**2.5 End-to-end length of** *n***-hexane during diffusion**

An interesting observation from the study was the variation of end-to-end length, L*e*-*<sup>e</sup>* of *n*-hexane during diffusion. The L*e*-*<sup>e</sup>* was computed at various temperatures for *n*-hexane. It showed that there is a decrease in the end-to-end length of *n*hexane as the temperature increases. A plot of average L*e*-*<sup>e</sup>* as a function of the temperature is shown in **Figure 17** [44]. The distribution of the L*e*-*<sup>e</sup>* has also been computed for various temperatures and these are shown in **Figure 18** [44]. As can be seen at higher temperatures the distribution has a higher probability for smaller values of L*e*-*e*, between 3 and 5 Å and less probability for higher values (5–6.4 Å) of L*e*-*e*. This is what leads to a decrease in average L*e*-*<sup>e</sup>* with temperature. These suggest that *n*-hexane curls up at higher temperatures and has a higher population of gauche conformers. In order to check if this was true, we have obtained the number of gauche conformer population and these are listed in **Table 7**.

The distribution of end-to-end length of *n*-hexane is shown in **Figure 19** for two specific situations: (i) when the center of mass of *n*-hexane is close to the 12-ring window (within 1.0 Å) and (ii) when the center of mass is greater than 2 Å from the window plane [44]. As can be seen, the probability for smaller values of L*e*-*<sup>e</sup>* is higher when the molecule of *n*-hexane is closer to the window. Thus, it appears that the *n*-hexane curls up trying to increase its cross-sectional diameter while passing through the 12-ring window. This leads to a slightly lower value of energetic barrier

Using the levitation effect, separation of molecular mixtures can be realized. This approach differs from the usual approach toward separation. In the usual approach separation is achieved because the smaller sized molecules generally diffuse faster as compared to larger sized guest molecules. Or alternately, certain molecules enter the pores while bigger sized molecules do not even enter the pore network. In this case only those which enter the pores are able to pass through the column of the zeolite while others are unable to pass through leading to good

Consider now a binary mixtures in which both the components are able to enter the pore network. When we use the levitation effect, both mixtures will diffuse but here the larger sized guest will diffuse faster provided the bottleneck of the zeolite has a dimaeter that is comparable to the diameter of the larger sized guest molecule. The smaller diameter guest molecule will diffuse slower and this leads to separation

In all these separations, however, one thing that is common is that both the components (in the case of a binary mixture) will diffuse in the same direction. This leads at best to a reasonable degree of separation. However, much higher degree of separation can be achieved if the two components move in opposite directions. We have devised a novel approach to separation in which the two components move in opposite directions [45]. In this approach, the fact that the guest in AR and the LR regimes have out-of-phase potential energy landscape is utilized. This is shown in **Figure 20** [45]. In addition, a hot zone is placed to the left of the 12-ring window in the system consisting of zeolite A with argon (of AR) and neon (of LR). The hot zone drives argon toward the left and the neon toward to right. The result is a very high degree of separation. This has been demonstrated through nonequilibrium Monte Carlo simulations with inhomogeneous temperature [45]. In **Figure 21** a plot of the separation factor as a function of Monte Carlo steps is shown. Normally separation factors that are achieved are of the order of 2000–4000. But here we see

that separation factors of the order of >108–<sup>10</sup> can be realized.

for *n*-hexane when it curls up.

separation.

**67**

**Figure 19.**

of the components.

**2.6 Separation using levitation effect**

*Variation of the distribution of end-to-end length of nC6 in zeolite NaY.*

*Anomalous Diffusivity in Porous Solids: Levitation Effect*

*DOI: http://dx.doi.org/10.5772/intechopen.92685*

**Figure 17.** *Variation of end-to-end length of n-hexane in zeolite NaY as a function of temperature.*

**Figure 18.** *Distribution of end-to-end length n-hexane in zeolite NaYat various temperatures.*


**Table 7.**

*% gauche conformations for each dihedral angle of nC6 inside zeolite NaY at various temperatures.*

*Anomalous Diffusivity in Porous Solids: Levitation Effect DOI: http://dx.doi.org/10.5772/intechopen.92685*

**2.5 End-to-end length of** *n***-hexane during diffusion**

*Zeolites - New Challenges*

gauche conformer population and these are listed in **Table 7**.

*Variation of end-to-end length of n-hexane in zeolite NaY as a function of temperature.*

*Distribution of end-to-end length n-hexane in zeolite NaYat various temperatures.*

**Temp (K)** *ϕ***<sup>1</sup>** *ϕ***<sup>2</sup>** *ϕ***<sup>3</sup>** 24.9 19.0 24.7 29.5 23.8 29.4 32.3 26.4 32.5 34.3 28.2 34.3 36.5 30.4 36.6

*% gauche conformations for each dihedral angle of nC6 inside zeolite NaY at various temperatures.*

**Figure 17.**

**Figure 18.**

**Table 7.**

**66**

An interesting observation from the study was the variation of end-to-end length, L*e*-*<sup>e</sup>* of *n*-hexane during diffusion. The L*e*-*<sup>e</sup>* was computed at various temperatures for *n*-hexane. It showed that there is a decrease in the end-to-end length of *n*hexane as the temperature increases. A plot of average L*e*-*<sup>e</sup>* as a function of the temperature is shown in **Figure 17** [44]. The distribution of the L*e*-*<sup>e</sup>* has also been computed for various temperatures and these are shown in **Figure 18** [44]. As can be seen at higher temperatures the distribution has a higher probability for smaller values of L*e*-*e*, between 3 and 5 Å and less probability for higher values (5–6.4 Å) of L*e*-*e*. This is what leads to a decrease in average L*e*-*<sup>e</sup>* with temperature. These suggest that *n*-hexane curls up at higher temperatures and has a higher population of gauche conformers. In order to check if this was true, we have obtained the number of

**Figure 19.** *Variation of the distribution of end-to-end length of nC6 in zeolite NaY.*

The distribution of end-to-end length of *n*-hexane is shown in **Figure 19** for two specific situations: (i) when the center of mass of *n*-hexane is close to the 12-ring window (within 1.0 Å) and (ii) when the center of mass is greater than 2 Å from the window plane [44]. As can be seen, the probability for smaller values of L*e*-*<sup>e</sup>* is higher when the molecule of *n*-hexane is closer to the window. Thus, it appears that the *n*-hexane curls up trying to increase its cross-sectional diameter while passing through the 12-ring window. This leads to a slightly lower value of energetic barrier for *n*-hexane when it curls up.

#### **2.6 Separation using levitation effect**

Using the levitation effect, separation of molecular mixtures can be realized. This approach differs from the usual approach toward separation. In the usual approach separation is achieved because the smaller sized molecules generally diffuse faster as compared to larger sized guest molecules. Or alternately, certain molecules enter the pores while bigger sized molecules do not even enter the pore network. In this case only those which enter the pores are able to pass through the column of the zeolite while others are unable to pass through leading to good separation.

Consider now a binary mixtures in which both the components are able to enter the pore network. When we use the levitation effect, both mixtures will diffuse but here the larger sized guest will diffuse faster provided the bottleneck of the zeolite has a dimaeter that is comparable to the diameter of the larger sized guest molecule. The smaller diameter guest molecule will diffuse slower and this leads to separation of the components.

In all these separations, however, one thing that is common is that both the components (in the case of a binary mixture) will diffuse in the same direction. This leads at best to a reasonable degree of separation. However, much higher degree of separation can be achieved if the two components move in opposite directions. We have devised a novel approach to separation in which the two components move in opposite directions [45]. In this approach, the fact that the guest in AR and the LR regimes have out-of-phase potential energy landscape is utilized. This is shown in **Figure 20** [45]. In addition, a hot zone is placed to the left of the 12-ring window in the system consisting of zeolite A with argon (of AR) and neon (of LR). The hot zone drives argon toward the left and the neon toward to right. The result is a very high degree of separation. This has been demonstrated through nonequilibrium Monte Carlo simulations with inhomogeneous temperature [45]. In **Figure 21** a plot of the separation factor as a function of Monte Carlo steps is shown. Normally separation factors that are achieved are of the order of 2000–4000. But here we see that separation factors of the order of >108–<sup>10</sup> can be realized.

#### **Figure 20.**

*Schematic of potential energy landscapes of AR (BLUE) and LR (RED) particles are shown below the unit cell crystal structure of zeolite NaCaA. The black dotted lines are the window planes of the zeolite.*

#### **Figure 21.**

*Evolution of separation factor with Monte Carlo steps. This shows that AR particles can be fully separated from LR particles using this separation technique.*
