. [1] Odijk T 1977 J. They have demonstrated that within linearized Debye-Huckel (DH) approximation, there is an additive electrostatic correc-tion to the persistence length of a semi-flexible WLC, and this term scales quadratically with Debye screening length r s. Odijk, and Skolnick and Fixman (OSF) [7]. 2 Polyelectrolyte gels 6. (2017) extended Dobrynin’s This is typically quantified using the Odijk-Skolnick-Fixman (OSF) electrostatic-stiffening model, in which salt-dependent Debye-Hückel (DH) screening modulates intrachain repulsion. Beyond mean field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counterions. 3 The case of poor solvents 5. Shell, J. This is just the Hamiltonian assumed by Odijk, Skolnick and Fixman (OSF) [9,10], and their expression for the persistence length can be easily reproduced lp = l0 +lOSF = l0 + 1 4z2κ2lB, (6) where l0 is the bare persistence length of the neutral polymer backbone and lOSF is the electrostatic contribution. However, the applicability of According to the Odijk–Skolnick–Fixman (OSF) theory, the persistence length of a polyelectrolyte such as DNA is described as l p = l 0 + l el, where l 0 is the intrinsic part that We show that for a dipolar chain the electrostatic persistence length in the same regime of the parameter phase space as the original Odijk-Skolnick-Fixman (OSF) form for a Odjik-Skolnick-Fixman (OSF) theory predicts that the polymer persistence length, q, for stiff macromolecules varies with the inverse of ionic strength, I−1. 1 Grafted polyelectrolyte layers 5. 05 M. It is shown to be in remarkable agreement with numerically obtained Poisson-Boltzmann theory results, thereby fully accounting for non-linearities, among which counter-ion condensation effects. 22 . The data are compared to the theory developed by We present a general coarse-grained model of sodium, magnesium, spermidine, and chlorine in implicit solvent. In this paper, we use Monte Carlo simulations to 4. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific We find that, contrary to the well-known Odijk-Skolnick-Fixman theory, the Kuhn length of single-stranded DNA is linearly proportional to the Debye length of the solution. (2017) extended Dobrynin’s The viscosities of aqueous sodium alginate solutions were measured in different NaCl concentrations (Cs) at 298 K. In a low-salt region, a exible polyelectrolyte extends more signi cantly than a semi scaling pertinent to the Odijk-Skolnick-Fixman electrostatic persistence length observed in the case of DNA. Hsieh et al. Recent detailed critical as-sessment of the OSF conjecture [3–5] confirmed the univer-sality of the dependence of the persistence length on the parameters of the electrostatic interaction. on the mean-field theory of Odijk (1977) and Skolnick and Fixman (1977) (OSF). 1 Ordering transitions in polyelectrolyte solutions added salt limit, and to the Odijk-Skolnick-Fixman value of the single chain persistence length in the high added salt limit. A linear or sublinear dependence of the persistence length on the Within a mean-field approximation, the well-known results of Odijk, Skolnick, and Fixman are reproduced. In this paper, we recover the classical results due to Odijk, Skolnick, and Fixman (OSF), namely, 1, = K-~ where K-~ is Debye screening length. Crossref Google Scholar [5] Förster S, Schmidt M and Antonietti The effective persistence lengths decreased as a function of ionic strength, as predicted by the Odijk-Skolnick-Fixman model of polyelectrolyte chains. Rs, 87. In contrast, 1, for intrinsically While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. the celebrated Odijk–Skolnick–Fixman ~OSF! formula4 that connects the value of the bending elastic modulus with the parameters of the interaction potential ~assumed to be of the Debye–Hu¨ckel form5! between the segments along the poly-mer chain. A linear or sublinear dependence of the persistence length on the screening length can We show that for a dipolar chain the electrostatic persistence length in the same regime of the parameter phase space as the original Odijk-Skolnick-Fixman (OSF) form for a monopolar chain depends logarithmically on the screening length rather than quadratically. We argue that the observed features of the kilohertz range relaxation are due to much weaker electrostatic interactions that lead to the absence of Manning condensation as well as a rather The electrostatic persistence length depends on the square of the screening length, le approximately kappa(-2), as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. analytically was made by Odijk [30], and independently by Skolnick and Fixman [31] (OSF) by introducing the concept of an “electrostaticpersistencelength”. Rs, 82. , Macromolecules, 1977, 10, 944), suggesting a negligible variation of DNA The viscosities of aqueous sodium alginate solutions were measured in different NaCl concentrations (C s) at 298 K. 1b). It where α = (1 - δK/K 0) 3, which represents a correction to the standard Odijk–Skolnick–Fixman formula for the [Na +] dependence of the persistence length (Odijk, 1977. The range of applications, which did not require adjusting any parameter after the initial construction based solely on PDB structures and melting pro les of dimers, attests to the transferability On the basis of simulation results together with a careful analysis of analytical approaches, including Odijk−Skolnick−Fixman (OSF) theory, variational calculations, and renormalization group results, it is possible to present a consistent picture, which contains a better understanding of the true behavior as well as an explanation for the Surprisingly, in terms of the effective charge, the electrostatically renormalized persistence length can be formally described by the classical Odijk-Skolnick-Fixman formula, whose domain of applicability is normally limited to the Simulations show DNA flexibility is independent of salt, in agreement with the Odijk-Skolnick-Fixman model. At 0. Persistence length of a polyelectrolyte in salty water: Monte Carlo study. A new dimensionless viscosity is derived and is successfully related to the dimensionless ratio of Debye-Hückel screening length to polyion The wormlike chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration not only for semiflexible and rigid chains but also for flexible chain. The effect of divalent ions and the omission in the theory of the dependence of non-electrostatic persistence length on salt concentration are qualitatively invoked. Odijk−Skolnick−Fixman (OSF) type formula [5] [6] (see Fig. We calculate the electrostatic persistence length I, both for flexible and for stiff polyelec- trolytes using a self-consistent variational theory. We performed a series of Molecular Dynamics simulations using the Debye-Hückel approximation for electrostatics to test several equations which go beyond the classical The persistence length exhibits a sublinear dependence on the Debye screening length, κ –1, L p e ∼ κ –y (with 0 < y < 1), deviating from the classical polyelectrolyte behavior expressed by Odijk–Skolnick–Fixman or Barrat length as is well known from the seminal work of Odijk, Skolnick, and Fixman (OSF)[2]. In addition to the electrostatic interaction between polymer and substrate, which depends linearly on the Debye screening length and the polymer’s At present, we have a qualitative understanding based on the theory of semi-flexible polymers and electrostatic models such as the electrical double-layer theory (46), the Odijk-Skolnick-Fixman theory (47, 48), or the tight-binding ion model (49), among others. Odijk-Skolnick-Fixman theory to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. 15 477. Swelling of biological and semiflexible polyelectrolytes. Our model predicts the melting temperatures of DNA hairpins with excellent accuracy, and we are able to recover the experimentally known sequence-specific 4. (12) and alternate value, l p,D , is computed using the theory from Dobrynin 90 in Eq. In the case of weakly charged chains the electrostatic persistence length has a sublinear dependence on the Debye screening length which is due to inverse logarithmic dependence of the linear charge density of Odijk (1977) and Skolnick and Fixman (1977). P. Macromolecules 10(5):944–948. , 24. The results of computer modeling are contradictory: some Monte Carlo simulations[28, 29] are consistent with l p ~ r D 2, while recent MD simulations support lp ~ r D at least in the range of experimentally relevant N. Cited by. (2008) showed that the Dobrynin model provides a superior description of DNA confined to a nanoslit when compared to the OSF theory. 1a). The standard Odijk, Skolnick, and Fixman (OSF) theory suggests l(e) proportional, variant r(2)s, while some variational theories and some computer simulations suggest l(e) proportional, variant r(s). The scaling exponent describing the concentration dependence of the plateau modulus G0 agrees well with predictions for polymers in good solvents. We advocate a fundamental change in the perspective regarding the dependence of Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. Beyond mean-field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counteri-ons. Polym. Download Electrostatic rigidity 4. 068301 PACS numbers: 82. Odijk, Macromolecules 21, 2848 (1988)] on the formation of nematic liquid crystals from uncharged semiflexible polymers to the charged case. Later on numerous experimental studies were published presenting the measured values of different with increasing salt concentration, is in accord with the Odijk-Skolnick-Fixman theory intended for sti polyelectrolyte chains near the rod limit. Odijk, Skolnick, and Fixman (OSF) developed a theory that breaks persistence length into two components: Intrinsic (\ Skolnick J, Fixman M (1977) Electrostatic persistence length of a wormlike polyelectrolyte. In contrast to the original theory, our approach takes into account the effect of fluctuations in the chain configuration. the OSF theory. The polyelectrolytes are modeled as long slender worm‐like cylinders interacting via both hard‐core and electrostatic repulsions in the second virial approximation. The results are in agreement with the picture outlined in the Odijk-Skolnick-Fixman theory, in which the behavior of charged polymers is described only in terms of increasing local rigidity and This analysis indicates that ℓ ∼ 1 / c ∼ r D , where c is the concentration of monovalent salt and r D is the solution Debye length. Based on the Odijk–Skolnick–Fixman theories, the electrostatic persistence lengths Expand Odijk-Skolnick-Fixman (OSF) [20,21] theory to a string. Sci. We compare our approach to previous theoretical works (including variational formulations) and While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. 1 M NaCl, for example, the maximum value of the OSF electrostatic persistence length (obtained from linear Debye-Hu¨ckel theory) is ,6 nm long-range flexibility. persistence length with the parameters of the interaction potential between the segmen ts. In contrast to the original theory, our approach takes Expand. Related. We argue that the observed features of the kHz range relaxation are due to much weaker. As a result, we find that the OSF theory, although correct for intrinsically Odijk-Skolnick-Fixman (OSF) theory. , 25. 2. Crossref Google Scholar [3] Manning G S 1969 J. 97 . An induced attraction between monomers is due to thermal fluctuations and correlations between bound In addition we have studied the expansion of the radius of gyration and of the end-to-end distance. Charged gels and brushes 5. In contrast to the original theory, our approach takes The latter is consistent with the Odijk-Skolnick-Fixman theory. S. Beyond mean field, it is found that density correlations between We find significant deviations from the classical Odijk, Skolnick and Fixman (OSF) result. The classical theory of the electrostatic persistence length of polyelectrolyte chains due to Odijk, Skolnick and Fixman (OSF) is revisited. 1103/PhysRevLett. 47. These theories calculate an electrostatic contribution to the persistence length that tends rapidly to zero with increasing ionic strength. theories of the Odijk-Skolnick-Fixman (OSF) type (23–25). To account for electrostatic contributions to the persistence length, Dobrynin (Reference Dobrynin 2005) proposed a semi-empirical formula to correct for the ionic strength dependence, correcting an approximation in the classic Odijk–Skolnick–Fixman (OSF) theory by Odijk (Reference Odijk 1977) and Skolnick and Fixman (Reference Skolnick and Fixman 1977). Based on the Odijk–Skolnick–Fixman theories, the electrostatic persistence lengths Expand This is just the Hamiltonian assumed by Odijk, Skolnick and Fixman (OSF) [9,10], and their expression for the persistence length can be easily reproduced lp = l0 +lOSF = l0 + 1 4z2κ2lB, (6) where l0 is the bare persistence length of the neutral polymer backbone and lOSF is the electrostatic contribution. of crumpled blobs. , the electrostatic contribution to q) at Cs<0. For an interaction potential of a screened Debye–Hückel type, renormalization of the stretching modulus is derived on the same level of approximation as the celebrated Odijk–Skolnick–Fixman result for the bending modulus. In addition to the electrostatic interaction between polymer and substrate, which depends linearly on the Debye screening length and the polymer’s For an interaction potential of a screened Debye–Hückel type, renormalization of the stretching modulus is derived on the same level of approximation as the celebrated Odijk–Skolnick–Fixman result for the bending modulus. From the theoretical work of Odijk, Skolnick, and Fixman (23, 24), we know that ionic strength is an important factor governing intrachain electrostatic repulsion affecting the persistence length of worm-like polyelectrolyte coils, estimated from The Odijk–Skolnick–Fixman (OSF) model [Citation 60, Citation 61] predicted a reduction of λ p by 10% when c N a C l < 0. Odijk-Skolnick-Fixman theory,butagrees with other predictions. In this paper, we use Monte Carlo simulations to The viscosities of aqueous sodium alginate solutions were measured in different NaCl concentrations (Cs) at 298 K. scaling pertinent to the Odijk-Skolnick-Fixman electrostatic persistence length observed in the case of DNA. As a result, we find that the OSF theory, although correct for intrinsically rigid polyelectrolytes, breaks down Odijk-Skolnick-Fixman result for the bending modulus. 51 924. For example, a piece of uncooked spaghetti has a persistence length on the order of m (taking in consideration a Young modulus of 5 GPa and a radius of 1 mm). 2 Alternative calculations for flexible chains 4. Furthermore, in order to describe their data, the au-thors of [1] invoke the scaling-based de Gennes theory persistence length can be formally described by the classical Odijk-Skolnick-Fixman (OSF) formula, whose domain of applicability is limited to linearized Debye Huckel (DH) approximation. As a result, we find that the OSF theory, although correct for intrinsically rigid polyelectrolytes, breaks down for flexible chains. The effective persistence lengths decreased as a function of ionic strength, as predicted by the Odijk-Skolnick-Fixman model of polyelectrolyte chains. Based on the Odijk–Skolnick–Fixman theories, the electrostatic persistence lengths Expand approximation, the well-known results of Odijk, Skolnick and Fixman are repro-duced. It is shown to be in remarkable agreement with numerically obtained Poisson-Boltzmann theory results, thereby fully accounting for non-linearities, among which counter-ion condensation effects. [8] Examples. The observed I-1/2 dependence of the electrostatic contribution to the persistence length le differed from the I-1 dependence predicted in the Odijk-Skolnick-Fixman theory and agreed, at least We study the properties of an isolated, self-interacting wormlike polymer chain on the basis of a nonperturbative 1/d-expansion, where d denotes the dimension of embedding space. In the case of weakly charged chains the electrostatic persistence length has a sublinear dependence on the Debye screening length which is due to inverse logarithmic dependence of the linear charge density of The Odijk-Skolnick-Fixman (OSF) theory [3,4] predicts the Cs'^ dependence (or more generally the K'^ dependence) of q^x differing from the Le Bret theory, but it (without ion condensation [26]) gives q values close to the Le Bret line, as indicated by a dashed curve in Figure 7; note that the charge parameter oQ for the hyaluronate chain is Within a mean-field approximation, the well-known results of Odijk, Skolnick, and Fixman are reproduced. As a result, we find that the OSF theory, although correct for intrinsically rigid polyelectrolytes, breaks down on the mean-field theory of Odijk (1977) and Skolnick and Fixman (1977) (OSF). 1 M < c N a C l < 1 M. The behavior of MC data so obtained for q and B as functions of added salt concentration c is examined in detail, comparing them with the Odijk–Skolnick–Fixman theory of q and the Fixman–Skolnick (FS) theory of B and also with literature experimental data. In the case of weakly charged chains the electrostatic persistence length has a sublinear dependence on the Debye screening length which is due to inverse logarithmic dependence of the linear charge density of The persistence length of a charged polymer is described by the OSF (Odijk, Skolnick and Fixman) model. The methods described by Skolnick and The results are in agreement with the picture outlined in the Odijk-Skolnick-Fixman theory, in which the behavior of charged polymers is described only in terms of increasing We find that, contrary to the well-known Odijk-Skolnick-Fixman theory, the Kuhn length of single-stranded DNA is linearly proportional to the Debye length of the solution. energy than that of a chain with the Odijk-Skolnick-Fixman electrostatic persistence length. 098303 P A CS numbers: 77 . , Macromolecules, 1977, 10, 944), suggesting a negligible variation of DNA Odijk-Skolnick-Fixman theory to the stretched de Gennes-Pincus-V elasco-Brochard polyelectrolyte blob. In this theory, the DNA is described as a polyion chain of infinite length and the electrostatic and nonelectrostatic contributions to its persistence length are assumed to be as separate and additive. the reciprocal ionic strength would be linear with a constant slope, the intercept of which denotes the intrinsic persistence length. the Odijk-Skolnick-Fixman (OSF) theory, applicable to rigid and semiflexible chains [33,34]. There is currently no consensus that the classical perspective of electrostatic persistence length (the so-called Odijk–Skolnick–Fixman, or While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. In contrast, 1, for intrinsically flexible polyelectrolytes is found to Odijk and Skolnick and Fixman (OSF) showed that the persistence length of a wormlike polyelectrolyte in aqueous salt is the sum of two contributions, that is, We flnd that the °uctuations do not invalidate the classical theory of electrostatic persistence length due to Odijk and to Skolnick and Fixman. btst gveexjq simykc renw fexbfc aupj nfxyih nwua eghj frq