Polymer dynamics and topology: Extension of stars and dendrimers in external fields

Abstract

We study the influence of topology on the extension of branched polymers subjected to external forces. Such forces can be applied mechanically (by micromanipulation techniques such as laser tweezers) or electrically (in the case of charged polymers). We focus on the unfold dynamics of star and dendrimer type structures. Some of the dynamical quantities of interest are: (i) the structural average of the mean monomer displacement, (ii) the elastic and the loss moduli and (iii) the mean displacement of a specified monomer. In a Gaussian‐type approach, (i) and (ii) depend only on the eigenvalues of the adjacency matrix whereas (iii) also requires the knowledge of the eigenvectors. Thus one can sometimes dispense with a full diagonalisation and use efficient recursion procedures. We highlight how the dynamic properties depend on topology: the number of branches and their length for stars and the number of generations for dendrimers. The intermediate time (crossover) behavior turns out to be most revealing of the underlying structure. We compare our results to those for fractal structures in external fields.

Orientational mobility and relaxation spectra of dendrimers: Theory and computer simulation

“…In Sec. II we briefly describe some results of the viscoelastic theory, [23][24][25][26][27][28][29][30][31][32] dendrimer with the help of the viscoelastic theory. 32 In Sec.…”

“…[23][24][25][26][27][28][29][30][31][32] In this model every two consequent branching points are connected by one segment of the same mean-squared length ͗l 2 ͘, described by the elasticity coefficient K. 33 The viscous friction is supposed to be concentrated in branching points and is characterized by the scalar friction coefficient . The free draining model is considered, and the excluded volume and hydrodynamic interactions ͑HIs͒ are not taken into account.…”

“…The local mobility of dendrimer segments is studied analytically using simple viscoelastic model of Gaussian subchains ͑segments͒. [23][24][25][26][27][28][29][30][31][32] However, hydrodynamic and excluded-volume interactions, which play a major role in defining the dynamic properties of dendrimers, are not taken into account in this model. Therefore, the question arises to which extent the conclusions and predictions of this analytical approach is correct, in particular, in describing the relaxation of the P 1 autocorrelation function ͑ACF͒.…”

Hydrodynamic effects on the extension of stars and dendrimers in external fields

“…[2,13,14] These procedures complement approaches based on more microscopic models, such as pursued by Olaj and Zifferer. [31][32][33] In a recent work [34] we have analysed in the framework of the Rouse model the dynamics of stars and of dendrimers in external fields. The basic idea was that nowadays the micromanipulation of polymers becomes readily feasible (through optical or magnetic means or by applying electrical fields on charged polymer units).…”

“…In ref. [34] we extended our studies of the dynamics of networks [12,[25][26][27][28][29] and of charged linear polymers [41][42][43] also to stars and to dendrimers, the idea being that the later class of branched objects (which are in a topological sense trees) is somewhat intermediate between simply-connected chains and highly-connected networks with loops. In ref.…”