The presented work aims at exploring the influence of the mobility of the sorbent framework on both the equilibrium and the kinetic properties of the sorbed phase by means of molecular dynamics computer experiments under isochoricÀisothermal and isobaricÀisothermal statistical ensembles for several host model options, combined by Widom averaging along the entire trajectory of the hostÀguest system toward rigorously obtained sorbate isotherms within a fully flexible lattice. The methodology is adapted to the study of the self-diffusivity and the collective (MaxwellÀStefan and transport) diffusivities of carbon dioxide (CO 2 ) and methane (CH 4 ) within the zeolite imidazolate framework-8 (ZIF-8). The simulation predictions are compared with measurements from pulsed-field gradient nuclear magnetic resonance (PFG NMR), as well as with recently conducted infrared microscopy (IRM) experiments elaborated on the basis of the current modeling in the flexible ZIF-8. The modeling results reveal a significant influence on sorbate transport exerted by the 2-methilimidazolate ligands surrounding the cage-to-cage entrances, whose apertures are commensurate with the guest molecular dimensions. Moreover, calculations of the singlet probability density distribution of the sorbate molecules at selected regions within the imidazolate framework provide a plausible explanation of the transport diffusivity as a function of sorbate occupancy, measured via IRM.

Self-diffusion measurements with methane and carbon dioxide adsorbed in the Zeolitic Imidazolate Framework-8 (ZIF-8) were performed by 1 H and 13 C pulsed field gradient nuclear magnetic resonance (PFG NMR). The experiments were conducted at 298 K and variable pressures of 7 to 15 bar in the gas phase above the ZIF-8 bed. Via known adsorption isotherms these pressures were converted to loadings of the adsorbed molecules. The self-diffusion coefficients of carbon dioxide measured by PFG NMR are found to be independent of loading. They are in good agreement with results from molecular dynamic (MD) simulations and resume the trend previously found by IR microscopy at lower loadings. Methane diffuses in ZIF-8 only slightly slower than carbon dioxide. Its experimentally obtained self-diffusion coefficients are about a factor of two smaller than the corresponding values determined by MD simulations using flexible frameworks.

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A standard X-observe NMR probe was equipped with a z-gradient coil to enable high-sensitivity pulsed field gradient NMR diffusion studies of Li+ and Cs+ cations of aqueous salt solutions in a high-porosity mesocellular silica foam (MCF) and of CO2 adsorbed in metal-organic frameworks (MOF). The coil design and the necessary probe modifications, which yield pulsed field gradients of up to ±16.2Tm-1, are introduced. The system was calibrated at 2H resonance frequency and successfully applied for diffusion studies at 7Li, 23Na, 13C and 133Cs frequencies. Significant reductions of the diffusivities of the cations in LiClac and CsClac solution introduced into MCFs are observed. By comparison of the diffusion behavior with the bulk solutions, a tortuosity of the silica foam of 4.5±0.6 was derived. Single component self-diffusion of CO2 and CH4 (measured by 1H NMR) as well as self-diffusion of the individual components in CO2/CH4 mixtures was studied in the MOF CuBTC. The experimental results confirm high mobilities of the adsorbed gases and trends for diffusion separation factors predicted by MD simulations.

Für NMR‐Diffusionsmessungen wurde ein z‐Gradientensystem zur Erzeugung intensiver Feldgradientenimpulse überarbeitet. Dazu wurde das Gradientenfeld einer aktiv abgeschirmten Spule mittels der Finite‐Elemente‐Methode optimiert. Das System wurde aus Glaskeramik als Spulenträger aufgebaut. Es besitzt kein 1H‐NMR‐Eigensignal und weist einen hohen Strom/Gradienten‐Wandlerfaktor von 0,37 T m–1A–1 auf. Mit dem Nachweis isotroper und anisotroper Diffusion in wässrigen Lösungen eines PEO‐PPO‐PEO Triblock‐Copolymers und adsorbierten Methans in zwei verschiedenen mikroporösen kristallinen Adsorbentien wird die Funktionstüchtigkeit des Systems demonstriert.

Acta Technologica Agriculturae 1/2016Dušan Páleš et al.The most effective way for determination of curves for practical use is to use a set of control points. These control points can be accompanied by other restriction for the curve, for example boundary conditions or conditions for curve continuity (Sederberg, 2012). When a smooth curve runs only through some control points, we refer to curve approximation. The B-spline curve is one of such approximation curves and is addressed in this contribution. A special case of the B-spline curve is the Bézier curve Rédl et al., 2014). The B-spline curve is applied to a set of control points in a space, which were obtained by measurement of real vehicle movement on a slope (Rédl, 2007(Rédl, , 2008. Data were processed into the resulting trajectory (Rédl, 2012;Rédl and Kučera, 2008). Except for this, the movement of the vehicle was simulated using motion equations (Rédl, 2003;Rédl and Kročko, 2007). B-spline basis functionsBézier basis functions known as Bernstein polynomials are used in a formula as a weighting function for parametric representation of the curve (Shene, 2014). B-spline basis functions are applied similarly, although they are more complicated. They have two different properties in comparison with Bézier basis functions and these are: 1) solitary curve is divided by knots, 2) basis functions are not nonzero on the whole area. Every B-spline basis function is nonzero only on several neighbouring subintervals and thereby it is changed only locally, so the change of one control point influences only the near region around it and not the whole curve.These numbers are called knots, the set U is called the knot vector, and the half-opened interval 〈u i , u i + 1 ) is the i-th knot span. Seeing that knots u i may be equal, some knot spans may not exist, thus they are zero. If the knot u i appears p times, hence u i = u i + 1 = ... = u i + p -1 , where p >1, u i is a multiple knot of multiplicity p, written as u i (p). If u i is only a solitary knot, it is also called a simple knot. If the knots are equally spaced, i.e. (u i + 1 -u i ) = constant, for every 0 ≤ i ≤ (m -1), the knot vector or knot sequence is said uniform, otherwise it is non-uniform.Knots can be considered as division points that subdivide the interval 〈u 0 , u m 〉 into knot spans. All B-spline basis functions are supposed to have their domain on 〈u 0 , u m 〉. We will use u 0 = 0 and u m = 1.To define B-spline basis functions, we need one more parameter k, which gives the degree of these basis functions. Recursive formula is defined as follows:This definition is usually referred to as the Cox-de Boor recursion formula. If the degree is zero, i.e. k = 0, these basis functions are all step functions that follows from Eq. (1). N i, 0 (u) = 1 is only in the i-th knot span 〈u i , u i + 1 ). For example, if we have four knots u 0 = 0, u 1 = 1, u 2 = 2 and u 3 = 3, knot spans 0, 1 and 2 are 〈0, 1), 〈1, 2) and 〈2, 3), and the basis functions of degree 0 are N 0, 0 (u) = 1 on interval 〈0, 1) Acta In this co...