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Molecular modeling and Rational Design of Flotation Reagents

Molecular modeling and Rational Design of Flotation Reagents
Molecular modeling and Rational Design of Flotation Reagents

Molecular modeling and rational design of flotation reagents

Pradip *,Beena Rai

Tata Research Development and Design Centre,54B,Hadapsar Industrial Estate,Pune 411013,India

Received 15January 2003;received in revised form 10March 2003;accepted 30June 2003

Abstract

A scientific design methodology based on molecular modeling tools available today is presented for arriving at the most suitable reagent combinations for a given flotation separation problem.The power and the utility of this approach are illustrated with examples taken mainly from our work on mineral flotation with alkyl hydroxamates.D 2003Elsevier B.V .All rights reserved.

Keywords:flotation reagents;atomistic simulation;hydroxamates;phosphonic acids;molecular modeling;force field

1.Introduction

The design and the selection of highly selective flotation reagents for specific applications remain a challenging task.Most commercially successful flo-tation reagents were discovered largely through a trial and error methodology based on educated guesswork and empirical rules of thumb.For the beneficiation of multicomponent,highly disseminated and difficult-to-treat ore deposits,the conventional approaches of reagent design and selection are likely to prove woefully inadequate.Considering the demands made of reagents,namely,cost and efficiency/selectivity,coupled with environmental constraints,the scientific challenge facing the mineral engineers today lies in developing highly selective reagents customized for a specific task (Pradip,1994).Moreover,there is now a perceptible shift in the mining chemicals industry to

design and market tailor-made performance chemi-cals customized for specific applications rather than offer conventional,generic,multipurpose commodity chemicals as flotation reagents (Cappuccitti,1994;Malhotra,1994;Nagaraj et al.,1999).

A critical review of the recent literature on this topic (Somasundaran and Nagaraj,1984;Nagaraj,1988;Pradip,1988,1991,1997,1998;Marabini et al.,1989;Fuerstenau and Herrera-Urbina,1989;Aplan,1994,Fuerstenau,1999a,b;Klimpel,1999;Ackermann et al.,2000;Pradip et al.,2002c)clearly reveals that there is an urgent need to develop a theoretically robust framework that can provide a rational basis for design and selection of novel reagent combinations for specific applications.Some of the important issues that need to be addressed in this context are discussed in the following paragraphs.It is not only intuitively obvious but also borne out by several examples in flotation practices that the selectivity of flotation reagents is determined to a large extent by the molecular recognition phenomena underlying their adsorption at mineral/water interfaces (Pradip,1994).Recognition at a molecular level is a

0301-7516/$-see front matter D 2003Elsevier B.V .All rights reserved.doi:10.1016/S0301-7516(03)00090-5

*Corresponding author.Tel.:+91-20-4042309;fax:+91-20-4042399.

E-mail address:pradip@pune.tcs.co.in (Pradip)https://www.doczj.com/doc/a014156097.html,/locate/ijminpro

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fundamental characteristic of several natural systems involving a wide variety of organic–inorganic inter-faces(Mann,1988;Weissbuch et al.,1991;Schneider, 1991;Lehn,1993;Abbott,2001).These molecular recognition mechanisms are essentially based on the structural/stereochemical compatibility between the molecular architecture of the adsorbing reagent and the specific surface structure(the nature and the spatial arrangement of adsorption sites on the surface) of the substrate it is interacting with.The strong templating effects of the surface have been noted and documented in several cases(Black et al.,1991; Davey et al.,1991;Grases et al.,1991;Heywood and Mann,1992;Arad et al.,1993;Bromely et al.,1994; Pradip,1994;Ravishankar et al.,1995;Manne and Gaub,1995;Coveney et al.,2000;Davey and Rebello,2001;Rai and Pradip,2002;Osman and Suter,2002).It is our contention that one can enhance selectivity of flotation reagents by orders of magni-tude if we are able to identify the specific molecular recognition mechanism and design the molecular architecture accordingly for a separation task which involves several competing surfaces for the same flotation reagent.It is therefore imperative to identify and catalogue different kinds of molecular recognition mechanisms controlling selectivity in flotation sepa-ration systems that are already known to be amenable to a high degree of separation efficiencies.This approach should help us in providing a scientific rationale as well as a methodology for designing more selective reagents.It is similar to designing a targeted drug delivery system guaranteeing the required quan-tity of specific drug molecule to reach the desired active site among so many other competing sites in biological systems.

Aforementioned strategy is,however,incomplete since there exists a whole host of molecular recogni-tion mechanisms that can be utilized to design several families of molecular architectures as possible candi-dates for the separation problem under investigation. Since it is not possible to synthesize all possible molecules and test each one of them to confirm their efficacy,there is a need for a sound,robust and,most importantly,a quantitative methodology to screen and shortlist the most promising ones from the list of possible candidates.It is in this context that we have proposed and validated a methodology based on molecular modeling computations.While there are several limitations in this approach and efforts are underway to overcome them,our results suggest that the essence of the underlying molecular recognition phenomena can certainly be captured in the interac-tion energy computations with the available tools.In the absence of any other quantitative methodology for selection,molecular modeling is,in our opinion,the best and most reliable option available at present.

We have made considerable progress in developing a robust and reliable methodology based on molecular modeling tools to arrive at the most promising mo-lecular structures for the separation problems which are considered not amenable to or too complex for a satisfactory solution(Pradip and Rai,2002;Pradip et al.,2002a,b,c).In this communication,we describe the most important components of this novel para-digm of reagent design with the help of our recent work on alkyl hydroxamates,a relatively new family of flotation reagents,commercialized recently in the mining industry.We demonstrate how molecular modeling tools available today can be gainfully employed for reagent design in this area.

Firstly,one can design and screen and thus pro-gressively narrow the focus on preferred molecular architecture for a given mineral surface which is based on the interaction energies computed through a com-pletely theoretical methodology of molecular model-ing.Since this search is based on completely theoretical computations,one can evaluate a much larger number of molecules than what is possible with conventional trial and error experimental approaches.

Secondly,based on similar computations,it is possible to select the most efficient(which may not be the most selective)reagent from several possible candidates for a given separation task involving more than one mineral surface.This selection is based on not the affinity of a reagent for a particular mineral alone,but a comparative assessment of its ability to discriminate among several competing surfaces.The reagent to which a particular mineral responds the best need not be the most preferred choice in case of multicomponent systems.

Several other research groups are currently en-gaged in studying surfactant–surface interactions using molecular modeling tools(Coveney and Humphries,1996;Frank et al.,1996;Goddard et al.,1997;de Leeuw et al.,1998;Hass et al.,1998; Numata et al.,1998;Shevchenko and Bailey,1998;

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de Leeuw and Parker,1999;Hirva and Tikka,2002; Tunega et al.,2002).We present in this paper the results of our molecular modeling computations on the interactions of alkyl hydroxamates with several minerals of interest.Alkyl hydroxamates have been found to be highly selective flotation collectors for a wide variety of minerals such as those containing iron,rare earths,tin and tungsten minerals,kaolin and,more recently,for separation among calcium minerals including flotation separation in apatite–dolomite system(Fuerstenau et al.,1967,1970, 1983;Fuerstenau and Petersen,1969;Gorlovskii et al.,1969;Bogdanov et al.,1973;Evrard and De Cuyper,1975;Fuerstenau and Pradip,1984;Pradip, 1987,1996;Ravishankar et al.,1988;Pradip and Fuerstenau,1989,1991;Pradip et al.,1991,1993, 1995,1997;Yoon et al.,1992;Pradip and Chaudhari, 1997;Lee et al.,1998;Miller et al.,2001a,b).As presented in the following sections,trends predicted on the basis of theoretically computed interaction energies correlate quite well with our own experi-mental microflotation results as well as with those available in the published literature.

2.Molecular modeling methodology

While we have utilized both the quantum chemical and force field(also known as atomistic simulation) computations in our work,for the sake of uniformity, all the results presented in this paper are confined to those obtained with one technique only,that is,the universal force field(UFF)(Casewit et al.,1992a,b, Rappe′et al.,1992,1993).The Cerius2program (Accelrys,USA)has been used to model the sur-face–reagent interactions by UFF.We have success-fully demonstrated through our earlier work that UFF can be used to model the mineral–reagent systems with reasonable accuracy.A detailed methodology of modeling the mineral–reagent interactions has been presented recently(Pradip and Rai,2002;Pradip et al.,2002a,b,c).A brief summary is presented in the following paragraphs.

2.1.Reagent molecule

The UFF-optimized atomic structure of octyl hydroxamic acid molecule along with partial charges on the constituent atoms is shown in Fig.1.The UFF-optimized structural parameters compare well with those reported in literature(Table1).

2.2.Mineral surface

A surface cell was created from the unit cell of the mineral at a given Miller plane(usually the cleavage plane)and then was optimized.The surface energy was then calculated for this optimized mineral surface. For a given mineral,the plane selected was either based on the literature data(experimentally observed cleavage plane)or the surface energy values(the one with lowest surface energy was considered as the cleavage plane).

To establish the validity of the UFF for modeling mineral surfaces,we optimized their crystal struc-tures and compare them with experimental measure-ments(Dana and Ford,1949).As summarized in Table2,the UFF-predicted values of lattice param-eters are in reasonable agreement with those exper-imentally reported.The computed surface energy for corresponding cleavage plane is also included in the

table.

Fig.1.UFF-optimized structure of HXMA-8with partial charges on the constituent atoms.

Pradip,B.Rai/Int.J.Miner.Process.72(2003)95–11097

As an illustration,we present in Fig.2a the opti-mized surface of bastnaesite mineral cleaved at {100}plane.Since the literature data on the cleavage plane for bastnaesite was not available,we computed surface energy values for different miller planes.The {100}plane was found to have the lowest surface energy and hence selected as the cleavage plane for bastnaesite.

The surface cell thus created was extended to a 2D

periodic superlattice of 26?32A

?.The atoms in top eight layers were allowed to relax,while the coordi-nates of those in the bottom eight layers were kept unchanged during optimization.The surface energy for this plane was computed to be 1.5J/m 2.2.3.Mineral–reagent complex

The optimized reagent molecule was then docked on the mineral surface.The initial geometry of sur-face–reagent complex was created physically on the screen with the help of molecular graphics tools,taking into consideration the possible interactions of reagent functional groups with surface atoms.The reagent molecule was then allowed to relax complete-ly on the surface.Several initial conformations (f 20)were assessed so as to locate the minimum energy conformation of the mineral–reagent complex.For illustration,the optimized complex of hydroxa-

Table 1

A comparison of UFF-optimized structural parameters of hydroxa-mic acid with literature values

Bond Length (A

?)UFF

(this work)

Ab initio

(Lipczynska-Kochany and Iwamura,1982)Experimental (Pakkanen et al.,1987)C M O 1.22 1.22 1.25C U N 1.37 1.34 1.30N U O 1.37 1.44

1.41C 1U C 2

1.51 1.51

Other C U C

1.53

Table 2

A comparison of UFF-optimized crystal structures with experimentally observed crystal structures of minerals

Mineral Lattice parameters (in j and A

)Plane

Surface UFF-predicted

Experimental (Dana and Ford,1949)energy (J/m 2)Alumina

a =

b =90,

c =120;a =b =4.32,c =11.64a =b =90,c =120;a =b =4.75,c =12.90{001} 1.22Barite

a =

b =

c =90;a =8.82,b =5.05,c =7.15a =b =c =90;a =8.88,b =5.45,c =7.15{001} 3.00Bastnaesite a =b =90,c =120;a =b =6.97,c =9.26a =b =90,c =120;a =b =7.16,c =9.78{100} 1.50Calcite a =b =90,c =120;a =b =4.92,c =15.5a =b =90,c =120;a =b =4.99,c =17.06{104} 1.50Cassiterite a =b =c =90;a =b =4.69,c =2.87

a =

b =

c =90;a =b =4.74,c =3.19

{110} 1.28Chalcocite a =c =90,b =116.47;a =15.4,b =12.4,c =13.2

a =c =90,

b =116.35;a =15.22,b =11.88,

c =13.5

{110}0.62Chalcopyrite a =b =c =90;a =b =5.93,c =11.52a =b =c =90;a =b =5.29,c =10.43{011}0.79Cerussite a =c =b =90;a =7.54,b =7.18,c =5.67a =c =b =90;a =6.15,b =8.44,c =5.19{110}0.06Covellite a =b =90,c =120;a =b =4.22,c =14.94a =b =90,c =120;a =b =3.79,c =16.34{001} 1.14Dolomite a =b =90,c =120;a =b =5.13,c =18.32a =b =90,c =120;a =b =4.81,c =16.01{101} 1.52Fluorite a =b =c =90;a =b =c =5.13

a =

b =

c =90;a =b =c =5.46

{111}0.80Fluorapatite a =b =90,c =120;a =b =9.22,c =6.52a =b =90,c =120;a =b =9.37,c =6.88{100} 1.20Hematite a =b =90,c =120;a =b =5.13,c =12.76a =b =90,c =120;a =b =5.03,c =13.75{001} 1.09Ilmenite a =b =90,c =120;a =b =5.20,c =14.11a =b =90,c =120;a =b =5.08,c =14.04{003} 3.11Malachite a =c =90,b =97.3;a =8.22,b =11.6,c =3.96

a =c =90,

b =98.8;a =9.50,b =11.97,

c =3.20

{001} 2.25Monazite a =c =90,b =102.6;a =6.79,b =7.01,c =6.30

a =c =90,

b =104.4;a =6.78,b =7.00,

c =6.45

{100}0.16Rutile a =b =c =90;a =b =4.39,c =3.02

a =

b =

c =90;a =b =4.59,c =2.96

{110}0.78Silica

a =

b =90,

c =120;a =b =5.25,c =5.80a =b =90,c =120;a =b =4.91,c =5.40{100} 1.10Smithsonite a =b =90,c =120;a =b =5.36,c =16.59

a =

b =90,

c =120;a =b =4.65,c =15.03{110}0.02Wolframite a =c =90,b =90.31;a =4.53,b =5.79,c =5.29a =c =90,b =90;a =4.83,b =5.74,c =4.99{010}0.54Zircon

a =

b =

c =90;a =b =7.13,c =6.35

a =

b =

c =90;a =b =6.60,c =5.98

{110}

1.53

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98

Pradip,B.Rai/Int.J.Miner.Process.72(2003)95–11099

Fig.2.(a)Top view of bastnaesite{100}surface.(b)Side view of the optimized complex of HXMA-8on bastnaesite{100}surface.

mate molecule on bastnaesite{100}surface is shown in Fig.2b.

2.4.Simulation details

The partial charges on the atoms were calculated using charge equilibration method(Rappe′and God-dard,1991).The intramolecular van der Waals inter-actions were calculated only between atoms which

were located at distances greater than fourth nearest neighbors.A modified Ewald summation method (Karasawa and Goddard,1989)was used for calcu-lating the nonbonded coulomb interactions,while for van der Waals interactions,a direct cutoff at a distance less than r/2(where r is the length of the simulation cell)was employed.Smart minimizer as implemented in Cerius2was used for geometry optimization.The optimization was considered to be converged when a gradient of0.0001kcal/mol was attained.

2.5.Interaction energy

The interaction energy was calculated for the most likely/favorable conformation using the following equation:

Interaction energyeD ET

?EecomplexTà?EereagentTtEesurfaceT

where E(complex),E(reagent)and E(surface)are the total energies of optimized surface–reagent complex,re-agent molecule and surface cluster,respectively.It is worth noting that the more negative the magnitude of interaction energy(D E),the more favorable is the interactions between the surface and the reagent. Accordingly,the interaction energy obtained is considered to be a quantitative measure of the intensity of interaction and correlated with experi-mentally measured macroscopic properties,as for example,flotation behavior of the system under investigation.

2.6.Effect of aqueous environment

In the current formulation,we cannot easily ac-count for the effect of aqueous environment on mineral–reagent interactions(Pradip et al.,2002a).It is possible,however,to compute separately the interaction energies for water molecules adsorbed on the surface.As the interaction energies for reagents adsorbed on the mineral surface are observed to be more negative than those computed for water,it indirectly supports the generally adopted mechanism of reagent replacing water on the surface.For exam-ple,the interaction energies for hydroxamates on bastnaesite and barite are compared with those for water(Table3).The interaction energies for the flotation reagent binding with the surface were com-puted to be consistently higher than those for water for all the systems reported in this paper.

3.Mineral flotation response and its correlation with theoretically computed interaction energies 3.1.Rare-earth ore minerals

Fuerstenau et al.(1983),Fuerstenau and Pradip (1984)and Pradip and Fuerstenau(1983,1985, 1989,1991)have reported the separation of bastnae-site from associated gangue minerals by flotation. They observed that selectivity of flotation separation of bastnaesite{(Ce,La)FCO3}from calcite(CaCO3) and barite(BaSO4)with hydroxamate collectors is higher than that observed with conventional fatty acids(oleate).It is interesting to note that the theoretically computed interaction energies accurate-ly predict the experimentally observed flotation trends(Fig.3).Bastnaesite responds to hydroxamate flotation more strongly as compared to barite and calcite.

Hydroxamates are known to be excellent flotation collectors for iron minerals.We compare the adsorp-tion data,that is,the equilibrium adsorption isotherms for the four minerals,namely,bastnaesite,hematite (Fe2O3),calcite and barite with corresponding com-Table3

UFF-computed interaction energies for water and hydroxamic acid molecules

Mineral surface Interaction energy(kcal/mol)

Hydroxamic acid Water Bastnaesite{100}à66.4à24.0 Barite{001}à33.0à22.4

Pradip,B.Rai/Int.J.Miner.Process.72(2003)95–110 100

puted interaction energies in Fig.4.The interaction of these four minerals with alkyl hydroxamates is found to be in the following order

Bastnaesite >hematite >calcite >barite

It is precisely the same order as predicted by our molecular modeling computations.It is worth noting

that hydroxamates are even stronger flotation collec-tors for bastnaesite as compared to hematite,as borne out by experimental data also (Fig.4).3.2.Calcium minerals

Separation among calcium minerals is one of the most difficult problems in mineral processing (Finkel-stein,1989;Pradip,1994).We have earlier reported results on this system using different families of flota-tion reagents,namely,oleate,alkyl hydroxamates (HXMA-8),octylimino-bis-methylene diphosphonic acids (IMPA-8)and 1-hydroxy-octylidene-1,1diphos-phonic acid (Flotol-8).Except for oleate,the order of flotation response to the three minerals,namely,fluo-rite (CaF 2),calcite and fluorapatite {Ca 10(PO 4)6F 2},is experimentally observed to be (Pradip and Rai,2002;Pradip et al.,2002a,b):

Fluorite >Calcite >Fluorapatite In case of oleate,the order is:Fluorite >Fluorapatite >Calcite

The order of flotation response to different reagents as predicted on the basis of molecular modeling computations is exactly the same.In fact,even though the reasons for different behavior of oleate from other reagents are still not clear,it is remarkable that the theoretical molecular modeling computations do predict the observed trends correctly in all cases (Table 4).

Even more significant is the result of our molecular modeling computations with respect to fluorapatite–dolomite {(Ca,Mg)CO 3}system.The interaction en-ergy calculations presented in Fig.5clearly indicate that alkyl hydroxamates are likely to be more selective reagents as compared to conventional oleate collec-tors.The gap is much higher for hydroxamate.While we ourselves have done considerable work to confirm this important finding,we have chosen to compare in Fig.5our theoretical predictions with recent experi-mental results reported by Miller et al.who have demonstrated that alkyl hydroxamates are more selec-tive collectors than fatty acids for the flotation sepa-ration of fluorapatite from dolomite (Miller et al.,2001a,b)

.

Fig.3.(a)Flotation recovery of bastnaesite,calcite and barite as function of molar concentration of HXMA-8.(b)UFF interaction energy of HXMA-8on bastnaesite {100},calcite {104}and barite {001}surfaces (experimental data taken from Pradip,1981).

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3.3.Rutile–hematite separation

We had earlier explored the utility of alkyl hydrox-amates for the flotation separation of rutile (TiO 2)from hematite,but our efforts were not successful (Fig.6).Subsequent molecular modeling computa-tions indicated that energies are comparable for both hematite and rutile interacting with alkyl hydroxa-mates as well as for the conventional oleate collector (Fig.6).It is therefore not surprising to find no selectivity in separation with these collectors.More significantly,our molecular modeling com-putations with another family of reagents,that is,octylimino-bis-methylene diphosphonic acids (IMPA-8),revealed that it is likely to be a more selective collector than oleate and hydroxamate for the flotation separation of hematite from its mixtures with rutile (Fig.6).While the interaction energies are similar in magnitude for oleate and hydroxamate interactions with these minerals,there is a substantial gap in interaction energies in case of IMPA-8.It is interesting therefore to cite the work of Collins et al.(1984)

who,

Fig.4.A comparison of equilibrium adsorption isotherms for octyl hydroxamate adsorption on bastnaesite,hematite,calcite and barite minerals with the corresponding interaction energy computed using UFF for HXMA-8adsorption on bastnaesite {100},hematite {001},calcite {104}and barite {001}surfaces (experimental data taken from Pradip,1987).

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102

working with Briquest 2N81-25S (same as IMPA-8),did observe this selectivity.Our predictions are con-sistent with their results,reproduced in Fig.9along with corresponding interaction energies computed by us.The shaded portion in the figures represents the region where flotation was observed by these authors.

Table 4

A comparison of experimentally observed flotation trends with those predicted on the basis of molecular modeling computations Reagent Computed UFF interaction energy (kcal/mol)Order of flotation

Fluorite (F)Calcite (C)Fluorapatite (A)response (experimental)IMPA-8à191.4à100.5à87.9F>C>A Flotol-8à198.2à128.5à120.7F>C>A HXMA-8à64.6à44.0à43.3F>C>A Oleate

à52.6

à40.2

à46.8

F>A>C

The number 8represents the alkyl chain length (8carbon)of the reagent.

Experimental data taken from Pradip et al.(2002a,b)for HXMA-8,Flotol-8and IMPA-8and Pugh and Stenius (1985)for

oleate.

Fig.5.Microflotation recovery of francolite (Florida apatite)and dolomite as a function of Aero 6493,a commercial hydroxamic acid from Cytec,USA (top left),FA/FO (commercial fatty acids/fuel oil reagent combination in 7:3ratio by volume)addition at natural pH 6.5,with distilled water (top right)and its corresponding UFF interaction energies for fluorapatite {100}and dolomite {110}surfaces interacting with octyl hydroxamic acid (bottom left)and oleate (bottom right),respectively (experimental data taken from Miller et al.,2001b ).

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103

3.4.Copper–lead–zinc ore minerals

Alkyl hydroxamates have been demonstrated to be excellent auxiliary collectors (in combination with conventional xanthates)for the beneficiation of mixed sulfide-oxide ore deposits.The work of Pradip et al.(1991,1995),including the final plant trials at Malanjkhand Copper Ore Beneficiation plant in India,clearly proved that xanthate–hydroxamate combina-tion is an excellent choice for this task.Copper recovery in the plant could be enhanced by as much as 10%in case of an oxidized ore reporting to the milling circuit.The ore contained significant amounts of secondary sulfides and oxide minerals of copper such as malachite {CuCO 3,Cu(OH)2},chalcocite (Cu 2S)and covellite (CuS)in addition to chalcopyrite {(Cu,Fe)S 2}.Minerals other than chalcopyrite are not

recovered with xanthate,but the addition of alkyl hydroxamates facilitates flotation of these minerals along with chalcopyrite.More recently,Lee et al.(1998)also reported their experiences with xan-thate–hydroxamate reagent combination in the bene-ficiation of similar ores.It was therefore of interest

to

Fig.6.Flotation recovery of rutile and hematite with oleate and hydroxamate collectors,respectively.Corresponding interaction energies for rutile {110}and hematite {001}surfaces with octyl hydroxamic acid and oleate are shown in the insert (experimental data taken from Pradip et al.,2003).

Table 5

Correlation of UFF-computed interaction energies on copper minerals with their experimental flotation response for hydroxamates Mineral

Interaction energy (kcal/mol)Dosage required for 100%flotation during Hallimond tube tests (g/l)(pH 9F 0.2)Chalcopyrite à54.5f 1Chalcocite à34.020Malachite

à34.0

34

Experimental data taken from Pradip et al.(1990)

.

Fig.7.Flotation recovery of malachite,cerussite and smithsonite with hydroxamate collector.Corresponding interaction energies for malachite {001},cerussite {110}and smithsonite {110}surfaces with octyl hydroxamic are shown in the insert (experimental data taken from Pradip et al.,1997).

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104

carry out molecular modeling computations on the interaction of hydroxamates with different copper minerals.The interaction energies are compared in Table5with corresponding microflotation results wherever available.

We have also studied the flotation of oxidized sulfide ores containing copper,lead and zinc minerals. We have reported earlier on the possibility of selective separation among malachite,cerussite(PbCO3)and smithsonite(ZnCO3)minerals using modified SALO compounds(Das et al.,1995)and alkyl hydroxamates (Pradip et al.,1997).Our experimental flotation results with potassium octyl hydroxamate indicated that malachite is significantly more amenable to hydroxamate flotation as compared to cerussite and smithsonite(Fig.7).The corresponding interaction energies computed for this system using UFF are also plotted in the same figure.There is a reasonable agreement between theoretically computed trends and experimental observations.

4.Customized flotation collectors for ore beneficiation:reagent interaction with other constituent minerals

The discussion in the preceding section demon-strates how molecular modeling computations can be utilized as a valuable quantitative measure to grade/ shortlist/screen various possible reagents(either designed or available off the shelf)for the flotation of a particular mineral.For instance,on the basis of above-mentioned computations,one can rule out certain family of reagents/certain molecular architec-tures for the flotation of a particular mineral and narrow down the choice.One can establish important structure–property relationships also based on these computations.

4.1.Fluorite ore

The next question to be addressed,in case of multicomponent ores,is whether the particular reagent is adequately selective against other gangue minerals present.One can prepare the comparative selective data for each reagent of interest for a particular set of mineral constituents of the ore based on molecular modeling computations without carrying out experi-ments.An illustrative set of nine minerals and three different reagents,for the beneficiation of fluorite ore, is shown in Fig.8as an example.Significant differ-ences are observed between the response of different minerals to the selected reagents,namely,oleate, hydroxamate and diphosphonic acids(IMPA-8).For example,based on the theoretical computational results presented in Fig.8,by virtue of having larger difference in the interaction energies for fluorite vis-a`-vis other minerals,one would prefer hydroxamate and IMPA-8for the flotation separation of fluorite from other minerals as compared to oleate.Even though it is selective against all minerals included in study,

IMPA-Fig.8.A comparison of UFF interaction energies computed for a set of nine minerals with three reagents,namely,oleate,hydroxamate and IMPA-8.

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8will not be the best choice in case ores contain barite. Barite is found to have interaction energies comparable to fluorite in case of IMPA-8.Hydroxamates,however, are likely to be more selective against barite.Our flotation results did confirm these findings.

One can thus prepare a comparative chart for all the mineral constituents of an ore and for each reagent under consideration.This information can be used to select/design the preferred reagent combination for best separation.4.2.Wolframite ore

Beneficiation of tungsten ores typically involves selective flotation of wolframite[(Fe,Mn)WO4]from its associated gangue minerals such as silicates,fluo-rite,hematite,barite,calcite,apatite and rutile(Pradip, 1996).One thus needs to design a powerful collector capable of not only floating wolframite effectively, but also being sufficiently selective against other minerals present in the ore.We present in the

follow-

ing paragraph our molecular modeling prediction/ results for a set of reagents selected for this study and a comparison of the predicted selectivity trends with experimental results.

The microflotation tests indicated that wolframite exhibited comparable flotation response with all three common family of reagents,namely,oleate,hydrox-amate and IMPA(Pradip and Chaudhari,1997).This finding is consistent with the magnitude of the inter-action energies computed for wolframite for these reagents(Fig.8).The choice of the reagent for wolframite flotation for a given ore,however,will depend on the selectivity of that reagent with respect to other constituent minerals.We illustrate the meth-odology with the help of experimental data available with respect to IMPA-8.

Collins et al.(1984)reported on the flotation of different minerals using IMPA reagents.Fig.9shows a correlation of our computed interaction energies with experimental flotation results of Collins et al. The shaded regions define the flotation limits in terms of dosage and pH for various minerals as reported by the authors.The closely shaded regions represent excellent flotation and the less densely shaded signifies relatively less flotation.Our interac-tion energy values are in general agreement with the experimentally observed trends.For example,in the absence of experimental data,we would have still predicted the flotation response to be in the order barite f fluorite>hematite f calcite>apatite>wolf-ramite H rutile>silica.

Based on such computations,therefore,one can a priori rule out IMPA-8for wolframite flotation for an ore containing fluorite,barite and hematite as constit-uent minerals.IMPA-8on the other hand will prove to be an excellent collector for ores containing wolfram-ite in association with rutile and silica.One can thus play around with the molecular architecture as well as the nature of different functional groups to shortlist the preferred molecules suitable for separation of wolframite from other constituent minerals present in the ore under investigation.The same exercise if carried out through conventional approach will be quite costly both with respect to resources as well as time and thus may not be even attempted.With the proposed methodology,however,we can very conve-niently simulate the anticipated flotation separation selectivity with a wide variety of reagents.We need to synthesize/test only those which meet the desired criteria.

5.Concluding remarks

As demonstrated through several examples in this paper,the proposed molecular modeling-based meth-odology provides a convenient and efficient means of screening the most promising molecules from a set of large number of possible candidates for a given application.Since this approach does not involve any experimentation except for validation,the search/design space can thus be enlarged immensely. One can conceive of several new families of molec-ular architectures for the separation problem under investigation and ultimately shortlist a few for detailed study and experimentation.The same technique can be extended to optimization of the molecular structure till we arrive at an acceptable level of efficiency and/ or cost criteria.Considering the usual constraints of time and resources,the proposed approach should certainly reduce the time to develop new tailor-made products for targeted applications in the mineral industry.

With rapid advances being made in the field of molecular modeling in terms of being able to con-duct molecular dynamics simulation of realistic sys-tems consisting of hundreds of molecules and perhaps thousands of atoms,in the very near future, it would be possible to model,simulate and thus predict much more subtle effects of molecular archi-tecture on the self-assembly at interfaces.This would certainly facilitate the design of highly selective reagents.The whole field of reagents design is thus on the threshold of a major breakthrough.A para-digm shift from conventional trial and error method-ology to a more rational design of reagents based on molecular modeling tools appears to be on the horizon.

Acknowledgements

Authors are grateful to Prof.Mathai Jospeh for his constant support and encouragement during the course of this work and to Prof.P.C.Kapur for critically reviewing the manuscript.

Pradip,B.Rai/Int.J.Miner.Process.72(2003)95–110107

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力创DTSD106-M100三相导轨式电能表RS485智能电表说明书

力创DTSD106-M100三相导轨式电能表RS485智能电表说明书

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浙江天普胜电气有限公司 1.概述 DT(S)S型三相电子式电能表,使用在供电部门、工厂、企业、商业、农业的动力、照明设备的有功电能计量,该表采用进口专用大规模集成电路,16位A/D转换、数字乘法器、数字采样处理技术及SMT工艺,根据工业用户实际用电状况所设计、制造的新型电能仪表。用于计量频率为50Hz的交流三相有功电能,并电量采用液晶显示,读数直观便于抄表,本仪表可扩展RS485通讯功能,为三相电能测量提供先进、可靠的计量工具。 本仪表采用的计量模块能精确地测量三相正反双向有功电能。计量准确、稳定、可靠、具有良好的抗电磁骚扰、低功耗、高准确度、防窃电、宽量程、长寿命等特点。 本仪表符合标准DL/T 645-1997《多功能表通讯规约》和GB/T 17215-2002《1级和2级静止式交流有功电能表》以及IEC 61036:2000。 2. 工作原理

本电能表采用三相供电方式,并在任一单相供电情况下都能正常工作。 电能表工作时,电压、电流经取样电路分别取样后,送至大规模专用集成电路缓冲放大,再由16位A/D转换器转换成数字信号,经数字乘法器运算后,转换成和电能大小成正比的脉冲,驱动计度器进行电能累加和驱动脉冲指示灯,并输出脉冲,供计量。 3. 规格型号及技术指标 3.1 规格型号 3.2基本误差(平衡负载基本误差极限)

注:(Ib为基本电流In为额定电流Imax为最大电流) 不平衡负载各电流点的百分数误差极限为1级表±2.0,2级表±3.0。 3.3 起动 在参比电压、参比频率及功率因数为1.0的条件下,负载电流为0.004Ib(1级)、0.005Ib(2级)仪表应能起动,并连续计量电能。 3.4 潜动 电压回路加1.15倍的参比电压,电流线路中无电流时,仪表的测试输出不应产生多于一个的脉冲。 3.5 工作电压范围 正常工作电压:0.9Un~1.1Un 极限工作电压:0.0Un~1.15Un 3.6 功耗 电压线路功耗:≤2W(10VA) 电流线路功耗:≤4.0VA 3.7 环境条件 正常工作温度:-10℃~+45℃, 工作极限温度:-25℃~+55℃, 存贮和运输温度:-25℃~+70℃ 相对湿度:年平均≤75% 3.8 外形尺寸:228mm×145mm×72mm; 3.9 重量:约1.5kg; 3.10安全性能:产品符合GB/T 17215-2002规定的各项安全指标和要求。 3.11 电量显示采用7位液晶显示,6位整数,1位小数。

des课程设计

DES加解密算法的实现 一、DES算法的概述 DES(Data Encryption Standard)是由美国IBM公司于20世纪70年代中期的一个密码算(LUCIFER)发展而来,在1977年1月15日,美国国家标准局正式公布实施,并得到了ISO的认可,在过去的20多年时间里,DES被广泛应用于美国联邦和各种商业信息的保密工作中,经受住了各种密码分析和攻击,有很好的安全性。然而,目前DES算法已经被更为安全的Rijndael算法取代,但是DES 加密算法还没有被彻底的破解掉,仍是目前使用最为普遍的对称密码算法。所以对DES的研究还有很大价值,在国内DES算法在POS、ATM、磁卡及智能卡(IC卡)、加油站、高速公路收费站等领域被广泛应用,以此来实现关键的数据保密,如信用卡持卡人的PIN码加密传输,IC卡与POS机之间的双向认证、金融交易数据包的MAC 校验等,均用到DES算法。 DES算法是一种采用传统的代替和置换操作加密的分组密码,明文以64比特为分组,密钥长度为64比特,有效密钥长度是56比特,其中加密密钥有8比特是奇偶校验,DES的加密和解密用的是同一算法,它的安全性依赖于所用的密钥。它首先把需要加密的明文划分为每64比特的二进制的数据块,用56比特有效密钥对64比特二进制数据块进行加密,每次加密可对64比特的明文输入进行16 轮的替换和移位后,输出完全不同的64比特密文数据。由于DES 算法仅使用最大为64比特的标准算法和逻辑运算,运算速度快,密

钥容易产生,适合于在大多数计算机上用软件快速实现,同样也适合于在专用芯片上实现。 二、DES算法描述 DES算法的加密过程首先对明文分组进行操作,需要加密的明文分组固定为64比特的块。图2-1是DES加密算法的加密流程。图2-2是密钥扩展处理过程。

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目录 一、概述 (1) 二、产品规格 (2) 三、技术参数 (3) 四、安装与接线 (5) 4.1安装外形图及接线图 (5) 4.2安装注意事项及方法 (11) 五、使用说明 (12) 5.1面板格式 (12) 5.2功能说明 (16) 5.3显示说明 (18) 5.3.1编程设置 (28) 5.4通信说明 (31) 5.5MODBUS-RTU通讯地址信息表 (38) 5.6注意事项 (54) 六、典型应用 (55)

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D E S加密解密课程设计报 告 Prepared on 22 November 2020

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目录

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DIN导轨式安装三相电子式有功电能表(液晶RS485型)

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DES算法及其程序实现

DES算法及其程序实现 一.D ES算法概述 ①DES算法为密码体制中的对称密码体制,又被成为美国数据加密标准,是1972年美国IBM公司研制的对称密码体制加密算法。明文按64位进行分组,密钥长64位,密钥事实上是56位参与DES运算(第8、16、24、32、40、48、56、64位是校验位,使得每个密钥都有奇数个1)分组后的明文组和56位的密钥按位替代或交换的方法形成密文组的加密方法。 ②DES算法的特点:分组比较短、密钥太短、密码生命周期短、运算速度较慢。 ③DES算法把64位的明文输入块变为64位的密文输出块,它所使用的密钥也是64位,整个算法的主流程图如下: 二.D ES算法的编程实现 #include #include using namespace std;

const static char ip[] = { //IP置换 58, 50, 42, 34, 26, 18, 10, 2, 60, 52, 44, 36, 28, 20, 12, 4, 62, 54, 46, 38, 30, 22, 14, 6, 64, 56, 48, 40, 32, 24, 16, 8, 57, 49, 41, 33, 25, 17, 9, 1, 59, 51, 43, 35, 27, 19, 11, 3, 61, 53, 45, 37, 29, 21, 13, 5, 63, 55, 47, 39, 31, 23, 15, 7 }; const static char fp[] = { //最终置换 40, 8, 48, 16, 56, 24, 64, 32, 39, 7, 47, 15, 55, 23, 63, 31, 38, 6, 46, 14, 54, 22, 62, 30, 37, 5, 45, 13, 53, 21, 61, 29, 36, 4, 44, 12, 52, 20, 60, 28, 35, 3, 43, 11, 51, 19, 59, 27, 34, 2, 42, 10, 50, 18, 58, 26, 33, 1, 41, 9, 49, 17, 57, 25 }; const static char sbox[8][64] = { //s_box /* S1 */ 14, 4, 13, 1, 2, 15, 11, 8, 3, 10, 6, 12, 5, 9, 0, 7, 0, 15, 7, 4, 14, 2, 13, 1, 10, 6, 12, 11, 9, 5, 3, 8, 4, 1, 14, 8, 13, 6, 2, 11, 15, 12, 9, 7, 3, 10, 5, 0, 15, 12, 8, 2, 4, 9, 1, 7, 5, 11, 3, 14, 10, 0, 6, 13, /* S2 */ 15, 1, 8, 14, 6, 11, 3, 4, 9, 7, 2, 13, 12, 0, 5, 10, 3, 13, 4, 7, 15, 2, 8, 14, 12, 0, 1, 10, 6, 9, 11, 5, 0, 14, 7, 11, 10, 4, 13, 1, 5, 8, 12, 6, 9, 3, 2, 15, 13, 8, 10, 1, 3, 15, 4, 2, 11, 6, 7, 12, 0, 5, 14, 9, /* S3 */ 10, 0, 9, 14, 6, 3, 15, 5, 1, 13, 12, 7, 11, 4, 2, 8, 13, 7, 0, 9, 3, 4, 6, 10, 2, 8, 5, 14, 12, 11, 15, 1, 13, 6, 4, 9, 8, 15, 3, 0, 11, 1, 2, 12, 5, 10, 14, 7, 1, 10, 13, 0, 6, 9, 8, 7, 4, 15, 14, 3, 11, 5, 2, 12, /* S4 */ 7, 13, 14, 3, 0, 6, 9, 10, 1, 2, 8, 5, 11, 12, 4, 15, 13, 8, 11, 5, 6, 15, 0, 3, 4, 7, 2, 12, 1, 10, 14, 9, 10, 6, 9, 0, 12, 11, 7, 13, 15, 1, 3, 14, 5, 2, 8, 4, 3, 15, 0, 6, 10, 1, 13, 8, 9, 4, 5, 11, 12, 7, 2, 14,

DES算法代码及实验报告

实验名称DES算法实验报告实验(实习)日期________得分 ______ 指导教师沈剑 计算机系专业软件工程年级 11 班次3 __________姓名张渊学号 931 1、实验目的 理解对称加解密算法的原理和特点 理解DES算法的加解密原理 2、D ES算法详述 DES算法把64位的明文输入块变为64位的密文输出块,它所使用的密钥也是64位,其功能是把输入的64位数据块按位重新组合,并把输出分为L0、R0两部分,每部分各长32 位,其置换规则见下表: 58,50,12,34,26,18,10,2,60,52,44,36,28,20,12,4, 62,54,46,38,30,22,14,6,64,56,48,40,32,24,16,8, 57,49,41,33,25,17, 9,1,59,51,43,35,27,19,11,3, 61,53,45,37,29,21,13,5,63,55,47,39,31,23,15,7, 即将输入的第58位换到第一位,第50位换到第2位,……,依此类推,最后一位是原来的第7位。L0、R0则是换位输出后的两部分,L0是输出的左32位,R0是右32位, 例:设置换前的输入值为D1D2D3? D64,则经过初始置换后的结果为:L0=D550 (8) R0=D57D49 (7) 经过26次迭代运算后,得到L16、R16,将此作为输入,进行逆置换,即得到密文输出。逆置换正好是初始置的逆运算,例如,第1位经过初始置换后,处于第40位,而通过逆置 换,又将第40位换回到第1位,其逆置换规则如下表所示: 40,8,48,16,56,24,64,32,39,7,47,15,55,23,63,31, 38,6,46,14,54,22,62,30,37,5,45,13,53,21,61,29, 36,4,44,12,52,20,60,28,35,3,43,11,51,19,59,27, 34,2,42,10,50,18,58 26,33,1,41, 9,49,17,57,25, 放大换位表 32,1,2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 8, 9, 10,11, 12,13,12,13,14,15,16,17,16,17,18,19,20,21,20,21, 22,23,24,25,24,25,26,27,28,29,28,29,30,31,32, 1, 单纯换位表 16,7,20,21,29,12,28,17, 1,15,23,26, 5,18,31,10,

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58, 50, 42, 34, 26, 18, 10, 2, 60, 52, 44, 36, 28, 20, 12, 4, 62, 54, 46, 38, 30, 22, 14, 6, 64, 56, 48, 40, 32, 24, 16, 8, 57, 49, 41, 33, 25, 17, 9, 1, 59, 51, 43, 35, 27, 19, 11, 3, 61, 53, 45, 37, 29, 21, 13, 5, 63, 55, 47, 39, 31, 23, 15, 7 }; const static char fp[] = { //最终置换 40, 8, 48, 16, 56, 24, 64, 32, 39, 7, 47, 15, 55, 23, 63, 31, 38, 6, 46, 14, 54, 22, 62, 30, 37, 5, 45, 13, 53, 21, 61, 29, 36, 4, 44, 12, 52, 20, 60, 28, 35, 3, 43, 11, 51, 19, 59, 27, 34, 2, 42, 10, 50, 18, 58, 26, 33, 1, 41, 9, 49, 17, 57, 25 }; const static char sbox[8][64] = { //s_box /* S1 */ 14, 4, 13, 1, 2, 15, 11, 8, 3, 10, 6, 12, 5, 9, 0, 7, 0, 15, 7, 4, 14, 2, 13, 1, 10, 6, 12, 11, 9, 5, 3, 8, 4, 1, 14, 8, 13, 6, 2, 11, 15, 12, 9, 7, 3, 10, 5, 0, 15, 12, 8, 2, 4, 9, 1, 7, 5, 11, 3, 14, 10, 0, 6, 13, /* S2 */ 15, 1, 8, 14, 6, 11, 3, 4, 9, 7, 2, 13, 12, 0, 5, 10, 3, 13, 4, 7, 15, 2, 8, 14, 12, 0, 1, 10, 6, 9, 11, 5, 0, 14, 7, 11, 10, 4, 13, 1, 5, 8, 12, 6, 9, 3, 2, 15, 13, 8, 10, 1, 3, 15, 4, 2, 11, 6, 7, 12, 0, 5, 14, 9, /* S3 */ 10, 0, 9, 14, 6, 3, 15, 5, 1, 13, 12, 7, 11, 4, 2, 8, 13, 7, 0, 9, 3, 4, 6, 10, 2, 8, 5, 14, 12, 11, 15, 1, 13, 6, 4, 9, 8, 15, 3, 0, 11, 1, 2, 12, 5, 10, 14, 7, 1, 10, 13, 0, 6, 9, 8, 7, 4, 15, 14, 3, 11, 5, 2, 12, /* S4 */ 7, 13, 14, 3, 0, 6, 9, 10, 1, 2, 8, 5, 11, 12, 4, 15, 13, 8, 11, 5, 6, 15, 0, 3, 4, 7, 2, 12, 1, 10, 14, 9, 10, 6, 9, 0, 12, 11, 7, 13, 15, 1, 3, 14, 5, 2, 8, 4, 3, 15, 0, 6, 10, 1, 13, 8, 9, 4, 5, 11, 12, 7, 2, 14,

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