МОДЕЛИРОВАНИЕ ВЗАИМОДЕЙСТВИЯ МАГНИТНОГО ПОЛЯ С ОБЪЁМНЫМИ ВЯЗАНЫМИ СТРУКТУРАМИ

Сусак И.П., Шигаев А.С., Пономарёв О.А., Фесенко Е.Е.

(Пущино, Томск)

Представлен механизм взаимодействия магнитного поля с жидкостью. В рамках концепции солитонной модели жидкости предлагается объяснение эффекта памяти в системах с водородными связями в магнитном поле.

MODELING OF INTERACTION MAGNETIC FIELD WITH BULK KNITTED STRUCTURES

Susak I.P., Shigaev A.S., Ponomarev O.A., Fesenko E.E.

(Pushchino, Tomsk)

A mechanism of interaction magnetic field with liquid is presented. The memory effect in systems with hydrogenous bonds in magnetic field within the framework of continual soliton concept of liquid structure is also explained.

The behavior of hydrogen atoms in systems with hydrogenous bonds plays an important role in transfer processes. It reveals a number of fine non-linear and quantum effects. Suppose the structure of such systems to be a bound band. The bands are tied by their edges between different parts, which builds up a three dimensional net, a bulk knitted structure. DNA - molecules, hydrogenous ferroelectrics, like triglycinsulphate and Rochelle salt, tied polymeric balls of linear and quasilinear polymers [1 - 5], fullerenes, kumulenes are all have these properties. There are data, that water also belongs to such systems [6]. Electric and magnetic fields, as well as electromagnetic radiation influence the position of phase transition points, shifting the temperature and smearing out the transitions themselves [7]. Even fields of 10⁶ – 10⁷ V/m change the properties of narrow-band polymers (biomembranes) [8 - 10], being critical field values for ferroelectrics or internal for membranes [11, 12].

Proton transition through a membrane may occur by soliton mechanism through the chain of H-bonds in liquid water lining channels (or in proteins, included in a membrane). It is known that the liquid structure changes when is influenced by constant and alternate magnetic fields, these changes being conserved during some tens of hours. These changes can be identified by kinetic properties, for instance by change of viscosity, reaction rate characteristics of dielectric relaxation spectra, IR -, UV - spectra and luminescence. We suppose that the structure of the liquid under consideration is defined by quantity of solitons on the band, between ties, soliton concentration, and by concentration of ties in the system. We neglect the contributions of optical and acoustic oscillations, assuming that more important role is played by rotation of a band around its axis. We also neglect (in first approximation) serpentine vibrations of a band. Usually a band has the length of approximately 20 sections. We will take into account molecular oscillations, taking out different vibronic states. The aim of our analysis is to obtain an expression for knitted liquid effective Hamiltonian, find out its connection with fluid parameters, and external electric, magnetic, and electromagnetic fields.

We consider the liquid structure as a three-dimensional surface composed in the following way. At temperature lower than the critical one, the 3D-surface is supposed to transform into dipole hexagonal structure such that dipole momenta of liquid molecules are arrange according to the action minimum principle. We suppose that in liquid state the amount of H-bonds per one molecule becomes less than 4.

The model is characterized by the following parameters: molecular field energy, proportional energy of hydrogen bonds kcal/mol 3D-surface transformation times, proportional to the one H-bond lifetime for liquid s [13-15], distances, proportional to molecular size m.

The model takes into account the interaction of neighboring molecules as well as ones that far from each other bulk interaction. The three-dimensional structure is assumed to be with elasticity defined analogously to that in the theory of nematics. Structure transformations are associated with transformations of H-bonds, and we call each structure breach or disturbance a topological defect, which has a dimension, that can be fractional. Our model may be thought of as quasi-polymeric liquid. Several liquid molecules form band sections, that in turn are tied by their edges with the help of H-bonds. As a break of an H-bond occurs, the transformation of 3D-structure is coming. The sections of molecules change their orientation according to the action minimum principle, and then a retieing is taking place. So, the model describes isotropic medium, which has local anisotropy. The elasticity of segments composed of several molecules of liquid for longitudinal bends is considered to be equal to its average value, and is sufficiently big comparing to the elasticity for twist, analogously to the solid rod model. Quantitative description of the relation between these constants and their dependence on molecular length in frames of the theory of self - consistent field is presented in ref. [16].

Let our model be placed in external electromagnetic field. To visualize electromagnetic field interaction on a segment of 3D-structure, imagine it schematically as three oriented bands with many-colored edges for determination of the direction of dipole momentum. We introduce dipole momentum density distribution on a band. Transverse-oriented bands consist of segments, built by molecules of the liquid. Instantaneous interaction of the edges of a chain composed by oriented segments is assumed to be much weaker than the interaction that builds the band itself. In the first approximation this interaction is neglected, and the behavior of the band twisted in a ball is considered. The system is placed into external electromagnetic field of low intensity. In such system, solitons and breathers appear, which essentially influence its properties. Let the direction of dipole momentum be from, say, white edge of the band to the black one. The kink propagation on the segments of 3D-structure along the band will turn it at angle , while breather propagation - at angle . Kinks and breathers propagate with velocities and correspondingly. Analytical form of breather and soliton type solutions of SG - equation is described by the expressions and correspondingly. During the interaction, a breather goes through a kink, undergoing a phase shift. As the collisions are elastic, no any additional perturbation (like "radiation") appears, and, secondly, the solutions can be found analytically for all times with the help of, for instance, the inverse problem method [17, 18]. We will not take into account their interaction. Consider the case when there are no breathers. Then, the knitted system in the ground state is described by the Hamiltonian

(1)

where - kinetic energy of the system minus the kinetic energy related to collective coordinates of solitons, - rotation angle of a twisting band on the segment between the points and , which is of length , at the points and the band is tied with another one with a potential , - the inertia momentum density corresponding to the twist per unit length of the band, - band's constant elasticity, - density of molecular field interaction energy, - dipole momentum density module, - the parameter of interaction of polymer chain with external magnetic field .

Notice that the points and are not tied with each other. The dot over denotes time derivative. The quantity is an external potential acting on the point with coordinate , for instance, from a capillary. Suppose that, on the band's segment between the points and there are solitons (i.e. we have an - soliton solution). Suppose also, that the concentration of solitons is not very high, so that we may consider each soliton to be sufficiently distant from each other.

Then

(2)

where - single-soliton solution [19], threaded on the band's segment between the points and , . Making use of (2) for the Hamiltonian (1) we have

(3)

where - the total kinetic energy of the system. The integration over s in (3) can be carried out explicitly, which leads to the effective Hamiltonian describing the system in terms of free particles, solitons and interactions between them. The Hamiltonian does not depend on time, and, therefore may be calculated at any time. The simplest way to do that is to chose .

Now, let us rewrite (3) in the form

(4)

From now on we use this effective Hamiltonian for the description of the system, which consists of twisted bands between the points and and with the positions of twirls on them in the points .

Describing liquid as continuous medium, we conclude that the minimal energy in the model of liquid corresponds to the absence of deformations in it. In liquid water, such state with minimal energy or the ground state is the configuration with uniform orientation in the whole bulk - hexagonal ice (Ih) for our model. Any deviation of director distribution from uniform (i.e. the same in the whole bulk) is connected with the presence of additional elastic energy in the model of liquid, that is may be implemented only by external influence, connected, for example, with the surfaces of a chosen segment, external electric and magnetic fields, etc. In the absence of these influences or after the termination of their action, the liquid tries to return to the state with uniform director orientation. In the soliton model of liquid, when affected by external magnetic field, turnings of certain band segments occur, which leads to the deviation of director orientation distribution from uniform. There appears some addition to the free energy (Gibbs' energy). Liquid in magnetic field has a state in which it can remain for a long time , where is hydrogen bond lifetime. The system will continue to be in the state with this energy until an external perturbation moves it to some other state, or until the temperature changes. Thus, it is possible to describe the "memory" mechanism in liquid water (MEW), including one-dimensional case for the soliton model. The addition to the free energy in the soliton model of liquid is conditioned by soliton and breather concentrations. They become apparent already at low values of magnetic field strength. This addition changes the value of the specific heat of the liquid in magnetic field: , - this is so called configurational specific heat of the liquid [20]. It is characterized by the amount of energy needed to change the configuration of chosen segments.

It turned out that the knitted systems, those liquid water belongs to, have unique properties, that can be explained by the existence in them solitons and breathers. Many properties of water are explained in terms of continual soliton conception of water structure. Moreover, the structures of different knitted liquids under different magnetic fields can be described in terms of shift solitons and breathers. Soliton models provide good description of such systems.

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