# Calculation scheme According to Buckingham s

2018-10-24

Calculation scheme. According to Buckingham\'s theory for a system of two polar components, the following relationships hold true: where ε is the dielectric permittivity; n is the refractive index; V is the molar volume, V= ( is the specific volume; М is the molecular weight); х is the molar fraction, Т is the absolute temperature, NA is Avogadro\'s number, k is the Boltzmann constant, is the effective dipole moment (the indices 1 and 2 refer to the solvent and the solute, respectively, the index 12 to the system under consideration). The dipole moments μ1 and μ2 were determined graphically, by extrapolating the concentration dependence of the total orientational polarization S12 to infinite dilution: Using the parameters а and b, the dipole moments (μ1)2 2=0 and (μ2)2 2=0 were calculated from the expressions: The dipole moment of the water molecule in liquid state was calculated from the Onsager formula: where ε, n, ρ are the dielectric permittivity, refractive index and density, respectively; μ, М are the dipole moment and the molecular weight of water. The values of the refraction index n were determined from the molar refraction by the formula The molar refraction for a GDC0068 unit of BC (cellobiose) was calculated as the additive sum of molar refractions of the bonds . The density of component 2 (cellobiose) was calculated using the Svedberg formula : where ρ12 is the density of the solution, ρ1 is the density of the solvent, с12 is the volume concentration of cellobiose in the solution. Tables 1 and 2 list the values of the BC CS parameters required for calculating the orientational dielectric polarization S12. Fig. 5 shows the concentration dependence of orientational dielectric polarization S12, obtained by the above-described calculation scheme. According to Eqs. (2) and (3), extrapolating the value of S12 to х2=0 yields the quantity (µ1)2, i.e., the value for the dipole moment of the solvent (water). The obtained dipole moment µ1 ≈ 3.1 D coincides with the dipole moment of the water molecule in its continuum when determined by the Onsager theory. The value of the dipole moment of the second component of the solution, BC CS, is equal to
If we take the value of the dipole moment of the BC molecule from , which is approximately equal to 25 D, we can then estimate the number of monomer units of cellobiose in an individual colloid:
Thus, the colloid of the aqueous suspension of disintegrated BC contains 113 cellobiose monomer units. Knowing the molecular weight of cellobiose, equal to 342, we can determine the molecular weight of the colloid: We then used the geometric dimensions given in Ref.  for a monomer unit and for microfibrils, and estimated the dimensions of the colloid. The monomer unit of cellobiose in a glucan chain has a length of 1nm and a width of 0.4–0.5nm; glucan chains are separated by an average of 0.66nm. These chains form microfibrils with a width of 3.5nm. A separate row of a microfibril contains The thickness of the microfibril is 6–7nm. By choosing the microfibril thickness of 6.5nm and the length of the monomer unit of 1.0nm, we obtain the volume of one microfibril with the length of 1 nm:
As a result, the dipole moment of one microfibril with the length of one monomer unit is equal to
To summarize, let us list the main characteristics of the BC colloid in aqueous suspension: Relaxation of dipole polarization in aqueous suspensions of disintegrated bacterial cellulose. Fig. 6 shows the frequency dependences of the dielectric loss tangent (tgδ) of aqueous suspensions of BC CS at the concentrations w2 (g/g), equal to 0.120 and 0.169. Using the value obtained above for the volume of the aqueous BC suspension colloid, equal to 364 nm3, we calculated the diameter D* of a cylinder with the height L*=1.0nm:
Fig. 7 shows for comparison the X-ray diffraction patterns of dried BC films in the native and the disintegrated states. Three main peaks were detected for both at reflection angles 2θ, equal to about 15.0°, 16.6° and 22.4°.