Lupine Publishers | Excellent Crystal Coloration and An Extraordinary Improvements of Developing Synthetic Quartz Single Crystals Growth and Defects

Lupine Publishers- Organic and inorganic chemical sciences

The analysis of the impurity content crystals grown in sodium carbonate solution is carried out using flame technique. Colored crystals have been produced from aqueous solutions of potassium carbonate under laboratory conditions and using a steel autoclave. The seeds were slices cut parallel to the planes (0001). With the impurity of aluminum and irradiation, defective color centers have generated quartz coloration phenomenon. This is occurred on the base of the electrical balance by exchanging aluminum ions with tetravalent silicon ions in the presence of alkali elements (monvalent) i.e. Na+ or Li+. Interestingly, the current paper introduces a method suggests the utilization of silica-rich rocks to develop the growth of large crystals of synthetic quartz.
Keywords: Metallic impurity, Quartz, Crystalline, Piezoelectric, Aluminum, Flame photometric emission

Introduction

Until recently, all the quartz required for the production of oscillator crystals for frequency control has been obtained from natural resources. Although quartz is one of the most abundant minerals in the earth’s crust, it is only found in large crystals of the required quality in a few isolated regions. During the past 20 years, work has been carried out to develop processes for the controlled growth of quartz in the laboratory [1,2]. Considerable success has been obtained by many teams [3], crystals of piezoelectric-quality weighing over 1 lb. having been grown [4]. All the modern processes used for the growth of synthetic quartz have been developed by pioneering works [5,6] in the current century. Although the methods adopted by various workers in this field are basically similar, there are certain fundamental differences which affect the properties of the crystals. Because of its glass forming properties and its allotropic modifications it is not possible to grow quartz from the vapor or the melt. Growth from solution must be used and as quartz is virtually insoluble in aqueous media under ordinary ambient conditions it is necessary to use elevated temperatures and pressures to obtain sufficient solubility. These so-called hydrothermal conditions are probably similar to those in which much natural quartz has been formed. At temperatures approaching 400°C and pressures of 1000 atm (about 7 tons/in.2) quartz is readily soluble in alkaline solutions such as sodium carbonate.

Materials and Methods

Crystal Growing Technique

A schematic diagram of the apparatus used by the authors is shown in Figure 1. In what will be called the standard process, a steel autoclave constructed to withstand high pressures has seed crystals suspended from the lid and a supply of crushed meltinggrade quartz at the bottom. The autoclave is about 80% filled with a solution containing 88 g/L of sodium carbonate and sealed. The simple furnace used consists of a hotplate on which the autoclave stands surrounded by micaceous-flake thermal insulation. By this means a temperature gradient is established so that it is hotter at the bottom in the region of the nutrient crushed quartz than at the top where the seeds are located. Under the working conditions, the autoclave is filled with a single-phase fluid. The pressure developed being a function of the temperature and of the percentage of the space originally occupied by the solution at room temperature. The temperature at the base of the autoclave is controlled at about 400°C and the temperature at the seeds reaches equilibrium some 40°C lower. The temperature gradient along the length of the autoclave is not uniform, a fall of about 20°C occurring across the metal at the base and most of the remaining drop being across the nutrient. The space above the nutrient is approximately isothermal and the supersaturation in this region remains constant. Thus, crystals can be grown at approximately the same rate of growth in any part of the autoclave.

Figure 1: Diagram of apparatus for the growth of synthetic quartz.

For a given design of the autoclave, the rate of growth is dependent on seed orientation, pressure, temperature and temperature differential. The seed orientation which has been adopted in most of the work to be described is the basal plane or Z-cut. Figure 2 shows the relation between this cut and the minor rhombohedral or T-cut which has also been used as a seed for the growth of synthetic quartz. It is shown subsequently that the seed orientation not only affects the rate of growth but also has a marked effect on the way in which impurities are incorporated in the crystal. It is most convenient to control the rate of growth by means of the temperature difference and this is done by adjusting the flow of solution but not exceed a certain maximum, which, for the conditions used in the standard process, is about 0.5mm/day on each side of the seed measured in the direction of the optic axis. In fact, the visual quality is in some respects a misleading criterion and the measurements of the mechanical damping recorded in Table 1; show that a progressive improvement in crystalline perfection takes place as the growth rate is reduced. As it happens, for most practical applications the quality corresponding to 0.5mm/day is adequate but for especially stringent requirements it may be necessary to employ a lower growth rate or an alternative growing technique. A small pilot plant has been set up to grow crystals by the standard process. A growth of 15mm takes place in a period of about a month, the resulting crystals weighing about 135g.

Figure 2: Relationship between crystals grown on the basal plane (Z-cut) and the minor rhombohedral plane (z-cut).

Table 1: Mechanical damping of quartz

Results and Discussion

Influence of impurities

The standard process recrystallizes a low-grade quartz-which due to size and imperfections such as twinning is unsuitable for piezoelectric use into crystals of a size and quality which are ideally suited to this purpose. However, the melting grade quartz used as nutrient still has to be imported and considerable work has been carried out over the last 5 years to develop processes which can be used with relatively impure nutrient materials. Reasonable success has been obtained using flint and a variety of quartzites. Early in this investigation it was found that quartz could be grown on Z-cut seeds using impure nutrient materials, but that the quality, particularly of large crystals, was not good enough for piezoelectric use. It is now known that the poor quality is due to the incorporation of impurities in the synthetic crystal during growth. However, it was found that it was possible to grow crystals of piezoelectric quality by modifying the solution in which the crystals were grown. Good crystals have been grown from flint and impure quartzite by using a solution containing 40g/L Na2CO3, 33g/L NaOH, and 3.4g/L NaF. Further examination of a number of different quartzites showed that many of them could be used satisfactorily with the standard process; these are referred to as class A quartzites. It is now known that the difference between class A and class B quartzites (class B being those quartzites which require the modified process) lies in the type of accessory minerals which are associated with the quartz. In particular, the structure of the feldspar, which is commonly the primary accessory mineral in quartzites, plays an important role in deciding whether the material will be class A or B [7,8].
Work by Dickson et al. [9] using a paramagnetic resonance technique has shown that aluminum is the impurity which affects the quality of synthetic quartz crystals grown from class B materials using the standard sodium carbonate solution. This result has been corroborated by spectrographic analysis on a number of specimens. In addition, the direct test has been made by deliberately adding aluminum in a number of forms along with a pure quartz nutrient. Such adulterated quartz now acts as a class B nutrient and crystals grown from it using the standard solution have the habit and poor quality of a crystal grown under similar conditions from flint or a class B quartzite. Further, by using the modified solution, the defects can again be overcome. Figure 3 shows four crystals which illustrate this result. The crystals from left to right were grown from nutrients and in solutions. The most notable feature which can be seen from the photograph is the nature of the growth surface approximating to (0001). This surface is smooth on the crystals grown from quartz in sodium carbonate solution and from quartz with aluminum in the modified solution, but it is rough and pitted in the case of the crystals grown from flint and from quartz with aluminum, in sodium carbonate solution. It will be shown that the nature of the growth surface is closely related to the manner in which aluminum is incorporated in synthetic quartz grown on Z-cut seeds.

Figure 3: Crystals grown to illustrate the importance of aluminum as an impurity in low-quality nutrients.

It has been known for some time that when natural quartz is irradiated with X-ray or any other ionizing radiation, the material darkens. Grasse et al. [10] studied this phenomenon in detail and showed that the darkening produced in natural quartz is often non-uniform showing a banded structure. The darkening occurs in sheets parallel to the major rhombohedral planes and is therefore connected with the growth of the crystal, probably being associated with changes in the environment in which the crystal grew. When large crystals of synthetic quartz were first grown by the authors, their behavior under X-irradiation was determined. Figure 4 shows the result of irradiating an X-cut section of a synthetic quartz crystal grown on a Z-cut seed. It can be seen that the central region corresponding to the natural quartz seed has darkened uniformly and that there are two regions beneath the minor rhombohedral faces which have also darkened rather more intensely than has the seed. The remainder of the synthetic growth has not darkened under this dose. The diagram in Figure 5 shows the region under the minor rhombohedral face on a larger scale. The triangular region abc corresponds to growth which has taken place on the minor rhombohedral face as it develops. Spectrographic analyses of material taken from various regions of a number of crystals grown by the standard process have shown that the total aluminum concentration in the growth on the Z-cut orientation is commonly less than 40 parts in 106 atomic replacements. However, in the growth under the minor rhombohedral face the aluminum content may be 10 times this figure, i.e. 400 parts in 106. The impurity content of the melting-grade nutrient lies between these two figures and the low aluminum concentration in quartz grown on a Z-cut seed is in part due to the “scavenger action” of the growth on the minor rhombohedral faces which are formed during the growth. This also illustrates a general result found in the growth of synthetic quartz, namely that it is easier to introduce impurities during growth on the minor rhombohedral face than on the basal plane.

Figure 4: Photomicrograph of an X-cut section from a synthetic quartz crystal grown on a Z-cut seed from a pure melting-grade quartz nutrient after X-irradiation.

If, however, there is a large excess of aluminum in the system, it is found that the crystals grown on the basal plane will darken readily in a characteristic way as shown in Figure 6. In addition to the darkening of the seed crystal and the growth under the minor rhombohedral face, there is darkening of the primary growth in the form of distorted narrow-angled cones directed along the c-axis. These cones terminate in the rough, pitted growth surface and are apparently associated with the pits. This can also be seen from the bands which run parallel to the seed surface. These bands which are regions of either more or less intense darkening than the surrounding material are reproduced precisely on both sides of the seed. It can, therefore, be deduced that these bands are produced either by changes of the temperature or pressure in the autoclave or, what is more likely, by changes in the concentration of aluminum in the solution. These bands will therefore represent the nature of the growth surface at the particular time when they are formed. The discontinuities in these bands tend to follow the boundaries between the cones of darkening.

Figure 5: Diagram showing the X-ray darkening of quartz deposited in the accessory growth on the minor rhombohedral face.

Figure 6: Characteristic X-ray darkening pattern found in an X-cut section of a synthetic quartz crystal grown on a Z-cut seed in the presence of a large excess of aluminum.

Mechanism of growth

The characteristic cone darkening structure can be used to obtain a model for the mechanism of growth on the basal plane. This is illustrated in Figure 7. It is assumed that growth takes place independently on a large number of centers in contrast to growth on a habit face where only a limited number of centers are active and growth takes place by sheets spreading across the growth surface. The growth centers on the basal plane may be associated with spiral dislocations but there is, as yet, no direct evidence for growth spirals. If it is now assumed that quartz is deposited on the individual centers at different rates it will be seen that those which are growing faster overtake their more slowly growing neighbors and render them inactive. In the schematic diagram in Figure 7, all nine centers are active at the beginning of the growth; at later stage only centers 2, 4, 6 and 8 are active and eventually only centers 4 and 6. If the aluminum incorporation is uniform on any one growth centre but differs from one to the next, it will be seen that this gives rise to the characteristic darkening pattern. Figure 7 also shows photomicrographs of the growth surfaces at various stages in the growth together with darkening patterns at similar stages for sections cut perpendicular to the c-axis. The individual “cobbles”, which are the termination of the growth cones in the surface of the crystal, and the tine structure in the darkening patterns both tend to become coarser as the growth proceeds. This is in agreement with the suggested growth mechanism.

Figure 7: Illustrating the mechanism of growth of synthetic quartz on Z-cut seeds.

The nature of the rough, pitted growth surface obtained when quartz is grown on the basal plane in the presence of a large excess of aluminum cannot be directly explained in terms of the suggested mechanism. Figure 8a is a photomicrograph of the surface and shows clearly that the pits have no obvious crystallographic orientation. However, crystals have been grown with only just sufficient aluminum present in the system to commence the incorporation of aluminum by the above mechanism. In this case, the aluminum apparently only goes into the growth on isolated centers and produces a growth surface of the type shown in Figure 8b. It will be seen that certain of the larger cobbles have triangular pits at their centre. The relation between these pits and the rough growth surface produced by a large excess of aluminum is shown in Figure 8c and 8d. Figure 8c shows the growth surface of a crystal grown in the presence of a somewhat larger concentration of aluminum than that of Figure 8b. The pits are here more numerous and are commencing to overlap so that they interfere and lose their obvious crystallographic orientation. The crystal shown in Figure 8d has a rough surface similar to that in Figure 8a and has been lapped to remove most of the disturbed surface. The bottoms of the pits of the rough surface show approximately the same form as those in Figure 8b. The characteristic rough surface is, therefore, formed from a large number of pits which overlap and interfere until the shape and symmetry of the pits is completely lost.

Figure 8: The nature of the rough growth surface formed in the presence of a large excess of aluminum. (a) Rough growth surface. (b) Isolated pits. c) Interfering pits. d) Rough surface after most of the damage has been removed by lapping.

Figure 9: Diagram of a pit formed at the center of a growth cobble.

The nature of the individual pits is more readily seen by reference to Figure 9, which shows a diagram of a single cobble and its pit. The sides of the pit form reasonably flat faces which have been indexed using a microscope. The reason for the formation of such a high index face, if it is a true face, in the presence of excess aluminum is not understood. Figure 9 also shows a section containing the c-axis. If as appears likely, the pit is associated with the incorporation of aluminum, on irradiating such a section the growth cones giving rise to the cobbles with pits at their centers will darken readily. This is shown diagrammatically in Figure 9 while Figure 10 shows a photomicrograph which clearly illustrates this phenomenon. It has been seen that when crystals are grown in a large excess of aluminum, this aluminum is not incorporated uniformly in the crystal as it grows but is taken up preferentially on certain centers at the expense of the neighboring centers. As the lattice spacing will be a function of the aluminum concentration, it is reasonable to expect that strains will be set up at the boundaries between regions of different aluminum content. This strain can be seen readily by examining sections cut either parallel to or perpendicular to the c-axis in a polarizing microscope between crossed nicols. Parallel to the c-axis there are deep fissures found under the rough growth surface where the stress exceeds that necessary to produce fracture. Instead of the crystal appearing dark as it should in the extinction position, the field is crossed by bands of light and dark produced by the strain. The same phenomenon is, perhaps, more readily studied by examining sections cut perpendicular to the c-axis. Depending on the angle between the polarizer and analyzer the section should appear to be a uniform color when viewed in white light. Instead, a section cut from a crystal which has non-uniform aluminum incorporation will have a mottled appearance. This is shown in Figures 11 & 12, which are photomicrographs of two sections of the same crystal, Figure 11 being taken near the seed crystal and Figure 12 near the end of the growth. This again illustrates the way in which the number of active growth centers decreases during the growth. In this particular example, the density of active centers has decreased by a factor of the order of 20 in about 5mm of growth along the c-axis.

Figure 10: Photomicrograph of an X-cut section showing the relationship between the cones of darkening and the pits.

Figure 11: Strain pattern observed in crossed nicols in a Z-cut section of a crystal containing a large excess of aluminum (Section taken near seed/growth interface).

Figure 12: As Figure 11, Section taken near end of growth.

Comparison of the results of experiments in which crystals are grown on Z-cut seeds in the presence of high and low concentrations of aluminum shows that the mechanism by which aluminum is incorporated in the growing crystal is dependent on the concentration of impurity in the system. This has been studied more closely by a set of controlled experiments in which the concentration of aluminum, added as y-alumina, was steadily increased. Six crystals grown in the presence of aluminum deliberately added to the nutrient in proportions varying from 0.05 to 2.50% by weight are shown in Figure 13. The concentration of aluminum added to the nutrient for the six crystals numbered 1 to 6 from left to right is given in the caption. Examining the nature of the growth surface, it will be seen that the first two crystals show no obvious signs of the inclusion of aluminum. By contrast, crystals 3-5 show the characteristic rough growth surface, crystal 5 being so strained that the growth is hardly single crystalline. With 2.5% aluminum added to the nutrient (crystal 6) all growth is prevented. Further experiments carried out using concentrations of aluminum in the range 0.10-0.25%, show that the results are not consistent, in that a number of experiments carried out with the same aluminum concentration sometimes give a rough growth surface corresponding to non-uniform impurity incorporation and at other times give the smooth cobbled surface of the pure crystal. This behavior can be explained in terms of the suggested growth mechanism as follows in this paragraph. For low concentrations of aluminum in the system, the incorporation apparently takes place uniformly. Most of this aluminum is probably interstitial as the material only darkens slightly under X-irradiation. For high concentrations, it has been seen that the aluminum is taken up preferentially on certain growth centers. This can be understood, when it is considered that the energy required introducing an impurity atom is a function of the number of impurity atoms already incorporated in the growth on this centre. As the number of impurity atoms incorporated increases, the distortion of the lattice becomes greater and it becomes easier to include more impurity atoms. Thus, once the concentration of aluminum in the growth on a given centre exceeds a certain figure, further aluminum atoms will tend to be taken up preferentially on this centre at the expense of the neighboring centers. In a physical system of this type, the probability that non-uniform inclusion will take place and is a rapidly changing function of the concentration of impurity in the nutrient. It can be seen that this qualitative analysis explains the observations. For low concentrations of aluminum, the probability of non-uniform take-up is very small. As the concentration is increased the stage is reached where there is a reasonable chance that the aluminum is incorporated non-uniformly. This is the region where the results will not be consistent. At still higher concentrations, non-uniform inclusion will be the rule.
Specimens cut from the crystals shown in Figure 13 have been analyzed for aluminum and sodium using spectrographic and flame photometric techniques, respectively. The results are given in Table 2 in terms of the percentage atomic replacement of silicon by these elements have showed that the concentrations of sodium and aluminum are of the same order for low concentrations of aluminum added to the nutrient. This can be attributed to the sodium content tendency to saturate while the aluminum content continues to increase. It seems reasonable to conclude that the substitutionally added aluminum is associated with a sodium atom situated interstially. This centre would be responsible for the visible darkening produced by X-irradiation [11], a model consistent with that suggested by Ratheneau [12]. The excess aluminum found when the concentration added to the nutrient is large, could be present either as interstitial atoms or as two substitutional atoms associated with an oxygen vacancy. There is, at present, no evidence to distinguish between these two alternatives. In discussing the incorporation of impurities in synthetic quarts, some mention must also be made of work which has been carried out in attempts to include impurities other than aluminum [13]. It is well known that small monovalent ions in particular lithium and sodium can readily be introduced into the quartz lattice under the action of an electric field. These ions lie interstitially in the “tunnels” which are parallel to the c-axis in the quartz structure. It has already been shown that sodium is present in all synthetic quartz grown by the authors. Attempts have been made to introduce a number of other elements which might be expected to substitute for silicon in the lattice. In general, it has been found extremely difficult to introduce impurities into quarts grown on the basal plane. This result would appear to be different from that found by other workers in this field who have used seeds cut parallel to the minor rhombohedral face. In addition to aluminum, attempts have been made to incorporate the elements in growth on Z-cut seeds. Of these elements only, germanium has been successfully incorporated. Bearing in mind the similar ionic radii of silicon and germanium, it is not surprising to find that germanium will readily go into quartz as a substitutional impurity. Large amounts of germanium can be taken up by the quartz lattice without setting up measurable strain. As would be expected, the centre is not sensitive to X-irradiation. It is interesting to note that boron is not taken up, although its small size and its valence of three would, at first sight, make it an ideal atom for incorporation in the quartz lattice. No explanation is known for this behavior.

Figure 13: Crystals grown in the presence of increasing concentrations of aluminum. Aluminum by weight of quartz nutrient: (1) 0.05%, (2) 0.125%, (3) 0.25%, (4) 0.50%, (5) 1.25%, and (6) 2.50%.

Coloration

A striking example has been the growth of intensely colored emerald green quartz, a variety which does not occur naturally. From the circumstances in which this crystal was grown, it has been deduced that the coloration is produced by the presence of a trace of chromium [13]. This diagnosis has still to be confirmed. The coloration in this crystal is very stable, being unaffected by heat treatment up to the a-ß inversion temperature or by prolonged X-irradiation. Preliminary transmission measurements show that the material has an apparent cutoff in the ultraviolet at 2800 Ǻ. It appears likely that this synthetic material is not related to the “greened” amethyst described by Samoylovich [14].

Table 2: Sodium and aluminum concentrations in synthetic quartz grown in Na2CO3 solution on Z-cut seeds in the presence of aluminum.

Conclusion

The recent investigation, still incomplete, has shown that the nature of the cation in the solution from which the crystals are grown can have a considerable effect on the way in which impurities are incorporated in synthetic quartz. An investigation of the type described can be of value to the worker studying color centers in quartz in a number of ways.
a. The process described for the growth of large crystals of synthetic quartz can provide material with total impurity content, and particularly substitutional aluminum content, lower than is found in natural quartz. This is of value to the worker, studying radiation damage in quartz. With regard to the substitutional aluminum content, it must be noted that the concentration in a number of specimens grown under nominally similar conditions will differ slightly and partly as a result of the statistical nature of the process and also as a result of variations in the purity of the nutrient.
b. Controlled amounts of the impurities present in natural quartz can, in certain instances, be introduced. This can be of considerable assist in identifying the nature of those color centers which are impurity-dependent.
c. By the introduction of impurities not found in natural quartz, material with new properties can be grown. For example, if sufficient chromium can be introduced into the green quartz it may be possible to obtain quartz which is paramagnetic.

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Optimization of Chitosan+Activated Carbon Nanocomposite. DFT Study | Lupine Publishers

Journal of Chemical Sciences | Lupine Publishers

 

Abstract

First, the minimum energy (geometry optimization DFT-DMol3) is obtained among C48 optimized ring carbon-system, and one non-optimized chitosan copolymer unit. Second, C24 and C9 optimized rings, each one interacting with an optimized chitosan copolymer unit (Ch). With the aim to investigate structural properties, the first case is optimized by applying smearing; and the second without smearing. Two parallel hypothetical carbon chains of 12 carbon atoms, symmetrically arranged are optimized in C24 carbyne ring; and one hypothetical 5 carbon-chain parallel to another 4 carbon-chain end optimized in a cumulene C9-ring. These carbon-ring structures here defined as activated carbons (AC), correspond to big pore size diameter obtained without chemical agent acting on them. Single point calculations are to build potential energy surfaces with GGA-PW91 functional to deal with exchange correlation energies for unrestricted spin, all-electron with dnd basis set. Only in the first case, orbital occupation is optimized with diverse smearing values. To determine structure stability, the minimum energy criterion is applied on AC+Ch nanocomposite. To generate fractional occupation, virtual orbitals are formed in this occupation space, whether homo-lumo gap is small and there is certain density near Fermi level. This fractional occupation pattern depends on the temperature. It must be noticed that when AC and Ch are solids, there is no adsorption; however, by applying smearing it was possible to find potential energy surfaces with a high equilibrium energy indicating glass phase transition in Chitosan due to the chemisorption given at the minimum of energy. AC+Ch molecular complex nanocomposite is expected to be applied not only in medicine but also in high technology.

Introduction

With the aim to figure out a molecular complex formed through the interaction between a system of 48 carbons arranged in planar way and a copolymer unit of chitosan, potential energy surfaces were built [1,2] using single point step by step calculations. The problem is studied considering that a molecular complex is obtained by changing smearing value according to the energy value convergence. Considering that electrons occupy orbitals with the lowest energies and with an integral occupation number in calculations of density functionals, a smearing change indicates a fractional occupation in virtual orbitals within this space of occupation. The smearing calculations correspond to the explicit inclusion of the fractional occupation numbers of the DFT calculations, requiring an additional term to achieve a functional energy from variation theory [35]. The contribution of this term to the density functional force exactly cancels the correction term as a function of the change in the occupation number. For occupation numbers satisfying a Fermi distribution, the variation total-energy functional is identical in form to the grand potential [3-6]. From the grand canonical distribution or Gibbs distribution, the normalized probability distribution of finding the system in a state with n particles and energy 𝐸𝑛𝑟 [7], the Z grand partition function of the system, and the number of particles remains according to the Fermi energy ℰf =μ(T,V,n). When T = 0 the fermion gas is in the state of minimum energy in which the particles occupy the n states of 𝜓𝑖 of lower energy, since the exclusion principle of Pauli does not allow more than one particle in each state. Therefore, the Fermi function 𝑓(ℰ) gives the probability that certain states of available electron energy are occupied at a given temperature.
Other options for the shape of the occupancy numbers result from the different associated functional with finite temperature to DFT but without physical meaning, such as the temperature or the entropy associated with this term [3]. These terms, although numerically small must be included in the practical calculations that allow numbers of fractional occupation [3,8]. To consider the scope of smearing, it is known that electrons occupy orbitals with the lowest energies, and occupancy numbers are integers; nonetheless, there is a need for a fractional occupation in virtual orbitals within this space of occupation. We apply this when the HOMO-LUMO gap is small and there is especially a significant density near of Fermi level [9], thus in order to obtain the fractional occupation a kT term is implemented. This fractional occupation pattern depends on the temperature. The systems C48 carbinoid, C24 carbyne-ring, and C9 cumulene-ring (almost-planar) are arrangements obtained through DFT geometry optimization of two hypothetical parallel zigzag linear carbon chains. We consider these systems as carbon physically activated, due to the pore size diameter, and since no activating chemical agent has been applied. Carbyne is known as linear carbons alternating single and triple bonds (-C≡C-) n or with double bonds (=C=C=)n (cumulene) [10]. Polyyne is known as a allotrope carbon having H(-C≡C-) nH chemical structure repeating chain, with alternating single and triple bonds [11] and hydrogen at every extremity, corresponding to hydrogenated linear carbon chain as any member of the polyyne family HC2nH [12] with sp hybridization atoms. It is known that polyyne, carbyne and carbinoid have been actually synthesized as documented by Cataldo [13]. Bond length alternation (BLA) of carbyne pattern is retained in the rings having an even number of atoms [10]. Additional care must be taken with carbyne rings since the Jahn-Teller distortion (the counterpart of Peierls instability in non-linear molecules) is different in the C4N and C4N+2 families of rings [14-16]. There is a great variety of applications of activated carbon as an adsorbent material, and it has been used in areas related to the energy, and the environment, generating materials with a high-energy storage capacity [17].
Chitin is, after cellulose, the most abundant biopolymer in nature. When the degree of deacetylation of chitin reaches about 50% (depending on the origin of the polymer), it becomes soluble in aqueous acidic media and is called chitosan [18]. Chitosan is applied to remediation of heavy metals in drinking water and other contaminants by adsorption. The affinity of chitosan with heavy metals makes the bisorption process stable and advantageous, being only by the alginates present in brown algae matched [19]. The glass transition temperature of chitosan is 203°C (476.15 K) according to Sakurai et al. [20], 225°C (498.15 K) according to Kadokawa [21], and 280°C (553.15 K) according to Cardona-Trujillo [22]. One can differentiate specific reactions involving the -NH2 group at nonspecific reactions of -OH groups. This is important to difference between chitosan and cellulose, where three -OH groups of nearly equal reactivity are available [23,24]. In industrial applications, several solids having pores close to molecular dimensions (micropores < 20 Å) are used as selective adsorbents because of the physicochemical specificity they display towards certain molecules in contrast to the mesoporous substrates (20-500 Å) and macropores (> 500 Å). Adsorbents with these selective properties include activated carbon among others [25]. Chitosan-based highly activated carbons have also application for hydrogen storage [26]. In principle, electronic structure of diatomic molecules has been built through the overlapping knowledge of the interacting atomic orbitals [27]. In this case, the orbitals correspond to bonding (σg, πg) and antibonding (σu, πu) orbitals of hydrogen, carbon, nitrogen and oxygen diatomic molecules, whose H2, C2, N2, and O2 groundstate electronic configurations are and with 2, 8, 10 and 12 valence electrons, respectively. Actually, the reactivity sites in a molecule correspond to the highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO). HOMO as base (donor), and LUMO as acid (acceptor) are particularly important MOs to predict reactivity in many types of reaction [28,29]. Activated carbon and chitosan have been independently applied as sorption materials to increase environmental quality standards. Then, we expect AC-Ch nanocomposite to have a powerful handleable adsorption property of pollutants that can be applied not only in wastewater treatment, but also in medicine against intoxication, in batteries to increase storage capacity, in electrodes of fuel cells, and in more possible applications, according to the pore size distribution to be generated on this new material.

Methodology

The interaction between an activated carbon molecule (AC) and a unit of the chitosan copolymer (Ch) is studied by means of DFTDMol3 [30-32]. The AC system is a hypothetical model of two parallel linear chains of 24 carbons each one geometrically optimized using DFT, converging into a plane molecular carbon system. In this system six nodes were formed allowing 7 interconnected rings of different bond lengths and sizes: 2 of 6 carbons, 4 of 8 carbons and one of 16 carbons. By summing these quantities gives 54 carbons since the carbons are in the nodes double counted. When subtracted they are the 48 carbons of the AC system. This system has a length of 28.4Å comparable to that of the chitosan copolymer unit (Ch). The reactants are AC + Ch corresponding to C48 + C14H24N2O9.
Single point potential energy curves were constructed [1,2] by using smearing. The following conditions to find AC+Ch (Activated Carbon+Chitosan) interaction energy are: functional GGA-PW91 [31,33-36], unrestricted spin, dnd bases, and orbital occupation with various smearing values. Considering that we obtained a solution for the energy value convergence, the interaction by changing the smearing value was studied. Since electrons occupy orbitals with lower energies and integral occupation numbers in calculations of density functional, a smearing change indicates fractional occupation and virtual orbital within this occupation space [19]. When generating a fractional occupation, virtual orbitals are in this occupation space generated, if the HOMO-LUMO gap is small, and there is certain density near the Fermi level [1], then it is implemented the fractional occupation term kT. This pattern of fractional occupation depends on temperature. Covalent connectivity calculations [37] according to DMol3 on no-bonding to s- and f-shell scheme, bond type, and converting representation to Kekulé, for bond length tolerances from 0.6 to 1.15 Ǻ were accomplished in this molecular complex mostly composed of carbon. Area calculations have been carried out by inserting triangles in each amorphous carbon ring and using the
Heron formula: where P=(a+b+c)/2 is the perimeter of a triangle of a, b, c sides; while the pore size diameter (PSD) is calculated as an approximation to the circle area. Periodic systems can be constructed using amorphous builder of BIOVIA Materials Studio, these are useful to calculate Radial Distribution Functions and the area under the curve on a significant interval.

Results

Chitosan Optimized by Applying Smearing

The default smearing value of 0.005Ha corresponds to T=1578.87 K and P=224.806 atm. We now exhibit electron smearing behavior using the known Fermi-Dirac statistic [38]. Facing two hydrogen atoms and using geometry optimization calculations, we built energy as a function of smearing value. Figure 1 shows the total energy variation when the system is optimized with respect to smearing value [39] (Figure 1). The fractional occupational pattern depends on the temperature, and this is derived from the energy change of Fermi distribution [6] as: 𝛿𝐸 = 𝑇𝑘; where k is Boltzmann constant. Considering a model in which the electrons are free and given that clouds of electrons are being a Fermi gas considered. The pressure is: 2/3 δE/δV [38]. From the latter two previous equations, temperature and pressure change is observed in Table 1 given the 𝛿𝐸 smearing energy. The planar molecular hypothetical system of 48 carbons is built by applying geometry optimization at two linear chains of 24 carbons as shown in Figure 2a, and the chitosan copolymer molecular system is built without applying geometry optimization, as observed in Figure 2b. Approaching enough these two molecular systems we studied a new molecular complex at different smearing values. The molecular model of carbon is symmetrically arranged in planar geometry, and it is physically activated through geometry optimization. We called activated carbon (AC) to the resulting planar carbon system. The length of this planar system is comparable to that one of chitosan (Ch). Each six-carbon ring has an area 4.34 Å2, each eight-carbon ring along with this has an area 8.74 Å2, each eight-carbon ring along with the sixteen-carbon ring has an area 8.55 Å2, and the sixteencarbon ring has an area 27.32 Å2. Considering each one of this area as circle areas the pore size diameter distribution is from 2.35 Å to 5.9 Å, which correspond to micropore size distribution of this carbon system. When considering the whole area of this system for calculating the pore size diameter 9.48 Å [40,41]. Chitosan is very well known to be macropore size [42] (Figure 2

Figure 1: Change in the total energy as a function of the electron smearing value [39].

Figure 2: C48 Carbon and Chitosan molecular systems. a) Input-Output of a C48 carbon system geometry optimization. Carbon atoms in gray color. b) Chitosan molecule (C14H24N2O9) without optimization. Hydrogen atoms in white color, Nitrogen in blue color and oxygen in red color.

Figure 3: INPUT for interaction among activated carbon (AC) and one copolymer unit of Chitosan (Ch). a) Chitosan without geometry optimization. b) Potential energy curve with well depth of 30Kcal/mol for smearing: 0.05Ha. c) Potential energy curve with well depth of -1089 kcal/mol for smearing of 0.03 Ha.

Searching for a new molecular complex, Figure 3 exhibits the potential energy curve of the interaction between AC and Ch having equilibrium at (1.6Å, -1089Kcal/mol). In this case chitosan was not geometrically optimized in order to build the potential energy curve observed in Figures 3b & 3c. It was really easy to build this curve using smearing energy 0.05 Ha for every single point calculated, and hard to build it at 0.03 Ha. We also tried lower values than this, and we obtained poor or none results (Figure 3). After applying geometry optimization at smearing 0.05 Ha, and subsequently at 0.03 Ha. The smearing at 0.02 Ha is shown in Figure 4a. Then, we built the potential energy curve as shown in Figure 4b in step by step single point calculations for AC + Ch face to face interaction, when 2.264 Å is the separation between their corresponding centers of mass. The latter has a potential well depth of 165 Kcal/ mol at a distance of 2.2 Å, meaning formation of a new molecular complex at an adsorption energy greater than 20 kcal/mol in the chemisorption range [43] (Figure 4). Covalent connectivity [37] to the resulting system in Figure 4a was applied under the conditions previously mentioned in methodology, and the molecular complex observed in Figure 5 is obtained. In this complex the reactants and products are C48 + C14H24N2O9 and C49H3O3 + CH2 + C4H6O2 + CH3NO + C2H2O + CH2O + C2H2 + CHNO + CH3, respectively. Carbon bonds are single, double, and triple, as an example the C12 ring has eight double bonds, one triple bond, and three single bonds, where all the carbon valence electrons are shared. Furthermore, C8 and C16 rings have double bonds in one side of the ring, and single and triple bonds in the other side; and C6 ring has four double bonds and two single bonds. This whole carbon system has been activated by chitosan, and double bonds, and single and triple bonds are the representative characteristics of carbine-type molecules (Figure 5).

Figure 4: OUTPUT for interaction among activated carbon (AC)and one copolymer unit of Chitosan (Ch) after DFT geometry optimization using smearing at 0.02Ha.

Figure 5: Connectivity applied after geometry optimization of CA+ Ch interaction (smearing at 0.02 Ha)

It must be noticed that geometry optimization of this whole system provides a lowest unoccupied molecular orbital (LUMO - electron acceptor) receiving an electron pair from the highest occupied molecular orbital (HOMO - electron donor). The donor HOMO from the base and the acceptor LUMO from the acid, combine with a molecular orbital bonding, which in our case corresponds to the orbitals 242-HOMO for E=-0.18317 Ha and 243-LUMO for E=- 0.17786, for a Fermi energy of -3136.28 Ha with A as irreducible representation of symmetry C1. The total orbitals number is 274. The orbital occupation is 202 A (2) plus 78 electrons in 65 orbitals, for a total number of 482 active electrons and binding energy of -22.997 Ha, at 2 steps. However, in order to get HOMO and LUMO drawn in this model, we run an energy calculation. Then, this molecular complex as seen in Figures 6a & 6b has HOMO-484 with E=-0.16398 Ha, LUMO-485 E=-0.16196 Ha, and Fermi energy Ef = -3161.44 Ha, for the reactivity sites with 482 active electrons. The total number of valence orbitals is 1070. The orbital occupation is 206 A (1) alpha and 206 A (1) beta, and 35.00 alpha electrons in 62 orbitals plus 35 beta electrons in 62 orbitals. HOMO as base-donor, and LUMO as acid-acceptor are the MOs locating possible reactivity in this reaction. An acid-acceptor can receive an electron pair in its lowest unoccupied molecular orbital from the base-donor highest occupied molecular orbital. That is to say, the HOMO from the base and the LUMO from the acid combine with a bonding molecular orbital in the ground state see Figure 6c.

Figure 6: We applied highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) to the previous AC+Ch molecular complex. a) HOMO. b) LUMO. c) HOMO-LUMO. Blue and yellow isosurfaces of the HOMO and LUMO denote positive and negative wave function phases, respectively.

Figure 7: After covalent connectivity and another geometry optimization at smearing 0.02 Ha we mostly obtain highest occupied molecular orbitals a) HOMO; and we scarcely obtain lowest unoccupied molecular orbitals b) LUMO. The most molecular orbitals c) HOMOLUMO correspond to bonds of carbon atoms.

After applying covalent connectivity [37] to the resulting system in Figure 6, we again applied geometry optimization for smearing 0.02Ha, and we obtain different molecular orbitals in the results, as shown in Figure 7. This molecular complex as seen in Figure 7 has HOMO-482 with E=-0.17650 Ha, LUMO-483 E=0.16060 Ha, and Fermi energy Ef = -3162.004 Ha, for the reactivity sites with 482 active electrons. The orbital occupation is 204 A (1) alpha and 204 A (1) beta, and 37.00 alpha electrons in 62 orbitals plus 37 beta electrons in 62 orbitals. The molecular complex observed in Figure 7 has the same products previously mentioned. It must be noticed that the lowest unoccupied molecular orbitals (LUMO-acceptor) only draw orbitals in the CH3 product, the rest of the molecular orbitals correspond to the highest occupied molecular orbitals (HOMOdonor) complex. Then, this is a very stable molecular system only allowing reactivity through the methyl radical CH3 (Figure 7) The potential energy curve in Figure 3b is very near to physisorption; however, smearing energy in this case corresponds with a very high temperature, which actually occurrs little inside sun surface. In this work, we gradually get down smearing energy searching until reaching the glass transition temperature of chitosan. The smearing energy value 0.02 Ha corresponds with temperature 6315.49 K according to Table 1, and it is still too high; however, is this way we have been achieving geometry optimization to reach right smearing values according to experimental measurements. After successful convergence in geometry optimizations at 0.01, 0.007, 0.005, 0.003, and 0.002 smearing energies, the convergence at smearing energy 0.0017 Ha has been unsuccessful after more than 10000 SCF iterations for an oscillating energy with an energy tolerance of 0.00002 Ha. After these calculations, we continued rising the smearing energy until 0.00175, and after more than 5000 SCF, convergence is successfully accomplished. The temperature 552.6 K reached for smearing at 0.00175 agrees with glass transition temperature range [498.15K, 553.15K] of chitosan, according to experimental measurements [20-22].

Table 1: Change of temperature and pressure due to smearing variation 𝛿𝐸[𝐻𝑎] at temperature T [K] and pressure P [atm], for a volumen of 638 Å3.

Figure 8 illustrates the final stage of the molecular complex formed. We can observe that while C48 has been deformed mainly in its planarity, the chitosan ended broken in the two initial groups of each polymer, also apparently divided in several smaller molecules. This fact is very well known experimentally, because one bonding solution (epichlorhydrine, glutaraldehyde, or EGDE -ethylene glycol glycidyl ether-) is commonly used to keep chitosan copolymer cross-linked for enhancing the resistance of sorbent beads against acid, alkali, or chemicals [19]. The products observed by applying covalent connectivity (under the bonding scheme for no bonding to s- and f- shell, covalent connectivity and bond type, and converting representation to Kekulé) are the following: C51H7NO4 + C4H6O2 + C2H2O + C2H2 + CH3O + CHNO + CH3. As it can be seen part of each polymer remain bonded to the AC system (Figure 8). Then, at smearing 0.00175 Ha we mostly obtain highest occupied molecular orbitals for the molecular complex observed in Figure 9. This output exhibits the orbitals a) HOMO-482 with an eigenvalue of -0.17013 Ha, b) LUMO-483 with an eigenvalue of -0.16923 Ha, and c) HOMOLUMO. The Fermi energy is Ef = 3162.0047053 Ha, for the reactivity sites with 482 active electrons. The orbital occupation is 238 A (1) alpha and 239 A (1) beta, and 2.96 alpha electrons in 5 orbitals plus 2.04 beta electrons in 4 orbitals (Figure 9)

Figure 8: OUTPUT of the AC+Ch interaction after geometry optimization using smearing at 0.00175 Ha, corresponding to 552.6 K and 78.68 atm according to Table 1.

Figure 9: After another geometry optimization at smearing 0.00175 Ha: a) we mostly obtain highest occupied molecular orbitals HOMO, b) we scarcely obtain lowest unoccupied molecular orbitals LUMO, c) the greatest part of molecular orbitals HOMOLUMO correspond to bonds of carbon atoms.

Chitosan Optimized Without Smearing

First of all, the C24 carbyne-type ring alternating single and triple bonds is obtained by applying connectivity [37] and bond type to a C24 carbon ring which is the output of the input shown in Figure 10a corresponding to the geometry optimization of two hypothetical C12-carbon chains (Figure 10b). Then, Figure 10c exhibits an alternating single and triple bonds C24-ring. Second, applying clean of BIOVIA Materials Studio on chitosan copolymer molecule designed in Figure 2b, we obtain the input of a chitosan copolymer molecule as in Figure10d, and the Output exhibiting geometry optimization of the previous molecule is shown in Figure 10e. As we can observe, in this case chitosan remained complete. We made this, after suspecting that the initial bonds lengths and angles were not right in our design of chitosan, because broken chitosan is not a satisfactory result. Then, mixing the optimized C24 and Ch systems as shown in Figure 10f in the Input of a C24-ring surrounding a chitosan copolymer molecule, and after applying geometry optimization we obtain the Output of the previous CA-Ch nanocomposite see Figure 10g. Finally, we applied bonding scheme criteria as in Figure 10h.The nanocomposite in Figure 10h is a good example of the possibility of modifying the pore size distribution of chitosan when it is embedded into activated carbon. Here we consider INPUT and OUTPUT for applying geometry optimization on activated carbon and chitosan C14H24N2O9 system after each part has been previously optimized, and we also applied bond criteria for connectivity, bond type and kekulé representation. The C24-ring is carbyne type, and the chitosan copolymer molecule has been optimized in three dimensions in this case. The position of C24- ring surrounding a chitosan copolymer molecule has been only proposed.

Figure 10: Here we consider INPUT and OUTPUT of the corresponding geometry optimization, and also applying bond criteria for connectivity, bond type and Kekulé representation. a) Input among two hypothetical C12-carbon chains. b) Output showing a disconnected C24-ring. c) The previous C24-ring linked using bond criteria. d) Input of a chitosan copolymer molecule. e) Output exhibiting the optimization of the previous molecule. f) Input of a C24-ring surrounding a chitosan copolymer molecule, g) Output of the previous CA-Chitosan, h) Bonding criteria applied to the previous output

From the interaction through geometry optimization of two linear carbon chains of four and five carbon atoms as in Figure 11a, cumulene C9-ring shown in Figure 11b is obtained. This is a clear evidence of Jahn-Teller effect, because we observe double bond lengths alternating long/short with a difference among .02 and .03 Å, and the angles in this non-planar (Figure 11b) cumulene molecule are also different. The expected angles in a planar symmetrical molecule should be the same according to a well-defined symmetry. We considered the interaction of chitosan with another almost planar carbon ring of nine carbon atoms, now one in front to the other as in Figure 11c. Then, in Figure 11d there is another example about building pore size distribution among chitosan and activated carbon. In this case, we consider INPUT and OUTPUT for geometry optimization of cumulene C9-ring and chitosan C14H24N2O9, each one previously optimized by applying geometry optimization to the whole system, and also considering the bond criteria for connectivity, bond type and Kekulé representation as shown in Figure 11e. The cumulene C9-ring and chitosan copolymer molecule have been optimized in three dimensions, and we clearly observe the cumulene passing from face to face to almost T-shape orientation taking three hydrogen atoms from chitosan. The input position of cumulene C9 ring face to face with chitosan in that precise location has been proposed, and the result has been excellent.

Figure 11: Here we consider INPUT and OUTPUT of the geometry optimization among a cumulene C9-ring and a Chitosan C14H24N2O9 molecule, and also applying bond criteria for connectivity, bond type and Kekulé representation. a) Input among a hypothetical C4- and C5- chains. b) Output showing a C9-ring. c) Input among the C9-ring and chitosan molecule. d) Output exhibiting the complex C9-ring into chitosan. e) Bonding criteria applied to the previous output.

Discussion

We consider each carbon ring as physically activated through geometry optimization, due to pore size diameter remains in the average size compared against experimental measurements [41]. The C48 optimized ring carbon-system and one non-optimized chitosan copolymer unit has been studied considering the result after geometry optimization, as a molecular complex obtained when smearing value changes for converging energy values. Different elongation among single and triple carbon bonds in the carbyne-type are due to Jahn-Teller effect [14]. Then, C24 carbynering when we optimize two carbon chains at 3.074 Å of separation distance, is due to the Jahn-Teller effect. The Jahn-Teller effect is also present in C48 carbinoid -ring for their C8- and C4- carbinoid -rings. Carbon rings C4N (N<~8) exhibit a substantial first-order Jahn-Teller distortion that leads to long/short (single/triple) bond alternation decreasing with increasing N [14]. Whether we want to draw HOMO-LUMO orbitals, it is necessary to ask for orbitals in the geometry optimization as input data. At this work, for smearing energy 0.02 Ha we found different HOMO LUMO orbital numbers among the initial system in Figure 5 without asking for orbitals in the geometry optimization calculation, and its output asking for orbitals in a new energy calculation shown in Figure 6. Again after practicing connectivity, bond type, and Kekulé representation at smearing energy 0.02 Ha, we asked for orbitals, and we found in Figure 7 a small change at the orbital numbers previously obtained, and the corresponding energies were little different to the previous ones. We infer that bonding type change produced the differences, and the correct values correspond to the correct bonding type in the new molecular complex system formed.
The strongly dependence on smearing means very closely spaced energy levels (high degeneracy) near Fermi level. When there is a degenerate electron state, any symmetrical position of the nuclei (except when they are collinear) is unstable. As a result of this instability, the nuclei move in such a way that the symmetry of their configuration is destroyed, the degeneracy of the term is being completely removed [44,45]. High degeneracy indicates a high symmetry of the molecule, then the system tends to be distorted, in such way that when moving, the occupied levels are down and the unoccupied ones are up [46]. When levels are very densely spaced, convergence is hard to reach, since very small changes will occupy completely different states, and we get oscillations. These can be damped by smearing out the occupancy over more states, so that we turn off the binary occupancy of the states. We get down smearing width to glass transition temperature by decreasing the smearing parameter in steps to gradually stabilize our molecular complex system at the right temperature.
We initially observe distortion of chitosan system, and then its possible breaking in some products. This is partially in agreement with the results presented by Chigo et al. [46] in a study of the interaction among graphene-chitosan for a relaxed system doped with boron, in which they consider the interaction of pristine graphene with the monomer of chitosan (G + MCh:C6H13O5N) in different configurations, whereas we consider a chitosan copolymer molecule: C14H24N2O9 in only one orientation. While Chigo et al. [46] found a perpendicular chitosan, molecule linked to a carbon nanotube system, we obtained a cumulene carbon ring almost perpendicularly linked to a chitosan copolymer molecule.

Conclusion

We found one mechanism to figure out an optimized big molecular complex system by using DFT geometry optimization. This mechanism is based on smearing calculations, and on decrements of smearing energy in the molecular complex system until reaching the glass transition temperature of one of the components, which in this case correspond to the chitosan copolymer molecule. In order to get a molecular complex system AC + Ch, it is needed a high temperature among them at least to the phase transition temperature of either AC or Ch, because when they are solids there is only a heterogeneous mixture at room temperature. The use of smearing allows to reach high temperatures because according to Table 1 temperature increases as the smearing energy increases. We observed that the use of smearing to optimize a molecule as complex as the chitosan causes this to be fractionated, nevertheless when putting it in a plate of coal we obtained the glass transition temperature of the chitosan reported experimentally. The potential well depth providing chemisorption indicates existence of phase transition in one of our two molecular systems. This phase change is attributed to chitosan, due to carbon is more stable, and because we reach glass transition temperature of chitosan when dealing with the whole molecular complex system. In addition, when applying covalent connectivity, the activated carbon is the most stable molecular system keeping its molecular structure. According to HOMO and LUMO in Figures 6 -9, the sites with the greatest reactivity correspond to double and triple bonds. Besides, Figure 9 exhibits one amine functional group linked to the carbon system now C51 carbon molecular complex formed with a particular pore size distribution. Considering that after geometry optimization physisorption provides bonding in two parts of the chitosan molecule, this is an indication of a more environmental linking than that caused by cross-linking solutions, because cross-linking solutions might be toxic in medicine applications. The first chitosan molecule used, and optimized using smearing resulted to be unstable, because finished broken in several products. The second chitosan molecule used, and optimized without smearing, or with a very small smearing value resulted to be very stable, on which we were able to add activated carbon and to obtain good results. We have been able to optimize chitosan and add activated carbon, and we have observed the change in pore size distribution, even though we are missing its calculation, to assign the type of material obtained (micropore, mesopore, or macropore). We are working on it.

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