SynopsisThe 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-Huckel potential. By the use of a physically valid approximation an expression is derived for the mean-square extension length of a short polyelectrolyte chain. Some remarks are made on the relationship between the electrostatic interaction and the usual excluded-volume problem for polymer solutions.

NMR spectra give information about the configurational sequences (cotacticity).

No abstract

A scaling analysis is presented of the statistics of long DNA confined in nanochannels and nanoslits. It is argued that there are several regimes in between the de Gennes and Odijk limits introduced long ago. The DNA chain folds back on itself giving rise to a global persistence length that may be very large owing to entropic deflection. Moreover, there is an orientational excluded-volume effect between the DNA segments imposed solely by the nanoconfinement. These two effects cause the chain statistics to be intricate leading to nontrivial power laws for the chain extension in the intermediate regimes. It is stressed that DNA confinement within nanochannels differs from that in nanoslits because the respective orientational excluded-volume effects are not the same. A perusal of the rapidly developing literature on nanoconfined DNA shows that its behavior is more complex than anticipated ͑see, e.g., ͓1-17͔ ͒. It appears that more regimes are needed besides those originally described by Daoud and de Gennes ͓18͔ and Odijk ͓19͔. The nanoconfinement of a semiflexible chain specifically introduces subtleties in the chain statistics that I address here within a scaling analysis. A complete theory would involve solving a Fokker-Planck equation subject to the boundary conditions arising from nanoconfinement ͓20͔. Nevertheless, backfolding or hairpin formation may be addressed in a mechanical approximation ͓21͔, though entropic depletion of the chain near a wall still needs to be resolved quantitatively ͓22͔. Numerical investigations of nanoconfined stiff chains interacting via excludedvolume interactions have appeared recently ͓23-25͔ but in the limit of ground-state dominance without accounting for hairpin formation.Let us first consider a very long double-stranded DNA chain confined in a nanochannel of square cross section whose side D is smaller than the persistence length P so that we are in the Odijk regime ͑D Ͻ P͒. Thus the chain may be conveniently viewed as a sequence of deflection segments of typical length ͓19͔ Ӎ D 2/3 P 1/3 . ͑1͒The orientational fluctuations with respect to the channel center axis are given by the mean-square average. ͑2͒It is important to note that the coefficient c 1 here is quite small, as has been determined numerically ͓26-28͔ and estimated analytically ͓12͔. Inevitably, a long chain must bear thermally activated hairpins leading to a global persistence length g as shown in Fig. 1. The entropic depletion caused by the nanowalls forces the hairpin bends to be tightened up so that g is often considerably larger than the persistence length P ͓21͔. Expressions for g are presented in Appendix A.In view of the backfolding, segments of the DNA interact with each other via the excluded-volume effect. Owing to the charges borne by the DNA backbone, one introduces an effective diameter d eff rather than a bare diameter ͓29͔ ͑P ӷ d eff ͒. If the interaction were purely isotropic, the excluded volume between a pair of deflection segments would scale as ͓30͔But the segments are aligned ͓see Eq. ͑2͔͒ ...

There is an interesting class of problems in the physics of polymeric materials which one may group under the heading "semiclassical elasticity". Herein, the question is raised how the deformational behavior of the material changes from entropy-dominated to elasticitydominated as one increases the level of stress exerted on it. Chain fluctuations and undulations are gradually frozen out during this process. Thus, the connotation "semiclassical" applies to an evaluation of the partition function in the limit of weak fluctuations, which may remain influential nonetheless. A simple example of this effect is the elongation of stiff microfilaments under tensions that are of practical interest. Both the fluctuations and material extension in this problem were already addressed qualitatively by Oosawal two decades ago, but a straightforward quantitative analysis is apparently lacking.Let us suppose it is possible to associate a center curve with the macromolecule or filament in a particular configuration. The center curve is described by the radius vector 7%) = (ds), y(s), z(s)), where s is the contour distance from one_end. The contour length L is a function of the tension f exerted at both ends of the chain (Figure 1). The consour length is LO in the state without external stress cf = 01, referred to here and below by index 0.The unstressed reference configuration without thermal undulations is assumed to be a straight line. A fairly general, effective Hamiltonian may be written as the sum of three termsThe bending energy2 valid for an extendible wormlike chain may be approximated by where k g is Boltzmann's constant, Tis the temperature, and P(L,s) is the persistence length, which will generally depend on the material elongation and hence implicitly on the tension. At the same level of approximation, we have for the energy of material elongationc-i The statistical physics of a filament or chain defined by %is obviously complicated but one limit is readily soluble. I consider the case of small elongations and weak undulations (AL L -LO < < LO; &Ids = 8, *: 1 gnd dy/ds 8, << 1 iff = fiz is in the z direction and 8 = (8,(s), 8Js)) is the angle between the tangential vector Glds and Zz.