Poly(3-hydroxybutyrate) (PHB) is a semicrystalline biodegradable polymer with chains consisting of methyl (CH3), methylene (CH2), methine (CH) and carbonyl (CO) groups. The 1 H-13 C cross polarization NMR measurements were performed on an as-supplied powder PHB sample at a magic-angle spinning rate of 10 kHz. The measured cross polarization build-up curves and their analysis provided information on the dynamics of 1 H-13 C NMR cross polarization in functional groups with directly bonded hydrogens. The measurements required setting up the Hartmann-Hahn condition, which was inferred from the Hartmann-Hahn matching profiles measured for each functional group. The cross polarization build-up curves displayed an oscillatory course, which indicates the presence of rigid 1 H-13 C spin pairs isolated from the lattice. The frequency of the observed oscillations is directly proportional to the 1 H-13 C dipolar coupling constant, which is related to the C-H distance and its value also reflects the mobility of particular functional groups. The values of dipolar coupling constants were derived from splittings in the Fourier transforms of cross polarization build-up curves. The mobility of particular groups was assessed with the order parameter S calculated using experimental and rigid lattice values of dipolar coupling constants.

Mechanical and thermal properties of composite polymer materials strongly depend on their local structure and molecular dynamics which can be effectively studied by the solid-state nuclear magnetic resonance (NMR) techniques. In the present paper, the influence of formamide (F) and sorbitol (S) plasticizers on molecular motion in thermoplastic starch (TPS) was studied using solid-state NMR spectroscopy and dynamic mechanical thermal analysis (DMTA). DMTA measurements carried out for formamide-(F-TPS) and sorbitol-plasticized (S-TPS) corn starches indicated heterogeneous plasticizer distribution of plasticizer-rich and starch-rich phases within the samples. The single pulse and cross-polarization 13 C NMR spectra measured for both plasticized starches confirmed the amorphous character of their structure and distinctly different chain mobility supported by the values of 13 C spin-lattice relaxation times. The results of the analysis of broad line and magic angle spinning 1 H NMR spectra are in accordance with the results of DMTA measurements, revealing lower mobility of starch chains within S-TPS in comparison to F-TPS. Crosslinking of the starch chains with sorbitol molecules was suggested as being responsible for the lower mobility of the starch chains in S-TPS.

Abstract. This is a review paper based on the series of our papers devoted to a structure of truepoly-analytic Bergman function spaces over the upper half-plane in the complex plane and to a detailed study of properties of Toeplitz operators with separate symbols acting on them via time-scale analysis approach.Mathematics subject classification (2010): Primary 47B35; Secondary 47G30, 47L80, 42C40.

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The standard experimental set-up enabling observation of rotational motion of a bar around its centre of mass, which is set into motion due to the external torque generated by the small weight, was extended with an optical gate and position sensor and connected to a computer with software, which made it possible to display measured values of bar half-rotations during accelerated and decelerated motion as well as to process the data immediately. The detailed analysis of experimental data obtained for decelerated rotational motion due to frictional torque only (without small weight) showed that, besides the constant term due to dry friction at an axle, the expression for friction forces in the system has to include terms depending on the first and/or second power of angular speed, which is evidence that viscous forces influence the motion of a bar. The frictional torque due to viscous forces can be evaluated as the difference between the effective frictional torque acting on the system and the frictional torque due to dry friction at an axle. The data obtained in the experiment in which the bar performed damped oscillatory motion provided the values of effective frictional torque and the moment of inertia of rotating bodies. The frictional torque due to dry friction can be obtained as a minimum torque (calculated using minimum mass of weight) needed to start rotational motion. The last two proposed experiments can be included in undergraduate laboratory practicals.