CC BY
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YflK 544.7+544.3
BecTHHK Cn6ry. Cep. 4. 2013. Bun. 1
S. Cumana, P. Gurikov, A. Belugin, M. Johannsen, N. Menshutina, I. Smirnova
APPLICATION OF SILICA AEROGELS AS STATIONARY PHASE IN SUPERCRITICAL FLUID CHROMATOGRAPHY: EXPERIMENTAL STUDY AND MODELLING WITH CELLULAR AUTOMATA*
1. Introduction. Silica aerogels are low-density highly porous solids, consisting of silicon oxide. Their pore content and their surface area can be as high as 99 % and 1000 m2/g, respectively [1]. As result of their unique structure they have found place in several nuclear and non-nuclear applications as Cerenkov detectors and thermal and sonic sound insulators [2-6].
Silica aerogels are prepared by means of the sol—gel process, which involves the hydrolysis and polycondensation of silicon alkoxides [7, 8]. The flexibility of the sol—gel chemistry allows the use of different precursors to obtain surfaces covered by different types of moieties like alkyl or phenyl groups [9, 10]. It enables the easy preparation of silica aerogels with functional groups adapted to specific requirements. Because of their high surface aerogels might be used as stationary phases for chromatography. Application of silica aerogel-like materials in liquid and gas chromatography have already been reported [11, 12].
However, since the scale of the mesh is typically in the order of tens of nanometers, strong capillary forces are generated and consequently partial collapse of the aerogel structure occurs upon contact with liquids [13, 14]. It invalidates their use for liquid chromatography but admits their application to supercritical fluid chromatography (SFC). SFC is a well established separation process mostly used for the separation of non-polar or slightly polar compounds. This method has been useful in the separation of low volatile substances where extreme temperatures are required to obtain adequate volatility [15]. It has been demonstrated that SFC is a suitable tool for drug analysis in the pharmaceutical industry and is often used for chiral separations [16]. Furthermore SFC can be also used as an orthogonal separation technique to confirm results from routine RP-HPLC [17].
The purpose of this work is to prove if silica aerogel particles can be used as stationary phase for SFC in combinations with supercritical carbon dioxide and modifiers as mobile phase, which is a task that until now had not been realized. Secondly, the ability of SFC to study the interactions between selected solutes and the surface of the silica aerogels under supercritical conditions is proved. The quantification of the interaction energy is an impor-
Sucre Cumana — PhD student, M. Sc., Institute of Thermal Separation Processes, Hamburg University of Technology, Germany.
Pavel Gurikov — Dr., postdoctoral fellow, Institute of Thermal Separation Processes, Hamburg University of Technology, Germany; e-mail: pavel.gurikov@tu-harburg.de
Alexander Belugin — PhD student, M. Sc., Computer Aided Process Engineering, Mendeleev University of Chemical Technology of Russia.
Monika Johannsen — Dr. habil., Associate lecturer, Institute of Bioprocess and Biosystems Engineering, Hamburg University of Technology, Germany.
Natalia Menshutina — Professor, Dean, Computer Aided Process Engineering, Mendeleev University of Chemical Technology of Russia.
Irina Smirnova — Professor Dr.-Ing., head of the Institute of Thermal Separation Processes, Hamburg University of Technology, Germany; e-mail: irina.smirnova@tu-harburg.de
* The authors are grateful for financial support from the DFG project SM 82/8-1 and RFBR project 12-08-91330.
© S. Cumana, P. Gurikov, A. Belugin, M. Johannsen, N. Menshutina, I. Smirnova, 2013
tant issue in adsorption applications. It has been recently shown that fast depressurization of supercritical solution into aerogel pores generates either amorphous or crystalline phases [18]. The degree of crystallinity of the compound loaded in the pores of aerogels is determined by its interaction with the solutes and is of special importance for pharmaceutical formulations [19].
Theoretical analysis and modeling of SFC is mainly based on numerical integration of the differential equations, involving the mass balance and the isothermal and isobaric dependence of the adsorption equilibrium constant [20], as well as simple statistical mechanical lattice theories [21]. Still there is a lack of the models, which are able to highlight dynamical aspects of SFC on molecular level at reasonable computational cost. This work firstly describes the application of the fully discrete cellular automata model taking into account the solute diffusion, its adsorption on the aerogel surface as well as translational movement under the influence of pressure gradient in the chromatographic column.
2. Experimental. Two types of aerogel particles were prepared to be used for the chro-matographic experiments: (1) crushed monolithic silica aerogels, which were then sieved to the desired size and (2) aerogel particles prepared by spraying the sol directly into an autoclave. The particles were characterized by their shape, size and porosity. SFC experiments were performed with both a commercial HPLC silica column and columns packed with the aerogel particles. As a model system for separation a mixture of polycyclic aromatic hydrocarbons (benzene, naphthalene and anthracene) was chosen, since they can be easily separated with a silica-packed commercial column, using n-pentane or n-hexane as mobile phases [22]. In some tests methanol was added to mobile phase (CO2) as a modifier.
2.1. Aerogel preparation. Crushed monolithic silica aerogels were prepared using the two-step sol—gel method described in our previous publications [1, 23, 24]. First, tetrametoxysilane (TMOS, purum, > 98.0 % for GC, Fluka), methanol (MeOH, > 99.9 %, Roth), deionized water and hydrochloric acid (puriss. p.a. plus 30 %, Merck) were mixed in molar ratios of 1 : 2.4 : 1.3 : 10~5, respectively, and stirred at room temperature for 30 min. Additional water and ammonia solution (puriss. pa. 25 %, Fluka) were added to achieve final molar ratios of 1 : 2.4 : 4 : 10~5 : 2 • 10~3 in TMOS : MeOH : Water : HCl : NH4OH, respectively. The system was further diluted with acetonitrile (ACN, gradient grade, for HPLC, ^ 99.9 % Sigma-Aldrich) to obtain a desired density of the aerogel (0.1 g/cm3). Gelation occurred in moulds after few minutes and the system was aged in acetone for approximately 24 h. Afterwards the aged and still wet gels were filled in an autoclave and drying was performed with supercritical CO2 at 100 bar and 40 °C for several hours. The gels were taken from the autoclave and crushed by using a conventional mortar. The crushed gels were then sieved to reach a fraction between 28 and 40 ^m.
Aerogel particles were prepared according the method used by Alnaief [25]. The sol was prepared as described above and immediately sprayed into an autoclave, where CO2 in its supercritical state was already present. Gelation occurred directly in the autoclave, accelerated by the presence of supercritical CO2, which acts as a catalyst for this system [24]. The particles were allowed to age and then the solvent inside the pores of the particles was extracted by supercritical CO2 in a continuous mode. After the pressure release aerogel particles were collected.
2.2. Characterization. The pore size distribution and surface area of the aerogels were determined via the nitrogen adsorption-desorption method, using a Nova 3000e surface area and pore analyzer (Quantachrome instruments). The particle size distribution of the aerogel particles prepared by spraying in the autoclave were determined by a laser diffractometer model HELOS (Sympatec). The particle size and particle shape of aerogel
particles were investigated by means of a scanning electron microscope (SEM) model Leo 1530 (Gemini).
2.3. Column packing. As aerogels are extremely porous materials, with pore sizes in the order of few nanometers, the capillary forces generated by immersing them into a liquid would lead to the collapse of their structure. Thus, it was necessary to employ a dry method to pack the chromatographic columns.
A semiautomated and manual method to dry-pack columns has already been used by Williams [26]. The method applied in this work consisted in successive filling of the column with the silica aerogel particles, followed by mechanical vibration and compression with supercritical CO2. An empty HPLC column (4.6 mm inner diameter and 250 mm length) was left one end open and coupled to a sieve shaker. Subsequently aerogel particles were introduced into the vibrating column helped by a funnel. After the column was full, the second column head was screwed, and the column placed into an equipment for supercritical fluid extraction (Speed SFE, Applied Separations). Then supercritical CO2 was pumped at 300 bar and 40 °C for several minutes. After fluid compression, one column head was newly removed and the filling process was repeated until the column was filled completely. The columns used were empty HPLC columns.
2.4. Chromatographic tests. First the separation of aromatic hydrocarbons was performed using a commercial HPLC column, Kromasil® 60-5-SIL (AkzoNobel) packed with silica-gel particles of 5 ^m in diameter. Benzene (for HPLC, Merck), naphthalene (for synthesis, Merck) and anthracene (for synthesis, Merck) were dissolved in n-hexane (95 % analytical grade, Lab Scan) at concentrations of 128.4, 17.3 and 1.1 mM, respectively. The columns were placed in the SFC equipment Model HP-G1205A (Hewlett-Packard). Different operating conditions of pressure, temperature and flow rate were tested, but only the results for the best operating conditions (2.5 cm3 CO2 min-1, 100 bar and 40 °C) are presented here. The hydrocarbons were detected at 254 nm by a UV-Detector (HP Series 1050).
Same conditions were used for the aerogel-packed columns. The number of theoretical plates N was calculated from the chromatograms which revealed that equations for peaks with Gaussian shape could be used [27]:
where h, A and tR are peak height, peak area and retention time of the less retained compound, respectively.
Finally, the influence of the modifier on the elution of aromatic hydrocarbons was investigated by adding methanol to the mobile phase in concentrations of 0.5, 1, 2 and 5 %.
2.5. Determination of interactions between active compounds and silica aerogels. For quantitative determination of the interactions between the aerogels and the solutes naphthalene was used as model compound since its crystallinity in the aerogel pores was studied in previous work [18, 19]. The experiments were performed analogous to those described in section 2.4 with both commercial and aerogel-filled columns, but instead of aromatic hydrocarbons mixture a solution of naphthalene in n-hexane was injected into the column accordingly. The retention times of the compound were determined for different flow rates and temperatures. The experiments were performed at constant density of the CO2. To calculate the thermodynamic parameters the retention factor k' was determined from the retention times (tR) and the hold-up time (to) and the plot of ln k' vs. Twas constructed [28]. The enthalpy and entropy of adsorption, respectively, were determined from the slope
(1)
and intersection of the straight line according to equation (2):
The phase ratio P = Vs/Vm, where Vs and Vm are the volume of the stationary and mobile phase, respectively.
The operating conditions were selected in order to obtain average densities of CO2 inside the column in the range of 0.22 and 0.86 g/cm3. The influence of the CO2 density on the thermodynamics of adsorption was then investigated.
3. Modeling of SFC with cellular automata.
3.1. Set of states and transition rules. One of the remarkable properties of cellular automata (CA) approach is the representation of the whole system as a set of independent cells, which are interacting only with their nearest neighbors. Large amount of potential deterministic and stochastic rules along with several reasonable choices of the neighborhood pattern induce the great diversity of possible behavior. Nevertheless, only a limited number of combinations is able to reflect physical and chemical phenomena in the real systems. Margolus cellular automation, MCA, [29] was chosen to be generalized and applied for the SFC problems. MCA is proved to be consistent with numerical and analytical solutions of the diffusion equation and has been recently used to model diffusion through the channel [30] and drug release from the porous matrix [31].
In this work the CA model was composed as a set of cells forming 2-dimentional rectangular grid. Each cell has one of three possible states: aerogel (A), solute molecule (M) and solvent (S). Molecular diffusion is realized by synchronous n/2-angel rotations of 2 x 2 blocks clockwise (cw) or counterclockwise (ccw) with certain probabilities pcw and pccw, respectively (Fig. 1). All A-cells are fixed and cannot be occupied by M-cells. At each discrete time step even and odd division patterns are changing over to ensure the isotropy of
Fig. 1. Grid divided by 2 x 2 blocks (a) and boundary conditions applied on the left and right sides (b)
space. In order to take into account molecular interaction the rotation probabilities govern by energetic and entropic effects. For instance, transfer of M-cell from bulk phase (where all neighbors are S-cells) to the aerogel surface yields the decreasing of energy and entropy. On the assumption of local equilibrium for each block 2 x 2 the probability pi to be rotated clockwise and counterclockwise are:
1
= fiT, (3)
where subscript i can be either "cw" or "ccw", Fi is the free energy of the rotated state, and Z is given by:
r, Fum Few Fccw
Z = e Rt + e Rt + e R? . (4)
Fum in eq. (4) is the free energy of the initial unmoved state (subscript "um").
In general case all three free energies will be different and rotation with the lowest energy can be interpreted as the most probable. The relation between energies and probabilities given above is an analogue of the partition function for a system with 3 energy levels. Probability to stay unmoved pum is calculated from normalization condition: pum = 1
pcw pccw.
Decision on direction of the rotation has to be taken locally, so Fi depends only on the states of the neighbors:
4
Fi = EE fjk, (5)
j=1 k£N
where the first summation is over each cell in the block, and the second one runs over all nearest neighbors as well as the cells in the block (set N). Matrix fjk is symmetrical and represents all possible molecular interactions in the system. As generally accepted in thermodynamics, fjk can be represented as sum of energetic and entropic terms:
fjk = £jk — Tsjk, (6)
where j (in K) and sjk (dimensionless) from now on are measured in R units (R = 8.314 J/(mol-K); T is temperature. Transition rules described above are applied for both diffusion and adsorption processes. It is reasonable that translational movement from inlet to outlet of the column can be also described in terms of probability. If rotation leads to the motion toward the outlet (6 = 1; 6 = 0 otherwise), such rotation is more favorable. Using FI instead of Fi the flow can be accounted as follows:
F! = Fi + 6Fflow, (7)
where Fflow is determined by energy of the flow in the column.
Thus, all possible types of molecular motions are embodied in rotations with probabilities, which depend only on the states of nearest neighbors and state of the current cell itself.
3.2. Aerogel structure. The structure of aerogel can be represented as a set of overlapping nanosized silica spheres. Pore space is formed by voids between such spheres and characterized by the pore size distribution. However, to be used in CA model 3-dimentional structure should be mapped into a two-dimensional set of A-cells. For given rectangular field N x M the number of A-cells Q is governed by following expression:
Q = N ■ M, (8)
Psilica
where Pag is true aerogel density and psilica = 2.19 g/cm3.
An isolated cell with linear size L (in nm) has four free sides and thus its specific surface area is equal to 4/(Lps¡l¡ca). When two cells have one side in common, specific area reduces to 3/(Lpsilica) or more general to x/(Lps¡l¡ca). The factor x reflects the number of free sides per one A-cell and is referred at a connectivity factor. Taking into account experimental specific surface area S (in m2/g) the connectivity factor can be calculated as follows:
_ PsüícaLS
A 1000 v 7
Instead of random placement the A-cells were placed in such a way that the final structure has the desired connectivity factor. The algorithm described above was used to generate the sets of A-cells with the density and specific surface area equal to those of silica aerogels used.
3.3. Observable quantities. In term of enthalpy and entropy of adsorption, an un-retained compound has j = 0 and sjk = 0 where j and k correspond to one M- and one A-cell. In contrast, the compound of interest has non-zero j = 0 and sjk = 0 and thus shows retention time greater than t0. The observations of the retention time in computational experiments were organized as follows. M-cells were placed at the left side of the field. Iterations were performed as described in section 3.1 until all molecules reached the last right column of field and then removed (Fig. 1). The number of removed molecules was counted and plotted against the number of iterations. Retention time then was calculated by the common moment method. Computational experiment provides the retention times measured in numbers of iteration. Regardless of this fact retention factor is dimensionless and can be calculated according the general formula: k' = (tR — t0)/t0. By changing temperature at constant j = 0 and sjk = 0 van't Hoff plot in coordinates ln k' vs. T-1 can be constructed.
4. Results and Discussion.
4.1. Particle morphology and particle size distribution. Kromasil® particles are claimed to be perfectly spherical and to have a smooth surface (Fig. 2). These particles are conventionally slurry packed and have a very narrow particle size distribution. The majority of the particles posses diameters between 5 and 10 |m.
The crushed aerogel particles were very small and completely irregular in form. Their longitudinal and transversal axes were very different (Fig. 3, a). Although their surface seems to be rather smooth, they possess a very high porosity consisting mainly of monomodal mesopores. The sprayed aerogels exhibited a completely different size, shape and surface smoothness (Fig. 3, b). They were not spherical, but the difference in length of perpendicular
Fig. 2. FE-SEM of Kromasil® 60-5-SIL, 5 |im particles (image courtesy of Kromasil®)
Fig. 3. SEM images of (a) crushed and (b) sprayed aerogels
axes was not as accentuated. Noteworthy is the coral like surface of the aerogels, which provides them with a very high surface area. Obvious possible disadvantages of this geometry are the lack of sphericity and smoothness of the particles, as well as their tendency to agglomerate.
The particle size distribution of the sprayed aerogel particles is presented in Fig. 4. The plot shows a monomodal distribution, while the majority of the particles have a diameter of around 14 ^m. It is expected that these particles offer advantages over the crushed ones, since they are more spherical. This should allow higher packing homogeneities and decrease peak broadening by diffusion differences through the packing.
4.2. Pore size distribution and surface area. Kromasil® 60 (5 ^m) particles have a very narrow pore size distribution with diameters of approximately 6 nm. The pore size distribution of crushed silica aerogels is also very narrow. The majority of the pores are at diameters of 10 nm. This is advantageous since the pore size distribution of a stationary phase should be narrow to warranty symmetric peaks [27]. The pore size distribution of aerogels particles formed by spraying into the autoclave exhibits a very broad pore size distribution. Peaks range from diameters between 4 nm and 100 nm (Fig. 5). There is also a considerable amount of small mesopores which normally are unfavorable for HPLC. However, this may be not the case for SFC, where a higher level of convection occurs into the pores [32].
Sprayed silica aerogels have the largest specific surface area of all the samples, 1095 m2/g, while crushed aerogels and commercial silica-gel had surfaces of 870 m2/g and 540 m2/g, respectively (see Table).
Since aerogels have specific surface areas much higher than commercial silica gel it was expected that lower amounts of packing material could have similar separation ability. The mass of crushed and sprayed aerogel particles packed were 0.80 g and 0.75 g, respectively,
Particle size, ^m
Fig. 4. Particle size distribution of silica aerogel particles (0.1 g/cm3)
10
Pore radius, nm
100
10
Pore radius, nm
100
Fig. 5. Pore size distribution of Kromasil® particles (a), crushed (b) and sprayed silica aerogels (c)
10
Pore radius, nm
100
1
1
c
1
while the commercial column had 1.87 g of silica-gel packing. Therefore the surface area available in the Kromasil® column was larger than in the aerogel ones.
4.3. Chromatographic tests. Separation feasibility and number of theoretical plates. The chromatographic separation of aromatic hydrocarbons was carried out firstly in a commercial column. Supercritical CO2 at 100 bar and 40 °C was used as mobile phase and pumped at 2.5 cm3/min. A mixture of benzene, naphthalene and anthracene was injected into a Kromasil® 60 column packed with 5 ^m silica-gel particles. In the corresponding chro-matogram, Fig. 6, a very good separation of the compounds is observed since quite narrow peaks are present. The number of theoretical plates in this column was close to 10 000.
The chromatographic experiments were then performed with the columns packed with crushed monolithic aerogel particles at the same conditions as with the Kromasil® column. According to the resulting chromatogram (Fig. 7) it is demonstrated that silica aerogels have potential to be used in SFC, as they proved to separate polycyclic aromatic hydrocarbons with adequate resolution. Since no appreciable tailing is observed, Gaussian peaks were assumed to perform the plate number calculations. The plate number calculated for this column was approximately 270. This value is rather low in comparison with methods like HPLC [27]. The reason for this may be due to the non-spherical form and the bigger size
14001200-
u1000-
0
1 800-J 600400 200
0
Fig. 6. Chromatogram of benzene, naphtalene and anthracene:
stationary phase — Kromasil® 60 (5 ^m particles); mobile phase — supercritical CO2 at 100 bar, 40 °C and 2.5 cm3/min
160140120100-
§
| 80-J 60-
^ 4020 0
1 2 3 4 5 6
Time, min
Fig. 7. Chromatogram of benzene, naphtalene and anthracene:
stationary phase — crushed silica aerogels 28—40 ^m; mobile phase — supercritical CO2 at 100 bar, 40 °C and 2.5 cm3/min
1 11 ^ 1 2 3 4 5 6
Time, min
of the aerogel particles, which reached values as high as 40 ^m. Nevertheless a satisfactory and complete separation of the hydrocarbons was reached.
Characteristics of the stationary phases Subsequently the chromatog-
raphy tests were performed with the sprayed aerogel particles at the same operating conditions mentioned above. The chro-matogram presented in Fig. 8 shows that the separation of aromatic hydrocarbons seemed to improve in comparison to crushed aerogels by using these more spherical particles. Narrower peaks are observed. The column presented approximately 300 theoretical plates as presented in the Table. This increase in efficiency of around 10 % came along with an almost two times longer analysis
Column Crushed aerogel Sprayed aerogel Kromasil® 60
Particle size, |im < 40 14 5
Mean pore size, 11111 6 24 6
Number of theoretical
plates (inner diameter 277 304 9690
4.6 111111, length 250 111111)
Specific surface, m2/g 870 1095 540
Total porosity, ml/g 0.91 0.92 0.79
Packed density, g/1113 0.19 0.18 0.45
80-
60-
I 40
20-
0
7.5 10 Time, min
Fig. 8. Chromatogram of benzene, naphtalene and anthracene: stationary phase — silica aerogels sprayed particles 28—40 ^m; mobile phase — supercritical CO2
at 100 bar, 40 °C and 2.5 cm3/min
time. It is to remark that anthracene was the only compound in the aerogel column which showed a much higher retention in comparison to the commercial one, while benzene and naphthalene showed no such increase in retention time values. The main reason for the peak broadening in the aerogel columns may be the irregular shape of the silica particles and the fact, that the columns were dried packed. It has been stated that microparticles, especially those smaller than 20 ^m, must be humid-filled in the column, otherwise agglomerates are formed. Inhomogeneity originated by dry packing would lead sample molecules through paths of different lengths, some being faster than others, and originating peak broadening (Eddy-Diffusion) [27].
Effect of a modifier. Since the polarity of carbon dioxide is similar to hexane, organic modifiers, such as methanol or 2-propanol, are frequently added to the eluent, since otherwise SFC would be limited to compounds of low polarity [15, 33]. It means that if aerogel columns are to be applied in SFC separations it should be possible to use modifiers.
To determine the influence of modifiers methanol was used to modify the polarity of the mobile phase at concentrations of 0.5, 1, 2 and 5 vol. %. Tests with CO2 free of methanol were performed before and after the tests with modifier to determine firstly how it influences retention times and secondly to determine if the modifier damaged the aerogel skeleton.
In Fig. 9 some peaks of the aromatic hydrocarbons for different modifier concentrations are shown. The addition of small amounts of methanol has a positive effect in our system as the analysis time becomes shorter and the peak width tends to decrease. However for too large amounts of modifier, larger than 1 %, the resolution is not high enough to separate benzene and naphthalene. Anthracene eluted at last as a single peak for concentrations as high as 2 %. This behavior is in agreement with the literature which states that to avoid excessive retention on packed columns, the polarity of the mobile and the stationary phases should be relatively similar. For pure CO2 as mobile phase a very non-polar stationary phase should be used [32]. Since in our experiments a polar silica phase is used, the addition of methanol as modifier makes the mobile phase more polar and decrease solute retention.
In Fig. 10 the chromatograms of the aromatic hydrocarbons before and after approximately 12 h of experiments with modifier are compared. Both chromatograms overlap very well to each other and only negligible differences are present. If the aerogel structure were damaged by capillary forces originated by the modifier voids should appear in the packing
Time, min
Fig. 9. Chromatograms of the aromatic hydrocarbons for different methanol concentrations: solid black line — 5 %; solid gray line — 1 %; striped line — no modifier
Time, min
Fig. 10. Chromatograms of the aromatic hydrocarbons before and after experiments
with methanol as a modifier
material and peak broadening could be expected. As the peaks do not seem to be distorted after treatment with modifier it can be assumed that this additional solvent does not represent any risk for the aerogel packing and therefore can be used without drawbacks. The majority of the SFC separations involve the use of a solvent modifier, therefore the possibility of using modifiers with aerogel as stationary phase extends their spectrum of application.
4.4. Determination of interactions between active compounds and silica aerogels. The retention times of naphthalene at different temperatures for constant density were used to calculate the retention factors on the Kromasil® and the aerogel column. In accordance to the literature the plot ln k' vs. T-1 yielded straight lines at every constant density used (Fig. 11) for both columns. In the plots the slope represents the enthalpy of adsorption AH and the intersection with ordinate axis gives the entropy of adsorption AS.
The values of AH in the Kromasil® column were between 8 and 16 kJ/mol and were lower than for the aerogel columns where the values varied from 10 to 20 kJ/mol in accordance with earlier reports [34]. It has been observed that the values of the heat of adsorption on the Kromasil® particles tended to decrease at higher scCO2 densities. The heat of adsorption is known to decrease when the surface covering of the adsorbate progresses since the sites with the highest energy are occupied first [35]. In case of aerogels the tendency is different as these values tend to increase with density; however a peak at densities between 550 and 650 kg/m3 was observed. One probable explanation to this phenomenon lies in
1/T ■ 1000, 1/K 1/T ■ 1000, 1/K
Fig. 11. Retention factor of naphthalene on Kromasil® (a) and aerogel column (b) vs. reciprocal temperature at different densities of the mobile phase (in kg/m3)
the competing character of the adsorption of scCO2 and naphthalene from the supercritical solution. As reported by Strubinger et al. [36] the highest adsorption of CO2 on silica takes place in the range of 300 to 600 kg/m3 with coverage of more than 50 % of the free surface. The results of Melnichenko et al. [37] indicate that adsorption of CO2 is significantly stronger in aerogels than in xerogels due to the extremely high porosity and suitable pore sizes. It is possible that due to the extremely high specific surface area of the aerogel the naphthalene does not "feel" the presence of scCO2 at low densities, thus the density of the CO2 on the aerogel surface is low and there is abundance of adsorption sites. However, by increasing the density of the fluid the adsorption sites start not to be "enough" and the competition for these sites becomes more important. The adsorption of naphthalene may occur not directly over the aerogel surface because it is occupied by the scCO2. Depending on density the solvation layer can have a defined geometry or cannot as shown by Benmore et al. [38]. Another explanation may consist in high accessibility of OH-groups in scCO2 [39].
The entropies of adsorption obtained from the experiments are negative (Fig. 12) which confirm that the adsorption of a solute, in this case naphthalene, involves entropy losses, reflecting the conversion of free translational and rotational degrees of freedom into bound motions [40]. The entropy of adsorption of commercial and aerogel particles are different. The values are somewhat lower in the case of the aerogels and a minimum of entropy at densities between 550 and 650 kg/m3 was also observed. The AS values of naphthalene on Kromasil® column at different CO2 densities did not vary substantially indicating a simple adsorption-like retention mechanism as reported by Shang et al. [34], while on the aerogel column the values decrease from 400 to 600 g/cm3 showing increasing interactions between the solute and the stationary phase. Entropy tends to less negative values, which might confirm that the bonding energy of naphthalene to the silica surface is indeed hindered by the encaging of the scCO2. It means that less naphthalene mobility is lost.
4.5. Cellular automata simulations. Linear size of a cell L was chosen to be equal to 1.0 nm close to the size of a naphthalene molecule surrounded by first solvation sphere. Field
20 18161412-1 J| 12H
,0-<i 86 4 2
40 35 30-
o25"
3 20-
15105 0
/ 1 4
♦
□ On Kromasil®
♦ On Aerogel
400 600 800 CO2 density, kg/m3
1000
200 400 600 800 CO2 density, kg/m3
1000
Fig. 12. Enthalpy (a) and entropy (b) of adsorption of naphthalene at different densities of the mobile phase (kg/m3)
height N does not influence on the retention times and was fixed at 100, whereas the field length M was found to have an influence on the retention time and the retention factor. At M > 3000, further increase does not influence the value of k' significantly (Fig. 13). Thus, M was fixed at 4000 in order to reach a compromise between the accuracy and the computational cost. The number of M-cells was set to 1000 for all runs.
Connectivity factor for crushed aerogels was calculated according to the surface area listed in Table and true density of 0.1 g/cm3. Since the aerogel structure was generated by a random placement of A-cells preserving connectivity factor, random in nature structures were tested to provide similar retentions. It was shown that k' deviation is less than 5 % for 10 different structures. Further, runs with three different structures were carried out and a number average was built for all corresponding values.
As mentioned above the CA model is fully discrete and the time has with necessity to be measured in number of iterations t. Furthermore the discontinuity allows to count the number of molecules ^(t), which were eluted from the column by given iteration. Thus function ^(t) is a computational analog of the experimental chromatogram. In real SFC experiments peaks tend to be broader when the flow rate decreases. Our model demonstrates a similar behavior. Fig. 14 depicts the calculated chromatograms at different iflow varied from 500 to 800 (in R units) meanwhile enthalpy and entropy were fixed: e = 800 K and s = —0.4, respectively, at T = 350 K.
In accordance with Eq. (2) changes in entropy have an impact on the intersection, while enthalpy of adsorption influences the slope of the van't Hoff plot. In order to test our model a van't Hoff plot was constructed for each e value in the range from 700 to 1200 K. The temperature was varied from 300 to 380 K, s was fixed at —0.4 and Fflow = 600 K. Slopes obtained from van't Hoff plots were compared further with corresponding e values. Greater divergence at low adsorption enthalpies (29 % at e = 700 K) in comparison with high adsorption enthalpies (less than 5 % at e = 1200 K) is caused by the term Fflow. For experimental AH values, which are between 15-20 kJ/mol and 1900-2400 K in R
22.05
1.9
Fig. 13. Retention factors of the trial molecules calculated at different column length:
interactions were fixed at e = 800 K, s = -0.4; T = 313 K
131.95
•j3
(U
.a ° 1.85
jl 1.8 s=
-Ji 1.75
H aj
3 1.7 oi
0
1000
2000 Length, nm
3000
4000
25 r
20 -
. 15 -
Fig. 14. Chromatograms of the trial molecules calculated at different Fflow:
numbers on the top of the each chromatogram correspond to Fflow in K
10 -
200
400 600 800 1000
Time in computational iterations
1200
units, respectively, the divergences found to be less than 1 %. It obviously shows that the "computational van't Hoff plot" provides enthalpies which are very close to the values used to calculate probabilities pum, pcw and pccw.
Thus, proposed model can principally be applied to describe the SFC experiments in a qualitative agreement with experimental observations. In order to reach quantitative agreement the inverse problem was solved for two carbon dioxide densities: 546 and 663 kg/m3. Fig. 15 demonstrates the best fit between experimental and calculated ln k'. Enthalpy values show relative deviations of 4.5 % and 2.4 % for densities 546 and 663 kg/m3, respectively. It indicates that experimental AH reflects indeed the transfer enthalpy of solvated solute molecule from the bulk phase to the aerogel surface with partially loss of the solvent molecules. At the same time the model underestimates the terms AS/R — P with the deviations of 26 % and 21 %, respectively. Such underestimation was expected because of the artificial character of 2-dimensional aerogel structure. In fine pores the reduction of entropy may be caused not only by adsorption itself, but also by steric interactions between two or more adsorbed molecules as well as ordering influence of the nearest porous walls. Introduction of more realistic topology and the lateral interactions is needed and is a topic of our further work.
5. Conclusions. The possibility to use silica aerogels as a stationary phase for supercritical fluid chromatography has been demonstrated. The separation of polycyclic aromatic
2
Fig. 15. Retention factor of naphthalene on aerogel vs. reciprocal temperature at density 546 kg/m3 (diamonds) and 663 kg/m3 (triangles): solid lines correspond to the best fit using CA model
hydrocarbons was achieved successfully in columns filled with crushed and spray-made silica aerogels. The number of theoretical plates for each column reveals that aerogels prepared by spraying the sol directly in the autoclave performs better than the crushed ones. Their performance is not as good as that for a commercial silica-gel column but the separation is quite satisfactory. Despite the huge surface area present in aerogels, their irregular shape, rough surface morphology and the lack of an efficient column packing method seem to be the main causes of peak broadening. The use of methanol as a modifier can improve the peak shape and excessive retention of the aromatic hydrocarbons. Chromatograms obtained before and after modifier experiments suggest that aerogel structure is not damaged by the modifier (methanol).
An enthalpy and entropy of adsorption on the aerogel show extremum suggesting that the retention mechanism may differ from that on the silica-gel. The test of active substances with different polarity as well as silica aerogel with different functional groups must still be performed in order to gain a better comprehension of the thermodynamics behind the adsorption on silica aerogels.
To model the SFC experiments the cellular automata approach taking into account three types of the molecular processes (diffusion, adsorption and translational movement under pressure gradient) was applied. Margolus transition rules were generalized by including an explicit dependence on energetic and entropic terms and applied iteratively in order to simulate molecular motion. It has been shown that computational experiments are in qualitative agreement with major observations in SFC experiments. Coarse-grained model of the porous media allows to represent the bulk of adsorption sites on the aerogel surface, but lacks for topology and interconnectivity. Failure to take into account these factors seems to be the main cause of divergence in experimental and calculated entropies, while enthalpies were found to be in good agreement.
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Статья поступила в редакцию 5 октября 2012 г.
