Electric Field Effects and Form Birefringence in Diblock Copolymers

Abstract

We investigate effects of the electric field on diblock copolymers by assuming an induced dipolar interaction among the composition fluctuations. First, we show that, when an electric field is applied perpendicularly to lamellae, undulations start to grow if their in-plane wavenumbers are smaller than an electric wavenumber qe proportional to the field. Subsequently, the undulations grow into larger spatial structures, eventually leading to a final square-lattice pattern. Second, we calculate the Maxwell stress tensor due to the electric field to predict a finite shear modulus in a lamellar state oriented by the electric field. Third, we examine form birefringence in disordered and ordered phases. In particular, the lamellar and hexagonal phases are shown to become birefringent on spatial scales longer than the spacing of lamellae or cylinders, even if the constituent monomers are optically isotropic. This gives rise to enhancement of depolarized light scattering from lamellar microstructures, which has indeed been observed recently. Most predictions in this paper are applicable to many situations other than those in the electric field.

Kinetic pathways of sphere-to-cylinder transition in diblock copolymer melt under electric field

“…3,4 It has been shown that by changing temperature [7][8][9] or by applying external fields such as shear flow [10][11][12][13][14][15] or electric fields [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] phase transitions between different ordered structures can be induced. Electric fields have been shown as an effective method of controlling the orientation of the structures.…”

Dynamics and electrorheology of sheared immiscible fluid mixtures

“…To do so, let us quickly note the derivation of relaxation terms in Eqs. (10) and (11) due to the interfacial tension [2]. Generally speaking, the effects of the interfacial tension are (i) to reduce the interfacial area and (ii) to make the system isotropic.…”

“…Throughout the present paper, we shall assume the above condition to hold but, as a new element, allow the two fluids to have a mismatch in their dielectric constants, which are denoted as 1 =¯ + δ and 2 =¯ − δ . Then the system acquires an ability to respond to an electric field, leading to the shape change of droplets and interfacial instabilities [3][4][5][6][7][8][9][10][11][12]. This change in the domain structure is expected to affect the flow properties of the system, thus giving rise to the electrorheological effect [13][14][15][16][17][18][19].…”

Fluctuation Effects in the Theory of Microphase Separation of Diblock Copolymers in the Presence of an Electric Field

“…However, the general relation between the derivatives of the thermodynamic potential and the correlation function of the order parameter, given by Eq. (6), requires the inclusion of the electric field into the correlation function of the Brazovskii self-consistent Hartree approach, too. The angular dependence of the structure factor without taking into account the fluctuation effects was derived previously for polymer solutions in [1], and for copolymer melts in [6].…”

“…(6), requires the inclusion of the electric field into the correlation function of the Brazovskii self-consistent Hartree approach, too. The angular dependence of the structure factor without taking into account the fluctuation effects was derived previously for polymer solutions in [1], and for copolymer melts in [6]. Intuitively it seems obvious that fluctuations become anisotropic in an electric field, and moreover fluctuations of modes with wave vectors parallel to the electric field are suppressed.…”