Fig. 1.7. Relation of the unfrozen water film thickness h to the energy of adsorption (E) under the negative temperatures t1>t2> t}: 1 - with the mineral surface MS; 2-4 - with the ice surface IS (2 - at h} and f3, 3 - at h2 and t2, 4 - at h1 and fj ).

adjacent water layers by the epitaxial mechanism. As the difference between the textural parameters of the ice and the water lattice is less than that between the textural parameters of mineral particles and water lattices, the hydrogen bond distortion caused by the ice surface will be weaker as compared with the mineral surface and must propagate over a shorter distance in the water. Therefore the thickness of the unfrozen water film bound by the mineral surface turns out to be essentially greater than that of the film subjected to the ice surface forces (see Fig. 1.7). Note that the lowering of the negative temperature of such an ice-soil system by an equal value (Afj = At2 = Af3...) must cause an equal and essential increase of the free surface ice energy (A£/s = AE,2S = AEfs =____). The increase of free surface energy of the ice will be an order of magnitude more than that of the mineral surface. In support of this fact it is noted that the coefficient of thermal expansion of ice (a -change of linear size of a body with change of its temperature by a unit) is more than one order of magnitude greater than that of minerals and soils (a = 40-60 x 10"6 K"1 for ice, 0.4-8 x 10"6 K"1 for the minerals of the skeleton of clay-rich soils, and 3 — 10 x 10~6 K~1 for granite, sandstones and shales). At the same time the contraction of the solid bodies at cooling is associated with the reduction in the textural parameters of their crystal lattices. A greater change of these textural parameters causes appropriate (larger in magnitude) distortion (strain) of the hydrogen bonds in the surrounding unfrozen water and will manifest itself over a greater distance from the distorting surface. In other words, the energy of binding of water by an ice surface £IS and the thickness of the layer of unfrozen water held by this surface will grow by an order of magnitude faster on lowering of the temperature than we can observe for the mineral surfaces of clay particles. In this connection the change of the value £m =f(l/h") with lowering of temperature can be neglected. At the same time the change in the curve E(i) —f(i/hn) on account, for example, of equal increase of ice surface energy A£IS on lowering of the temperature by an equal value At, must occur and is shown graphically in Fig. 1.7. In this case:

where t1 > t2> t3 while |ix — t2 \ = \ t2 — t3 \ = Ai and £IS(i2) — £iS(tx) = £IS(i3) — £IS(i2) = A£|<j. In other words, the ice surface forces will grow so profoundly on lowering the temperature that a portion of the unfrozen water previously bound by the mineral surface will experience the ice surface forces, i.e. the phase transition of a portion of unfrozen water into ice will occur. At the same time the thickness of the layer of water bound by the ice surface must increase.

On this basis the possibility exists of explaining the reason for further phase transitions of bound (unfrozen) water into ice (after the formation of the first holocrystalline ice nuclei at the temperature of the beginning of crystallization i'c") not under a constant temperature t'"r but over a range of negative temperatures.

From the moment of the formation of the holocrystalline ice nuclei in freezing soil at t1 = t'c" it can be assumed that in the case of no further heat removal from the unfrozen soil the system reaches a quasi-equilibrium state between the unfrozen water and ice and there will be no further freezing of bound water. In this case, given the thickness h1 of the bound water film being responsible for the distance from the mineral surface hl determining the temperature tv the following condition should be fulfilled:

where £IS(ix) is the surface energy of ice expended in the interaction (bond) with the adjacent molecules of the unfrozen water. Eb(tj) and £m(ix) are, respectively, the energy of the bond between H20 molecules and the energy of the bond between unfrozen water molecules and the mineral surface situated at a distance h1 from the surface at the temperature tv Such a

quasi-equilibrium state can be disturbed only by additional heat input or removal from the system. The process of ice nuclei disappearing and their transition into the water texture, i.e. the process of soil thawing, will begin if there is an input of heat. At the same time the removal of a quantity of heat from the freezing ground system will cause the temperature of the ice, bound water and mineral particles to fall (for example, by At = tl —12), where t2 < t'"r). Such temperature lowering will cause an increase in the surface energy of the ice by the value A£IS = £IS(f2 ) — ^is^i) an(i growth of energy of bonding between H20 molecules in the bound water by A£b (as E^iJ < Eb(t2)). The value of the energy of bonding of unfrozen water molecules with the mineral surface, as is obvious from the foregoing, will not be changed essentially (£m(ii) ~ Em(t2), in contrast to that of the ice, which results in violating the condition (1.14) in such a manner that:

Consequently, on account of the greater bond energy between the unfrozen water molecules and the ice surface some of them will be released from the effect of mineral surface forces and experience the effect of ice surface forces, i.e. phase transition of unfrozen water into ice will occur, provided the liberated heat of crystallization is removed from the system. Freezing out of some portion of the unfrozen water and, consequently, a movement of the ice-unfrozen water interface from the hx position to the new equilibrium interface position h2 should occur, fulfilling the condition:

Further heat removal from the freezing soil will cause renewed lowering of the negative temperature (for example by At = t2 — t3 = tx — t2, where f3 < f2). The temperature lowering by the At value (as in the first case under consideration) will provide for the surface energy of ice increasing by the value A£IS = £IS(f2) — £iS(fi) = Els(t3) — Els(t2) and for the energy of the bonds between H20 molecules in the unfrozen water to increase, such that Eb(f3) > Eb(f2) > EJiJ. This will violate the steady-state quasi-equilibrium condition resulting in freezing-out of an additional amount of unfrozen water, provided there is the necessary removal of latent heat of phase transition from the soil. It is easy (as in the previous case) to find the new h3 position of the ice surface corresponding to the negative temperature f3 < t2 in Fig. 1.7.

Fig. 1.8 presents a curve well-known from experiments, showing the dependence of the unfrozen water content on the negative temperature.

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