By S.O. Gladkov

ISBN-10: 3642055214

ISBN-13: 9783642055218

ISBN-10: 3662067056

ISBN-13: 9783662067055

This monograph systematically provides the basics of theoretical and experimental learn into crucial actual features of porous constructions. Non-standard habit of yes actual parameters, corresponding to the breakdown of the electrical box of porous ingredients, is defined. the strategy of calculation of the thermal conductivity coefficient of porous dielectrics, in line with the non-equilibrium precept, is illustrated intimately. the current procedure will be utilized to the research of the homes of "disparate" components resembling cellulose matrices, composites, and fibrous buildings. The e-book is meant for physicists, actual chemists and fabrics scientists at study and postgraduate and undergraduate degrees. it could even be useful for engineers and technical employees within the utilized sciences.

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**Example text**

44) The new parameter ﬁguring in the upper integration limit and determined by the formula θD = cs π/a is called the Debye temperature. 4 Temperature-Behavior Estimation of Porous Media Heat Capacity 45 substituted by inﬁnity, and therefore the function J(T ) becomes a constant, that is, ∞ J(T ) = 0 x3 dx π4 = . x (e − 1) 15 Thus, in the range of low temperatures the equation for the Helmholtz free energy is F = π2 45 4 T cs V cs . 45) So, for a solid-phase crystal structure thermodynamic the potential F has been calculated.

The operators a+ k (ak ) characterize not abstract conjugate operators, but purely physical creation (annihilation) operators of a phonon with wave vector k. 38) where the symbol Δkk is deﬁned by the conditions Δkk = 1, if k = k , and Δkk = 0, if k = k . 37) by means of this model the heat capacity of a crystal dielectric may be easily estimated. To demonstrate it we shall write the equation for free energy in the form: ⎧ ∞ ⎫⎞ ⎛ ⎪ ⎪ ⎪ ⎪ ω n k ⎨ ⎬⎟ ⎜ n=0 ⎜exp − ⎟. 39) F = −T ln ⎝ ⎠ ⎪ ⎪ T ⎪ ⎪ k ⎩ ⎭ The sum over “n” is, as it is easy to notice, a simple summation series of inﬁnitely descending geometric progression with the common ratio q = exp(− ωk /T ).

Indeed, the ﬁbril interaction energy (see Fig. 5), as it has already been stated, has an electromagnetic nature 52 3 Equilibrium Physical Parameters of Porous Dielectrics Fig. 6. Schematic representation of the experiment of mechanical strength study (a) and the structure after disrupture (b). Section A shows the chaotic arrangement of the ﬁbrils. and is determined by Van der Waals forces on condition that the distance between the interacting bodies is of order of 10−4 cm or less (for more details of the nature of these forces refer to the monograph [14]).

### Dielectric Properties of Porous Media by S.O. Gladkov

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