Electrical birefringence in solutions of p-aromatic polyamides

Analysis of polydispersity of macromolecular and nanodisperse systems by electrooptical methods

“…From the manifold of the above considered penalty functions, functions are selected such that nonuse of even one of the them leads to conflict between the model and reconstructed distribution function within a certain interval for Eqs. (8), (10), (12), (16)- (18), (22), and (23). However, depending on additional conditions of the stated problem, other conditions can be obtained and their addition to func tional G as penalty functions can provide better agree ment between the model and reconstructed distribu tion function.…”

“…Consider boundary conditions with respect to f and its derivatives f (i) assuming for Eqs. (24) and (23), respec tively, Here, f k is the polynomial presentation of the desired function in the kth interval. Using Eqs.…”

“…Kernels and K s (x, y) = are selected for (24), and these kernels are similar to the kernels of Eqs. (17) and (22); this operation makes it possible to calculate the free term according to the model function and a given kernel. Then, to the free term, a certain ran dom variable is added, and this term corresponds to the relative error ε = 0-5%.…”

“…Electric birefringence can be studied only when orientation is low because macromolecules and small sized particles cannot be fully oriented in actually attainable fields [22,23]. The main types of electric fields used for studying relaxation processes are rectan gular impulse and periodic (sinusoidal) fields [9,24].…”

“…Equations (8), (10), (12), (16), (17), (18), (22), and (23) are the integral Fredholm first order equations with respect to the distribution functions of particles over and with analytically described kernels and experimentally measured free terms. In general form, these equations can be written as…”