Branched versus linear alkane adsorption in carbonaceous slit pores
Supplemental Information
A. Harrison1, R. F. Cracknell2, J. Krueger-Venus3, L. Sarkisov1,*
1University of Edinburgh, Institute for Materials and Processes, Edinburgh, United Kingdom
2Shell Projects and Technology, Shell Technology Centre Thornton, Chester, United Kingdom
3Shell Projects and Technology, Shell Global Solutions (Deutschland) GmbH, Hamburg, Germany
Abstract
The presence of carbonaceous deposits on the internal surfaces of a spark ignition engine has been linked in the literature to impaired vehicle performance, as manifested by increased knocking, higher fuel consumption, higher emissions and other adverse effects. One of the proposed mechanisms, in which the deposits affect the processes in the engine, is the adsorption and desorption of fuel components in the pores within the deposit. In this article we investigate this mechanism in more detail by considering single component adsorption of normal and branched alkanes in selected model slit pores representing the structure of the deposits. We further extend these studies to the binary mixture of normal heptane and isooctane, corresponding to a primary reference fuel blend. In particular, we show that in larger pores adsorption selectivity towards isooctane is about 1.2 on average throughout the pressure range. However, in the smaller 10Å pore selectivity towards isooctane can be in excess of three as a result of packing effects. These results are then placed in the context of engine performance issues.
1. Simulation Details
1.1 Lennard-Jones interaction parameters for species used in this work
United atom / s [Å] / ε/kB [K] / RefC / 6.400 / 0.50 / [1, 2]
CH / 4.680 / 10.00 / [1, 2]
CH2 / 3.950 / 46.00 / [1, 2]
CH3 / 3.750 / 98.00 / [1, 2]
Cwall / 3.400 / 12.00 / [3, 4]
Table 1: Lennard-Jones interaction parameters
1.2 Generation of potential maps (PMAPs):
PMAPs were generated using cut-off of 30Å. The supercell consisted of 2x2x2 simulation cells for both 10Å and 20Å pores, and of 2x2x1 simulation cells for 40Å pores. Grid spacing for the PMAP generation was set at 0.2Å.
1.3 Generation of a library of canonical conformations for branched alkanes
Generation of a library of molecular conformations, corresponding to the canonical distribution at a particular temperature, involved a molecular dynamics simulation of 100-200 ideal molecules of branched species at constant temperature of 390 K (NVT ensemble). For this the Nose-Hoover thermostat was used. The only interactions considered were the internal molecular interactions including bond constraints, bond bending, bond torsions and internal 1-5 Lennard-Jones interactions between sites of the same molecule, according to the TraPPE forcefield [1, 2]. A sufficient number of steps were run to generate libraries of 200,000 conformations in each case.
1.4 Grand canonical adsorption simulations of branched alkanes using library insertions
An energy-biased grand canonical Monte Carlo simulation [5] was combined with library-insertions to simulate the adsorption of branched alkanes. Each system consisted of a 1x1x1 simulation cells arrangement with one of four possible movements attempted per iteration, specifically biased library insertion (insertion from a generated library of molecular conformations), biased deletion, random rotation and random translation. Each type of move was attempted with equal probability. The number of attempted steps varied from 5 to 100 million, with the more complex and larger systems requiring longer equilibration.
1.5 Configuration bias grand canonical Monte Carlo simulations of linear alkanes
The employed configuration bias - energy bias grand canonical Monte Carlo (CB/EB GCMC) was as described by Snurr et al [5] and implemented in Multipurpose Simulation Code[6]. The number of iterations per simulation ranged from 5 to 50 million. Each iteration consisted of either configurational bias insertion, deletion, cut and re-growth move, or random translation move. Each type of move was attempted with equal probability.
2. Comparison of library insertion GCMC with CB -GCMC for isooctane in a 35Å slit pore at 390 K
Here we compare the accuracy of the GCMC method based on library insertions with CB GCMC method for branched molecules as implemented by Smit and co-workers[7]. In both cases (GCMC with library insertions and CB-GCMC), energy biasing is employed using pre-calculated potential maps [5] . The test system is isooctane in 35Å slit pore at 390 K. For generation of potential maps cut-off of 15Å was used. All other parameters are as described before.
Figure 1: Adsorption isotherms for isooctane in 35Å slit pore at 390 K. Black squares are from Music [6] with energy bias library insertions, red circles are reference results from the code kindly provided by Prof. Berend Smit, University of California, Berkeley.
3. Adsorption isotherms as functions of reduced pressure
3.1 Butanes in 10Å pores
Figure 2: Adsorption isotherms for n-butane (black triangles and lines) and i-butane (white triangles and black lines) in 10Å slit pore at 390K as functions of reduced pressure. Right panel uses the logarithmic scale for pressure.
3.2 Butanes in 20Å and 40Å pores
Figure 2: Adsorption isotherms for n-butane (black triangles and lines) and i-butane (white triangles and lines) in 20Å slit pore (left panel) and 40Å slit pore (right panel) at 390K shown as functions of reduced pressure.
3.3 Heptane, octane and isooctane in 10Å slit pore
Figure 3: Adsorption isotherms for n-heptane (grey squares and lines) and n-octane (black circles and lines) and i-octane (black diamonds and lines) in 10Å slit pore at 390K. Right panel shows the data using the logarithmic scale.
3.4 Heptane, octane and iso-octane in 20Å and 40Å slit pores
Figure 4: Adsorption (grey squares and black lines) and desorption (white squares and red lines) isotherms for n-heptane, n-octane (black circles and lines for adsorption and white circles and red lines for desorption, respectively) and i-octane (black diamonds and lines for adsorption and white diamonds and red lines for desorption, respectively) in 20Å slit pore (on the left) and 40Å slit pore (on the right) at 390K.
3.5 Layering effects in 10Å pores
Shown in Figure 5 are visualisation snapshots of n-heptane and i-octane at high loadings in the 10Å pore. It is clear that a double layer of linear alkanes does not form.
Figure 5: Visualisations of n-heptane (orange) and i-octane (cyan) loadings in the 10Å slit pore. Only two layers of the wall out of six are shown on each side of the slit pore.
This can also be assessed via a quick calculation. The available space in the z-direction has already been mentioned to be equal to the pore-width minus 3.4Å to account for the size of the wall atoms, or 6.6Å. From Table 1, it can be seen that the smallest united atom corresponding to the CH3 group, has diameter of s = 3.75Å. The size of the double layer of linear alkanes is about 7.5Å and this can not be attained in 10Å without severe energetic penalties.
3.6 Pore Size Distributions:
Figure 6 shows the PSDs for both combustion chamber deposits and intake valve deposits as reported in previous publications and further enhanced in our more recent studies [3, 4].
Figure 6: Pore size distributions (PSDs) for combustion chamber (on the left) and intake valve (on the right) deposits. The blue lines corresponds to the PSDs presented in the original publications by Costa and co-workers [3, 4], the red lines correspond to a recent refinement of the model using isotherm kernels with finely spaced pore widths.
We emphasize here that 10Å pore is present in both samples of deposits, 40Å was selected to represent a characteristic width from the 30-50Å range, while 20Å pores do not exist in the deposits, but this width was selected for the studies to understand any possible transitions in the adsorption regimes between 10Å and 40Å pores.
4. Example calculation: Mole fraction composition of reference fuel
A reference fuel mixture is composed of 90% i-octane and 10% n-heptane by volume of liquid. Density of n-heptane is 0.6837 g/mL, and molecular mass is 100.21 g/mole. Density of i-octane is 0.6919 g/mL and molecular mass is 114.23 g/mole. From these molar densities of n-heptane is 6.823 mmol/mL and molar density of i-octane 6.057 mmol/mL. A 90:10 liquid volume mixture corresponds to a mole fraction ratio of 0.889 : 0.111 (i-octane : n-heptane).
4. Critical temperatures and saturation pressures of adsorbate species
Species / Critical Temperature [K] / Saturation Vapour Pressure at 390K [kPa]n-Butane / 425.0 / 2002.45
Isobutane / 408.05 / 2590.64
n-Heptane / 540.0 / 174.18
n-Octane / 568.7 / 78.94
Isooctane / 543.9 / 162.62
5. Example Calculation of Fuel Injection:
A quick, somewhat coarse calculation can show how much fuel is introduced into a typical internal combustion engine. We consider a four cylinder engine with a two litre capacity. The calculation is based on the following assumptions:
1. The fuel is composed of isooctane only
2. The fuel is introduced together with air in stoichiometric air to fuel ratio, corresponding to the following combustion reaction:
12.5(O2 +3.76N2) + C8H18 -> 8CO2 + 9H2O + 47N2 (r1)
3. The intake pressure is 1 atmosphere
4. All of the fuel is vaporized
5. The pre-combustion mixture of fuel and air follows the ideal gas law
Based on these assumptions:
Volume of one cylinder V=0.5L = 0.5·10-3m3
Mole fraction of isooctane in the gas phase: yC8H18 = 1/60.5 = 0.01652, where
60.5 is the total number of moles nitrogen + oxygen + isooctane, according to reaction (r1)
Amount of fuel introduced in one cylinder during a single engine stroke:
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