Interactions Between Star Polymers: High-Order Calculations of the Scaling Exponents

Abstract

The scaling behavior of star polymers can be calculated in the m → 0 limit of an m -component spin system with an additional composite operator. The resulting scaling exponents describe the effective interaction of such polymer stars, i.e. objects whose behavior interpolates between that of polymer coils and that of hard sphere colloidal particles. We extend the existing renormalization group calculations from the third to the fourth order.

Scaling of star polymers: high order results

“…Moreover, due to the special convexity properties of the spectrum of copolymer star exponents [9,10] they can be re-written in the multifractal formalism, in terms of a spectral function and Hölder exponents [5,7,9]. Such a program is well outside the scope of this Letter and is the subject of separate publications [14,15]. We also hope that our study will motivate the analysis of these and similar problems by other tools.…”

“…The expansions (8)-(10) are the starting point for the construction of analytic expressions for a number of physical quantities describing various phenomena (we mention some of them in the section 1): the exponents govern the short distance interaction of star polymers in colloidal solutions [1,15] as well as the reaction rate of diffusion controlled reactions with traps or reaction sites attached to polymer chains or to a star polymer [1,5]. One more recent application concern scaling of distribution of denaturated loops and unzipped end segments for a model of DNA denaturation [8].…”

DNA thermal denaturation by polymer field theory approach: effects of the environment

“…Therefore, the only difference that may be observed in asymptotic scaling of chains of different species (in our case these are the double-and single-stranded chains) is due to the difference in asymptotic scaling properties of mutually interacting SAWs and RWs. Based on this fact, recently [5] we have applied polymer field theory [9,25,[32][33][34] to derive scaling relations that express the loop exponent c (1.1) in terms of the familiar copolymer star exponents η f 1 f 2 . The latter govern the scaling of star-like polymer structures that are created by linking together the end points of polymer chains of two different species at a common core, as shown in figure 2.…”

“…When such a copolymer star is immersed in a good solvent, its asymptotic properties are universal in the limit of long chains. In particular, the partition function (the number of configurations) of a copolymer star made of two sets of f 1 and f 2 mutually avoiding RWs scales with its size R as [9,[32][33][34]:…”

Scattering From Ramified Polymeric Systems

“…To go beyond this approach, and in order to get a correct asymptotic behavior near criticality where these fluctuations are strong enough, it would be interesting to use the Renormalization-Group (RG) techniques [9,10]. The RG approach has been successfully achieved for linear polymers 1 [5,7,8,11] and recently for star-polymers [12][13][14][15][16][17][18][19][20]. Concerning these last systems, most of works have focused on the investigation of the configurational properties associated with star-polymers in dilute solution.…”