Application of the Zimm-Bragg Model to the Removal of Azo Dyes with Pectin

In this work, the ability of pectin (Pec) to remove direct red 80 (DR80), Congo red (CR), methyl orange (MO), and methyl red (MR) was studied. The removal percentages under adequate pH and ionic strength conditions were as follows: DR80 (99.5%), CR (99.8%), MO (88.6%), and MR (68%), showing that this methodology is efficient to remove azo dyes. The proposed method included the addition of native Pec to the dye aqueous solution and the formation of a gel that occurred when a calcium salt solution was added. This gel retains the molecules adsorbed onto the molecular surface of Pec through hydrogen bonds and electrostatic and hydrophobic interactions. To our knowledge, it is the first time that the Zimm-Bragg model is used to describe the removal of azo dyes with native Pec. This model includes two parameters: K u (nucleation constant), which is related to the tendency exerted by a dye molecule attached to the Pec to bind to other molecules present in the aqueous phase, and U (cooperativity parameter), which determines the aggregation capacity of the dye molecules already attached to the Pec. This model fits the experimental isotherms very well, suggesting that Pec binds single molecules and dye aggregates. The obtained results in the values of K u ranged from 922 mol/kg (MR) to 1,157,462 mol/kg (CR), and U varied from 2.51 (MR) to 169.19 (MO). These results suggest that the use of Pec is a viable option to remove azo dyes from aqueous effluents and that the Zimm-Bragg model fits adequately the isotherms of dyes that have a high tendency to form aggregates.

Coherence-controlled stationary entanglement between two atoms embedded in a bad cavity injected with squeezed vacuum

We investigate the entanglement between two atoms in an overdamped cavity injected with squeezed vacuum when these two atoms are initially prepared in coherent states. It is shown that the stationary entanglement exhibits a strong dependence on the initial state of the two atoms when the spontaneous emission rate of each atom is equal to the collective spontaneous emission rate, corresponding to the case where the two atoms are close together. It is found that the stationary entanglement of two atoms increases with decreasing effective atomic cooperativity parameter. The squeezed vacuum can enhance the entanglement of two atoms when the atoms are initially in coherent states. Valuably, this provides us with a feasible way to manipulate and control the entanglement, by changing the relative phases and the amplitudes of the polarized atoms and by varying the effective atomic cooperativity parameter of the system, even though the cavity is a bad one. When the spontaneous emission rate of each atom is not equal to the collective spontaneous emission rate, the steady-state entanglement of two atoms always maintains the same value, as the amplitudes of the polarized atoms varies. Moreover, the larger the degree of two-photon correlation, the stronger the steady-state entanglement between the atoms.

ENTANGLEMENT FOR THE TWO-MODE FIELD IN THREE-LEVEL ATOMIC SYSTEMS

We investigate entanglement for the two-mode field in three-level atomic systems. Entanglement of the system is demonstrated according to the Duan's criterion.16 It shows that the entanglement has a close relation with the pump intensity. For large pump intensity, particular choice of its phase, zero detuning and cooperativity parameter, perfect entanglement for the two-mode field can be generated outside the cavity.