Effect of the Polydispersity of Molecular Length on the Decay Process of Transient Electric Birefringence of Rodlike Macromolecules in Dilute Solution

Abstract

The effect of polydispersity on transient electric birefringence (EB) was examined for a dilute solution which contains like macromolecules of varying lengths. The molecules were assumed to be rigid rods of cylindrical symmetry, so that the molecular weight is linearly proportional to length. Polydispersity was expressed by the ratio of the weight-average to the number-average lengths lw/ln. A logarithmic-normal type continuous length distribution was generally used. Calculations were performed for the birefringence-average relaxation time 〈τ〉EB and initial slope 〈S〉EB as a function of the electric field strength E, which is applied prior to the start of the decay process, with the electric parameter (βw)2/2γw, which is related to the weight-average permanent dipole moment (the βw-term) and polarizability anisotropy (the γw-term). Both 〈τ〉EB and 〈S〉EB are very sensitive to E, lw/ln, and (βw)2/2γw. A convenient method was devised for determining the polydispersity parameters (lw/ln and lw) from the weight-averages of relaxation time and initial slope, which are free from the mechanism of field orientation. Examples are given for a polydisperse, rigid rodlike sonicated DNA sample in aqueous solution.

Pulsed Electric Linear Dichroism of Triphenylmethane Dyes Adsorbed on Montmorillonite K10 in Aqueous Media

“…Since the MK-10 sample used in this work is polydisperse in terms of the particle size (19,20,43), the relaxation time is an averaged quantity. By analogy with the oft-cited electric birefringence-average relaxation time τ EB (19,47) for a transparent clay or macromolecular solution, the electric dichroism-average relaxation time τ ED may be defined as…”

“…1). The practical methods for evaluating τ ED values are described elsewhere in detail (19,47). Although the relaxation time is observed for a dye molecule bound to an MK-10 particle, it represents the overall rotational relaxation of the dye-MK-10 system in the case in which the dye is bound rigidly to the MK-10 particle.…”

Reversing‐pulse electric birefringence of poly (γ‐benzyl‐L‐glutamate). II. Field‐strength dependence of steady‐state and decay signals of well‐fractionated samples

“…Comparison of these two sets of the parameters ( l u , / l m I , , pl,, and ha,) for the Poisson distribution, one from the dependence of steady-state 6 and decay time on electric field and the other from the dependence of steady-state 6 on electric field and the low-field reverse-transient, shows that the ratio l,JI,, is the same in both cases (Table I). The calculated curve from the latter, eg., for S1, is slightly longer than the one from ( T )~; however, the difference in ( T )~~ and lfc is less than 1 ps and is, at most, 20 A, since the relaxation time is proportional to the third power of the length.…”

“…The decay time is dependent of the applied field strength and orientation mechanism, i. e., permanent dipole moment, p( I ) , versus electric polarizability anisotropy, ha( Z). 20 In this work, the value of T ( I) was calculated by using the Broersma equation …”

“…The values of ( T )~ are 8.0 ,us for S1 and 15.0 ps for S2 (the uncertainty is about *0.5 ,us), which are obtained by extrapolating observed values of ( T & plotted against Eto infinitely high field strength. 20 The dashed line for sample S2, for example, intersects the theoretical curves at numerous points, each of which gives a pair of l,L/l,, and I,,, but many paired values may be discarded as unreasonable. The best-fit paired values ( l L L / l n , I,) can be searched by the trial-and-error method in combination with the observed steady-state relation, 6 vs E2, from which P, and y u may also be separately evaluated.…”