Transient electric birefringence of wormlike macromolecules in electric fields of arbitrary strength: A computer simulation study H. E. Pérez Sánchez, J. García de la Torre, and F. G. Díaz Baños a Departamento de Química Física, Universidad de Murcia, 30071 Murcia, Spain Received 19 November 2004; accepted 7 January 2005; published online 25 March 2005 We have studied the birefringence decay of linear models of macromolecules for two different types of flexibility, the broken-rod chain and the wormlike chain, using a computer simulation of a transient electric birefringence experiment. We have paid particular attention to the influence of the intensity of the orienting field, including two orienting mechanisms, the induced dipole, and the permanent dipole. We have compared wormlike and broken-rod models of the same radius of gyration, finding that they present a different decay curve under the influence of the same intensity of the field. We have seen that these differences are due to the faster relaxation times smaller in the wormlike chain model and amplitudes, because, regardless of the type of flexibility, the overall size of a molecule measured by the radius of gyration essentially determines the longest relaxation time. We have also analyzed how the relaxation process is affected by the degree of flexibility, the orientation mechanisms, and the intensity of the field. Studying a different aspect, we have paid attention to the deformation of a molecule in a transient electric birefringence experiment as a source of information. In this work we have developed equations to characterize this deformation in terms of one of the components of the gyration tensor, if a dynamic light scattering experiment under the influence of an electric field could be performed. To develop this work we have simulated the Brownian dynamics of the different models, relaxing after the removal of an orienting external electric field of arbitrary strength. A comparison with other methods such a the rigid body treatment or the correlation analysis of Brownian trajectories has also been included. We have seen that differences between the two Brownian dynamics methods are small and that the rigid-body treatment is only an acceptable approximation to obtain the longest relaxation time. © 2005 American Institute of Physics. DOI: 10.1063/1.1863892 I. INTRODUCTION Transient electric birefringence TEB, which is based on the time-dependent behavior of a macromolecular solu- tion under the influence of an electric field, 1–3 is well known as an interesting source of information about macromol- ecules. For example, TEB has been used to characterize the global geometry and flexibility of nucleic acids. 4,5 In such experiments, each system can be characterized from an analysis of the on-field rise or the off-field decay with a set of times and their corresponding amplitudes, although to properly understand the results appropriate models, methods, and theories are needed. A. Models For chain macromolecules, such as some helical nucleic acids, it is usually assumed that their flexibility is distributed more or less uniformly along the chain, despite the fact that, sometimes, simple nonhelical structural elements are found in its structure. When modeling flexible macromolecules, the first idea is ideally represented by the wormlike chain model WLC, while the second can be described by the once- broken-rod chain BRC. These two extreme models, plus some others, mainly the weakly bending rod and the ran- domly broken chain have been used to understand TEB ex- perimental results of DNA and RNA see, for example, Lu et al. 6 . It is usual to simplify the models in the form of chains of beads. B. Orienting mechanisms One of the basis of a TEB experiment is the mechanism that orients the molecule when an electric field is present. When the orienting mechanism is only based on the interac- tion of the electric field with a molecular permanent dipole it is accepted as a simple description see, for example, Fred- erick and Houssier 1 . But many macromolecules are macro- ions and in this case the orienting mechanism is complex and not well understood at the present time see, for example, Grycuk et al. 7 and references therein. It is assumed that the induced electric dipole of linear macroions arises from a long range phenomenon which is the distortion of the ion atmo- sphere from equilibrium by the imposed electric field. In the special case of rigid polylectrolytes this problem has been addressed with relevant contributions through analytical theory see, for example, Fixman and Jagannathan, 8 Rau and Charney, 9,10 Bellini et al. 11  and simulation procedures. 7 It should be emphasized, however, that the treatment of flexible structures will be even more complex. For flexible models made up of beads connected by virtual bonds, the usual ap- a Author to whom correspondence should be addressed. Electronic mail: fgb@um.es THE JOURNAL OF CHEMICAL PHYSICS 122, 124902 2005 0021-9606/2005/12212/124902/13/$22.50 © 2005 American Institute of Physics 122, 124902-1 Downloaded 05 Apr 2005 to 155.54.98.94. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp