Establecimientos y matrícula: variedad en la oferta, crecimiento del sector

Longer simulation times were required to facilitate extended molecular migration through the zeolite framework. Analysis o f simulation runs lasting up to lOOps suggested restricted molecular diffusion. Typically the para-xylene m olecule would remain localized in a 10 or a 12 MR for the duration o f the lOOps experiments. Simulations o f up to 440ps for NVT and N VE ensem bles demonstrated greater movement throughout the rings and interconnected channels. Several discrete diffusion rates within a single simulation were calculated. These gave rise to M SD plots, graph 5.3, which exhibited two regimes. The first which had a large, positive gradient [which is linear] and other regimes, where the gradient o f the line approaches zero, where the m olecules are stationary. These M SD plots were correlated to the exact molecule location. That is, the molecular diffusion in a ring system corresponded to the linear region o f the M SD plot; whereas a plateau region reflected slower hydrocarbon movement via the smaller interconnecting rings, indicated by the

region labelled I, shown in figure 5.4. The calculated diffusion coefficients reflecting the diffusion regimes are depicted in table 5.4.

Table 5.4. Diffusion coefficients o f para-xylene in the lOMR, 12MR and intra- connecting region o f CIT-1 for 300ps o f NVT dynam ics perform ed at 500K for 0.125 loading.

lOMR 12 MR intra-region

diffusion coefficient, D l l . T x l O ' W s ’' 17.3 x l O ' W s ' ' 11.0 x lO '^ c m V

Figure 5.4. Outlines the area o f the framework in which m olecules are confined tem porarily in transit to lOMR or 12MR channels.

NB: the 'intra-region, / ’ refers to the network connecting the lOMR and 12MR channels.

rT" 400 Q 300 5 200 100 200 300 SIMULATION TIME /ps 400

G ra p h 5.3. M ean squared diffusion profile for the CIT-1/para xylene NVT ensemble system performed at 500K.

The trend o f the results reported in table 5.4 corroborate previous studies;^'" in particular that the para-xylene isomer has a greater diffusivity in the larger 12MR system than the lOMR system. The plateau [flat] regions o f the diffusion plot shown in graph 5.3 are consistent with a ‘cooling o f f period’ for the m olecule reflected in the slight decrease in diffusion coefficient.

A 360ps, 450K dynamics simulation was performed using the NVE ensemble. The results are reported in table 5.5. In this simulation significantly higher diffusion rates were reached. The diffusion plot in graph 5.4 displayed clear regions o f m olecular m obility and relatively static periods within the sm aller channel system. An initial linear relationship between MSD and simulation tim e was observed from Ops-lOOps. O bservations revealed the para-xylene to be located within the lOMR channel at this point. The calculated diffusion coefficient was 76.6 xlO'^cm^s''. A large deceleration in diffusivity [41.7 xlO'^cm^s''] occurred between 133ps and 220 ps w here the m olecule was ‘hopping’ between the ‘inter’ ring regions and the lOMR channel.

Therefore between 133ps and 145ps the molecule was in the lOMR channel system; the diffusion coefficient was 34.7x10'^cm^s’’, the m olecule was then observed to move out into the ‘interconnecting channel’ region between 161ps and 219ps. This led to a value o f 44.5x10‘^cm^s''. However, From 225ps to 360ps a linear increase in diffusion occurred representing the increased para-xylene m obility in the 12MR. The diffusion coefficient calculated here was 67.9x10'^cm^s'’. Snapshots o f the superim posed m olecule’s locations as described above are shown in figures 5.5-5.7.

Table 5.5. Diffusion coefficients o f para-xylene in the lOMR, 12MR and intra- connecting region o f ClT-1 for up to 360ps o f NVE dynam ics perform ed at 500K.

ÎOMR I2M R Intra-region

diffusion coefficient, D 4 l.7 x lO " c m V 67.9x10'^cm^s'' 34.7 x lO 'W s ''

Q 1500

^

50 100 150 200 250 300 350

SIMULATION TIME (ps)

Graph 5.4. M SD versus simulation time plot for approxim ately 360ps N VE CIT- 1 /para system perform ed at 450K dem onstrating distinct diffusion processes.

f v

Figure 5.5. Snapshot o f overlaid para-xylene molecules within the lOMR channel showing molecule location during the course o f an NVE simulation perform ed at 450K for 360ps.

;

%

Figure 5.6. Snapshot o f overlaid para-xylene molecules within the 12MR channel viewed along the [010] projection showing m olecule location during the course o f an NVE simulation performed at 450K for 360ps.

Figure 5.7. Snapshot o f overlaid para-xylene molecules within the 12MR channel viewed along the [001] projection showing m olecule location during the course o f an NVE simulation performed at 450K for 360ps.

5.4.4 Diffusion o f ortho-xylene isomers within zeolite CIT-1: rigid ion m odel dynamics

M olecular dynam ics simulations lasting 440ps and using NVT dynam ics at 450K were run for the ortho-xylene isomer. The calculated diffusion coefficients were lower than those for the streamlined para-xylene m olecule as reported in table 5.6 below.

Table 5.6. Com parison o f aggregate diffusion coefficients for the two xylene isomers after 440ps o f NVT dynamics.

ortho-xylene [440ps] para-xylene [440ps]

The M SD graph 5.5, shows diffusion regimes are present, providing evidence o f non- uniform m olecule diffusion within the CIT-1 macro-cell. Diffusion coefficients generated from the simulation at lOOps, 200ps and 300ps have been evaluated.

From Ops to lOOps the M SD/simulation time relationship is linear except for a deviation between 32ps to 47ps. The diffusion coefficient calculated for this period was approxim ately 18 xlO'^cm^s''. At this point, the m olecule had passed into the inter-channel region and moved into the 12MR channel; hence diffusion was uninterrupted by the constriction o f the 12MR aperture. In the following lOOps, the diffusion rate was maintained until the molecule moved out into sm aller channels at 168ps and remains there until 201ps. After this point [201ps-440ps] a marked decrease in diffusion coefficient was determined o f 8.3x10'^cm^s'' up until the end o f the simulation. This deceleration in diffusivity over a very long time-scale is characterised by a parabolic region o f the MSD plot, which remained linear until 201ps. After the ‘p ost’ 201ps dynamics, the molecule was observed to ‘h o p ’ around the macro-cell network and did not reside in any o f the larger cells for any appreciable length o f time.

g 100

100 150 200

SIMULATION TIME (ps)

Graph 5.5. M ean squared diffusion profile for the CIT-1/ortho-xylene system performed at 450K.