摘要:

J . Chem. SOC., Faradaj’ Trans. 1, 1989, 85(9), 3019-3032 Preferential Solvation of Ions in Mixed Solvents Part 4.-Comparison of the Kirkwood-Buff and Quasi-lattice Quasi-chemical Approaches Yizhak Marcus Department of Inorganic and Analytical Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel and Institute of Radiochemistry, Technical University of Munich, 8046 Garching, Federal Republic of Germany The relation of the Kirkwood-Buff integrals G.. = 4nr2[gij(r) - 11 dr J: where i is an ion solute and j one of two solvents in their mixture, to measurable quantities is examined in the light of recent work of Ben-Naim and Newman. The derived local excess of one of the solvents Bxij is compared with the same quantity calculated for the author’s quasi-lattice quasi-chemical model.The results for three aqueous solvent mixtures, involving a protic solvent (methanol), a strong donor aprotic solvent (dimethyl sulphoxide) and a weak donor aprotic solvent (acetonitrile) and several ions are compared and discussed. It is concluded that the need for the derivative of the standard Gibbs free energy of transfer of the ion with respect to the solvent composition limits the reliability of the Kirkwood-Buff approach. Two recent applications by Ben-Naiml and Newman2 of the Kirkwood-Buff theory3 permit the evaluation of the Kirkwood-Buff integral Gi, = loz 4nr2[gi,(r)- 13 dr and similarly for G, for the distribution of the solvents a and p in a mixture of a and /? around a solute particle i. In expression (l), r is the distance from the centre of i and g,(r) is the pair correlation function of a around i.This quantity measures the conditional probability of finding a particle of a in a volume element, given the presence of a particle of i at the origin, a distance r away. It has the value zero at r values below the contact distance of i and a, a maximum (> 1) at the most probable distance of approach of the two, then a minimum and series of decreasing maxima and minima at larger values of r. It approaches unity asymptotically, and does so practically beyond four or five dimeters of a. Beyond this distance, therefore, its contribution to Gi, is ordinarily negligible. The Kirkwood-Buff integral G, is a measure of the ‘affinity’ of a to i. Its product with the number density of a is the overall excess or deficiency of particles of a in the volume around i.’ Whereas Ben-Naim confined his treatment to non-electrolyte solutes i,’ Newman considered individual ionic solutes,2 without dealing with the complications entailed thereby. The complications that arise in the case of ionic solutes are due to the requirement of electroneutrality of the solution as a whole.As Hall4 has pointed out (and using the present notation), G,, = G-, if + and - denote the cation and anion of an electrolyte (having the same but opposite charges). This is due to the fact that each 30193020 Preferential Solvation of Ions in Mixed Solvents ion has its ‘ionic atmosphere’, and even at infinite dilution there exists somewhere in the solution the ion of opposite charge.Since Gi, given in expression (1) has infinity as its upper limit of r, the distance from the ion i, the counter-ion and its effect on the solvent distribution is necessarily also included. Thus g+z, although practically equal to unity at most of the space beyond the few diameters of a away from the cation, becomes significantly different from unity in the vicinity of the anion, with an appreciable contribution to the integral G,,, and vice versa for G-,. Therefore G, does not describe the distribution of the solvent a near i alone, as it would for an infinitely dilute non- electrolyte i. Since, furthermore, the same arguments apply also to the solvent p, the unexpected result is that G,, - G,, = G-, - G+, i.e. that the preferential solvation of the cation equals that of the anion, which is contrary to experience.The way Hall4 circumvented this difficulty is by employing a distance R instead of infinity as the upper limit of the integral (l), which is sufficiently large to encompass the entire region of the solvent affected by the ion i, but at the same time providing a negligible probability of there being in it another ion (the counter-ion). Thus = 1; 4zr2[g,,(r) - 13 dr. As the concentration of ions tends to zero this condition can be fulfilled, and the quantity G;, becomes effectively independent of R [since g J r > R)- 1 M 01, provided R is large enough but finite. The Gi, depends now only on the properties of the ion i (and of a ) and does not depend on those of the other ionic species present. In general, therefore, GLz # G’, in a very dilute solution of an electrolyte in the solvent mixture of sc and a.Newman2 disregarded this problem altogether [he did not give the limits of the integral corresponding to eqn (l)]. However, in the following the prime on Gila is omitted in order to simplify the notation and make it more similar to Newman’s. Ben-Naiml employed substantially the same device as Hall,* setting R = rcor, where COr = (4n/3) r:or is the correlation volume. Ben-Naim’s approach’ yields additionally the local excess or deficit of each solvent near the solute relative to the bulk composition in a very dilute solution of the solute i : (2) Here x, is the bulk mole fraction of solvent a (thus x,+xp 2 l), xi”, is its local mole fraction near the solute particle i, and cor is the volume around i where a correlation exists between the presence of i and the composition of the solvent. The estimation of 6xi, from eqn (2) requires the knowledge of the Gii ( j = a and a) values and of the value of KO,.as a function of the composition for given a, and i. The difference Gi,- G, can be obtained according to Newman’s development2 of the ideas of Hall4 from three sets of data. One is the excess molar Gibbs free energy of mixing of the two solvents, Gf,(xp). Another is the molar volume of the mixed solvent, V(x,) = (x, M, + x, MB)/p, where Mi is the molar mass of solventj and p is the density of the mixture. The third is the standard molar Gibbs free energy of transfer of the solute i from the solvent a to the solvent mixture a +p, Atr G;(x,), all as functions of the composition. Thus at a given temperature T and pressure P where D = dA,,G;/dxp and SX~, = XL - X, = X, ~p(Gi,- G~)/[x, Gi, + x, Gip + <or].Gin - Gip = VD/X, xp Q Q = RT/x, x,+ d2 Gfp/dxi = (a2 G$/~x;)~, (3) (4) G$ being the molar Gibbs free energy of mixing of a and p. The evaluation of the individual G, values needed for the denominator of eqn (2) requires2 additional sets of data. These are the isothermal compressibility of the solventY . Marcus 302 1 mixture, K ~ ( X ~ ) and the partial molar volume of the solute at infinite dilution in the mixture, vp(xp). Thus2 ( 5 ) (6) Gip = K T RT- Vp+#, VD/X,X~Q Gi, = K T RT- VP-Qp VD/X~X,Q Kor = (4mV/3) (ri + Ej Fj)3 where #, is the volume fraction of the solvent j in the mixture.The correlation volume KO,. may be expressed as (7) where ri is the radius of the solute particle, F, is a weighted mean of the radius of the solvent particles and ti, is a weighted mean of the extent of the correlation in terms of the mean solvent radii. It is the ignorance of the appropriate weighting, and in particular of the extent of the correlation, Ej, that precludes a straightforward application of eqn ( 2 ) for the estimation of the local composition of the solvent mixture near the solute, even if all the required input data were available. Calculations Various approximations are required for a comparison of the theoretical results from eqn (1)-(7) with other data derived from experiment. The least serious approximation is made by ignoring the finite excess volume of mixing and setting V = x, V: + xp V i , hence q5, V = xi Vy, where Vy is the molar volume of the pure solvent j .If the value of K , RT- VP is small relative to the other term in eqn ( 5 ) and (6), then G, and G, are seen to have opposite signs (see the case of NaCl in aqueous methanol, illustrated by Newman2). Their weighted sum, appearing in the denominator of the r.h.s. of eqn (2), is (8) In view of the small size of X, Gi,+xDGig relative to Kor, even for the smallest value of E j F j (one diameter of the smaller of the two solvents, see below), the approximation K , RT- Vy z (x, K , , + RT- [x, VP(a) + xp Vp(p)], employing the values applic- able to the individual solvents, is entirely adequate. X, Gi, + xp Gqj = K T R T - vp + ( v," - V i ) D / Q .Eqn ( 2 ) can therefore be rewritten as 6xia = (x, VE + xp V,")/[( V," - yB0) + ( K T RT- Vs + KO,.) Q/D]. GJ"B = x, x&a + b(x, - xp) + c(x, - x ~ ) ~ ] d2G$/d$ = (- 2a + 6b - 1 OC) + ( - 12b + 4 8 ~ ) xp- 4 8 ~ ~ ; . (9) The function Q can be readily evaluated for many solvent mixtures, for which the expression holds5 within ca. 20 J mol-'. Then (10) (1 1) The second derivative is, of course, quite sensitive to the accuracy of the fitting of G,E,(xD), and is a source for considerable uncertainty in the G,, values (as pointed out by Newman2) and of 6xt,. However, it is a linear function of the uncertainties in the fitting coefficients A(d2G,EB/dX2) = 21Aal+(6- 12xp) [A61 + (10-48~p+48~;) [ A c ~ (12) and is mainly sensitive to the uncertainty in c.For the evaluation of the Kirkwood-Buff function Gi, - GiB (and, approximately, the individual G,,) the remaining quantity required is D = dA,,G:/dx,. There are many standard molar Gibbs free energy data in the literature for the transfer of electrolytes from a reference solvent (e.g. water) to a solvent mixture (e.g. aqueous alcohols,6 aqueous dimethyl sulphoxide,' aqueous acetonitrile,' or some non-aqueous mixturesg).3022 Preferential Solvation of Ions in Mixed Solvents These can be divided into the individual ionic contributions by the use of the TATB assumption, i.e. that A\,,G"(Ph,As+)/A,,G"(BPh~) = k , where k is a constant very near unity (1.07 k 0.02 according to Kim', ' 7 lo). The approximation k z 1 will serve here for reasons stated elsewhere.'' However, the agreement between the values given by different authors for a given system, in the relatively few cases where several independent studies have been reported, is not very good.6 Even in the work of a given author, large limits of error are reported, e.g. from f0.6 to k 1.2 kJ mol-' in At, Go, ranging from zero to - 12.8 kJ mol-' for transfer of Cs' and from zero to + 16.0 for transfer of I- from water into aqueous dimethyl s~lphoxide.~ Therefore, the derivative of At, G: with respect to the solvent composition is beset by a large uncertainty. It is doubtful whether standard molar Gibbs free energies of transfer of ions into solvent mixtures can be determined with a higher accuracy than f 10 O/O (including the errors in A,, Go of the constituents of TATB), but the uncertainty in the slope is magnified manyfold, since often cubic or quartic dependencies of At, G: on xB are required for an adequate expression of the data.At xB values near zero or unity the slope dAtr G:/dxB may become very small or even change sign, and a small uncertainty in At, G: can cause a large uncertainty (even change of sign) in axia calculated according to eqn (9). The quantities V, G$, K , , vp and D = dA,, G:/dxB required for the evaluation of the Gij and of axia, though beset with considerable experimental uncertainties in some of the cases, are at least conceptually well defined. Not so KO,, the correlation volume, or the product i i j F j defined by eqn (7), required for the calculation of Sx,. The correlation in question may take place up to several diameters of the solvent molecules away from the solute particle.For the following, it is expedient to consider only the first solvation shell, i.e. the volume to which the solvent molecules nearest to the solute particle i are confined. That is, in all cases iij = 2 exactly defines Kor. This view permits a comparison of the hi,, values, now valid for the first solvation shell, with the values calculated according to the quasi-lattice quasi-chemical theory.12 The diameters of solvent molecules have been estimated by Kim13 from their molar volumes as 2(rj/nm) = 0.1363( Vj"/cm3 mol-')~- 0.085. (13) It remains to specify how the value of rj is to be weighted to obtain Fj for use in eqn (7). It appears appropriate to use the local mole fractions of the solvents as the weighting factors of their molar volumes, i.e.to use (xk V," + x$ V i ) in place of Vj" in eqn (13) to give Fj. This, then, requires an iterative computation. In view of the many other approximations and uncertainties, the simpler form using the bulk composition is employed here. This leads to K0,/cm3 mol-' = (4 x 10-2'~N/3) [(r,/nm) + 0.1363{x,( V,"/cm3 mol-') + xB( Vi/cm3 mol-l)>f - 0.08513. (14) The weighting could have been applied to the diameters rather than to the volumes, so that a somewhat different value of Kor would have resulted. There is no basis for the preference of one way or another. The uncertainties in the molar volumes of the solvents appearing in eqn (9) are negligible, hence A6xia/S~ia = A(KT RT- V: + f / c o r ) / ( ~ T RT- Vp + KO,) + AQ/Q + AD/D.(15) The first term on the r.h.s. can also be neglected, since with the definition of KO, according to eqn (14) and the fact that ( K ~ RT- Vg) < KO, (see below) its uncertainty is negligible. For the equimolar mixture ASx,, x O.O051A01+ 0.08)Acl (16)Y. Marcus 3023 where D and c [of eqn (lo)] are expressed in kJ mol-l, typical values being 1.5 and 0.5, respectively. The typical uncertainty of &xi, is therefore k0.012 at the equimolar mixture, and somewhat lower at compositions nearer the pure solvents. The quasi-lattice quasi-chemical theory12 specifies the following expression axi, = [ 1 + (NBB/NZ1)~ exp (A/2)]-' - x, where (N/?p/N,,)~ = [(xp- N,p12S)/(xz - N,p/2S)Ii (18) NZp/2S = [ 1 - { 1 - 4x, x8 P}i]/2P.and Here Nij is the number of i and j nearest neighbours, S is the total number of nearest- neighbour pairs, (19) A = -Atr GY/ZRT (20) and P = 1 -{2exp[-2Gfp(x, = 0.5)/ZRT]- If-' (21) where 2 is the lattice parameter, for which values between 4 and 12 may be taken as reasonable. Note that eqn (18) and (19) depend only on the two solvents a and p [through P which depends on GZ(x, = 0.5) = 0 . 2 5 ~ of eqn (lo)] but not on the ion i. The dependence on the solute is introduced only in eqn (17) through the quantity A, defined in eqn (20). A composition-dependent lattice parameter Z could have been em- ployed,14- l5 but this complicates the calculations and introduces further arbitrariness to that inherent in the quasi-lattice quasi-chemical approach. Ignorance of the true value of 2 (the value 2 = 6 was previously suggested12) leads t? the major uncertainty in this approach.In fact, the quantities P, NZp/2S and (NPp/N,,)". and eqn (21), (19) and (18) hardly depend on 2, whereas, through the inverse proportionality of A on 2 [eqn (20)] 6xi, also becomes approximately inversely proportional to 2. A typical uncertainty at the equimolar mixture (for rf: Atr GP x 10 kJ mol-l) and for A Z = & 1 at 2 = 6 is Adxi, = k0.014, but this decreases for higher values It is now contended that the values of 6xi, calculated from eqn (9) and (14) on the one 617 and at compositions nearer the pure solvents. hand and from eqn (17) on the other should be directly comparable. Applications Aqueous Methanol Solutions at 25 "C The input data required for calculations are taken from the author's compilations5* where appropriate.With the identifications a = H,O and /3 = CH,OH(MeOH), the molar volumes of the solvents are Y," = 18.07 and V" - 40.7 cm3 mol-' and their Gibbs free energy of mixing obeys eqn (1 1) with a = 1.200, b = - 0.087 and c = 0.330 kJ mol-' [ref. (9, p. 1901. The necessary data for the ionic constituents of sodium chloride and caesium iodide are shown in table 1. The values of Atr Go of the salts and their ions into aqueous methanol were given by Feakins and Voice," Cox1' and Popovych,18 among others, and are shown in the authors' compilations6 at even values of the mass fraction of methanol, w. ' Selected ' values are given there, on the basis of the TATB assumption (with k = 1). They are expressed as power series in w up to terms with w4.The derivatives with respect to xB could thus be readily calculated, with the conversion formula xB = wp/[wp+ (Mp/M,) w,], and are cubic expressions in xB, shown in table 2. The Kirkwood-Buff functions Gij pertain to individual solute particles and their surroundings, and ought, therefore, to be evaluated for the individual ions. For the sake of comparison with Newman's results,* given for the salt s = NaCl, the sum of the values for Na+ and Cl- calculated with the input data mentioned above is taken to represent compressibilities are K , , = 0.452 and K~~ = 1.195 GPa- 8 - [ref. (9, p. 1331. the excess3024 Preferential Solvation of Ions in Mixed Solvents Table 1. Data for the ions required for the calculations Atr V0/cm3 mol-' Atr G"/kJ mol-le VP/cm3 mol-' r,/nma in H,O CH,OH (CH,),SO CH,CN CH,OH (CH,),SO CH,CN Na- 0.095 - 7.6 - 10 -3 - 13 8.2 -13.4 - CS' 0.169 14.9 -11 -6 - 16 8.9 - 13.0 - Ag' 0.126 -7.1 - lod - 3d - 13d I- 0.2 16 42.6 - 14 + 3 - 17 7.3 10.4 - -34.8 -23.2 - c1- 0.181 24.2 - 10 +2 - 18 13.2 40.3 42.1 a Ref.( 5 ) , pp. 46,47. Ref. (9, p. 100. ' Ref, (9, p. 174. d Taken as the same as for Na' (or K+). Ref. (9, pp. 167-169. Table 2. Expressions for D = dA,,GP/dx, For H,O(a) + CH,OH(P) [according to ref. (6)] : Na' CS' C1- I- For H,O(a) + (CH,),SO(P) (data from Kim and Gomaa' and Coxs) : Na' D = (0.1935-0.6112~ 10-2wp+1.2510x 10-4w;-0.8844x 10-6w$)xdwp/dxp D = (0.1932-0.7968 x 10-2~p+ 1.8837 x 1 0 - 4 ~ 2 - 1.3348 x 10%;) x dwp/dxp D = (0.0019+0.4262 x 10-2wp-0.6024 x 10-4wg+0.4748 x 10-6w$) x dwp/dxp D = (0.0467+0.3470 x 10-2wp-0.4737 x 10-4wj+0.4196 x lo%$) x dwp/dx, du'D/dxp = ( ~ ~ z O / ~ ~ ~ O H ) [ ( ~ ~ e ~ ~ / ~ H ~ o ) + (l - M,eo"/M"zO) wp], = 1 *7779[i -O-4375wpl2 Ag' D = -52.8+41.2~, CS' C1- I- D = 10.25 -287.9xp+ 595.0~;-249.2~; (up to xp = 0.6) D = 5.175 - 216.2xp+ 445.2~; - 224.7~; D = 29.75 + 2 6 8 .4 ~ ~ - 544.7~; + 16.72~; D = 0.041 + 7 2 . 4 6 ~ ~ - 105.8~; + 55.48~; (UP to xp = 0.6) For H,O(a) + CH,CN(P) (data of Kim et l9): Ag' D = -33.60- 156.6~,+530.1~j-359.2~~ C1- D = -24.50+446.0~,-743.1~j+384.4~; GSj. Eqn (3)-(6) and the linear approximations of Vand K,RT- %p with respect to the composition are employed for the calculation. The comparison is shown in fig. 1. The discrepancies are due to the use of different input data [Newman2 employed A,,G" (NaCl) data of Feakins and VoicelS), and illustrate the uncertainties inherent in these calculations, due mainly to those in D = dA,,GP/dx,, as pointed out above.The excess of water molecules in the vicinity of the ions, &cia, was calculated from both eqn (9) and (17), and in the latter case with three values of Z , for both NaCl and CsI, again as the sums of the values for the individual ions. The results, Sx,, = d~+,+Sx-~, where the subscripts s, + and - denote the salt, cation and anion, are shown in fig. 2. The signs of Sx,, and Sx-, are the same (positive), so that their summation to yield SX,, values does not obscure essential information. Water is preferred over methanol for all the curves.Agreement of the results from the two expressions within the, admittedly wide, margins of uncertainty is noted. That the Z relevant to the quasi-lattice quasi- chemical (QLQC) calculations of axi, seems to vary with the methanol content, in order for agreement with the values of dx, qbtained from the Kirkwood-Buff (KB) approach to be achieved, is probably an artifgct. Note that both approaches lead to somewhat asymmetrical curves with respect to the composition, with maxima in axi, near xp 0.40.3025 300 2 00 100 - I d -5 \ 0 -, u" -1 00 -2 00 -3 00 Y. Marcus 1 I I 1 Gsa -Gsp 1 0.0 0.2 0.4 0.6 0.8 1.0 XM~OH Fig. 1. The Kirkwood-Buff functions GSi for s = NaCl (the sum of the values for Na' and Cl-), a = H,O and = CH,OH(MeOH). Continuous lines from ref. (2), dashed lines from this work.Note the opposite designation of a and p from the usage in ref. (2), in order to conform with that of the rest of this work. Aqueous Dimethyl Sulphoxide at 25 "C In this case the identifications 01 = H,O and = (CH,),SO(Me,SO) are used, the molar volume of the latter being V i = 71.3 cm3 mol-' and its isothermal compressibility K , = 0.52 GPa-' [ref. ( 5 ) , p. 1341. The parameters for G$ are a = -4.909, b = 2.168 and c = -0.005 kJ mol-' [ref. ( 9 , p. 1911. The relevant data for the ions Na+, Cs+, Ag+, C1- and I- are shown in table 1 . Values of Atr GP for these ions (except Ag+, see below) were given by Kim and Gomaa7 on the molal scale, using k = 1.08+0.02 for the TATB assumption. These were converted to the molar scale by addition of -RT{ln [ 1 - x,( 1 - MB/M,)] - In [ 1 - x,( 1 - V i / V,")]) to correct for the ratio of the density of the solvent mixture relative to that of water, and recalculated with k = 1.They were then fitted to power series in x, and the expressions for the derivatives D are shown in table 2. Values of AtrG: for Ag' are from Cox et aZ.,' on the molar scale, and the TATB assumption with k = 1 is used, but they are given at specified volume fractions of Me,SO, $,. These were converted to mole fractions by the formula (22) where R = V i / V z . The Kirkwood-Buff integrals Gp G, and G,-G,, and the dx, values for the preference of water around the Ag+ ions in aqueous Me,SO are shown in fig. 3(a) and 3 (b), respectively. Reasonable agreement between the dxi, results of the Kirkwood-Buff approach (KB) and the quasi-lattice quasi-chemical approach (QLQC) for 2 = 10 is x, = $,/[$/I+ w- $,)I3026 Preferential Solvation of Ions in Mixed Solvents 0.1 0.0 2 W 0,2 0.1 0.0 ( b ) 0.1 0.3 0.5 0.7 0.9 XMeOH Fig.2. The sums of the local excess mole fraction of water ( a ) near the ions of (a) CsI and (b) NaCl in aqueous methanol 0. Vertical lines : KB approach with probable uncertainty limits; curves: QLQC approach with the indicated values of Z . noted. It appears that better agreement might be achieved at the lower xs for 2 values lower than 10 and at the higher xs for 2 values higher than 10, but this may, again, be an artifact, given the large uncertainties in D. [The values of Atr GP are presentedg in kcal mol-' (1 kcal = 4.184 kJ) to one decimal place only !] The calculated ax, values for the preference of water in the vicinity of CS' and I- ions in aqueous Me,SO according to the KB and QLQC approaches are compared in fig.4. The quantitative agreement is seen to be poor, even if the wide limits of uncertainty are taken into account. The KB-curves are seen to peak quite markedly compared with the QLQC-curves, although for both approaches the extremum for CS' comes at a larger xs value than for I-. The KB-curve for Na+ ions is also shown in fig. 4, and is seen to be similar to that for Cs+. However, no curve for C1- ions is shown, since the ax,, values calculated for it by eqn (9) are larger than xs, which is physically impossible. Either some of the data used for the calculation (e.g.D = dAtr GP/dx,) are wrong, or some of the premises on which the KB calculations are based are not valid. A clearer picture of this problem is had when the approximation axiu VD/ K o r Q is considered. It is valid when Cor + (VE- V,") D / Q + Vy-rcrc,RT, this being the case for the relative bulky Me,SO for any ion. The large positive values of D are responsible for these physically impossible ax, values at xB < 0.4, since V / Kor Q is not sufficiently smallY. Marcus 3027 I I I I I I I I I I 0.1 0.3 0.5 0.7 0.9 '-hld)t1 Fig. 3. (a) The KB functions Gij for i = Ag' in mixtures of water (a) and Me,SO Cp). (6) The local deficiency of water (a) near the Ag' ions in aqueous Me,SO. Vertical lines: KB approach with probable uncertainty limits; curves: QLQC approach with indicated Z values.in this range. The data' for C1- and Na' are incomplete at 0.55 < xB < 1, so that nothing can be said about this part of the composition range. The KB calculations were repeated with the volume fractions Q replacing mole fractions x. Values of d2G,E,/dQi were calculated from appropriate expressions, involving a, h, c and R and eqn (22), to give Q,,(Q,). Also, dA,,GP/dQp was calculated by means of eqn (22) and the data in table 2. Thus, the expression analogous to eqn (9) but in terms of QB rather than xB could be evaluated for the four ions Na+, Cs', CI- and I-. The results are shown in fig. 5. In this case somewhat better agreement between the results of the KB and QLQC approaches (with 2 zz 10 for Cs' and 2 z 6 for Na') is observed, although the extrema for the latter appear at considerably higher values of $B than those of the former.The disagreement remains very bad for I-, and for C1- the calculated values of dxi3 are still larger than xB (note that 6x,,,/2 is plotted in fig. 5), which is physically impossible. Aqueous Acetonitrile Solutions at 25 "C The identifications cc = H,O and p = CH,CN (MeCN) apply in this case, with the molar volume Vp" = 52.9 cm3 mol-1 and the compressibility K , = 1.07 GPa-' [ref. (5), p. 1351. The parameters for G$ are a = 5.335, b = -0.446 and c = 0.654 kJ mol-1 [calculated from the data in ref. (20)], and it should be noted that GfB is large and positive over the entire composition (contrary to the case of Me2SO). As a consequence, Q is small for 100 F A R I3028 Preferential Solvation of Ions in Mixed Solvents I I I I 1 I 1 I 1 - \ \ \ \ / / / I % - __ - - /' Na' \\, I I I I 0.1 0.3 0.5 0.7 0.9 Fig.4. The local excess or deficiency of water (a) near the ions in aqueous Me,SO, plotted against the mole fraction of the latter. Continuous lines, KB approach; long-dashed lines, QLQC approach with indicated Z values; short-dashed line, KB approach for Na'. XMezSO some of the composition range (i.e. Q < 0.6 kJ mol-1 for 0.25 < xg < 0.50). Very similar results are obtained from the data of Villamaiian and Van Ness.21 The earlier data of Treiner et a1.,22 though generally quite similar, yield Q < 0 for 0.17 < xs < 0.31, denoting phase separation over this composition range. Since this is not observed, this set of data [used in ref.(9, p. 1911 is now superceded by the more recent work. Standard molar Gibbs free energies of transfer of ions from water into aqueous acetonitrile were published by Cox et al.9323 and by Kim and Du~chner.'~ The data of Cox et ~ 1 . ~ were given for Ag+ and Cl- separately as a function of $B, and they were converted to depend on xs by means of eqn (22). The TATB assumption with k = 1 applied in this case. The latter set of Cox et al.23 was given for AgI, KI, Ph,AsI, KCl and KBPh,, also as a function of q5b, and was converted as above, using the additivity rule, to yield values for Ag+ and C1-. Kim and Du~chner's'~ set of data pertained to AgCl and AgBPh,, and they were converted to the individual ionic values by means of the data* for Ph,AsBPh,, again applying the TATB assumption with k = 1.A further conversion was necessary from the molal scale used by Kim et aL8, l9 to the mol dm-3 scale used for the rest of the data (see above). It was noted that the three sets of data were not in good agreement, either for AgCl (i.e. the sum of the datag for Ag+ and C1- and the data19.23 for AgCl) or for the individual ions, although the general trends did agree. Silver ions have negative values of dAtr Gp/dxs up to xs = 0.6 for all sets of data, and small negative, near zero or small positive values for this derivative at xs > 0.6 (see table 2). Due to the small values of Q (< 3 kJ mol-' for 0.15 < xs < 0.70), however, physically impossible much too large negative values of dx, < - 2 + xB result over this wide range of compositions.On the other hand, the derivative dAtr Go/dxp is near zero at 0.7 < xB < 0.9 for the data of Kim et a1.8.19 and at 0.5 6 ~ ~ 0 . 7 for those of Cox et al.,9*23 so thatY . Marcus 3029 0.3 0.2 0.1 e 4 0.0 -0.1 1 I I I I I I I 1 I I I I I I 0.1 0.3 0.5 0.7 0.9 h e 2 S O Fig. 5. Same as fig. 4, but plotted against the volume fraction $ of Me,SO 0, usilizing Q instead of x in the KB calculations. Short-dashed curve shows how xb lags behind QP, and that although 6xi, for I- is < xb, as it should, dx, for C1- is > xB, as it couldn’t be. Continuous lines, KB approach ; long-dashed lines, QLQC approach. dx,, values near zero result for these composition ranges, contrary to the expected behaviour that acetonitrile is preferred to water in the vicinity of the silver ions, The QLQC approach conforms to this expectation [see curve 5 in fig.3 of ref. (12)]. Chloride ions have large positive values of dAtr G:/dx, over the entire composition range for both sets of data (see table 2). Again, due to the low values of Q, much too large values of ax,, result for 0.15 < xp < 0.70. The results from the QLQC approach, are consistent with the expectation [see curve 1, fig. 3, in ref. (1 2)], that water is preferred in the vicinity of the chloride ions over the aprotic acetonitrile. Discussion The Kirkwood-Buff theory provides, according to Ben-Naiml and Newman,2 the criterion Gia-Gig > 0 for the decision that solvent a is preferred over solvent /3 in the vicinity of the solute i. The alternative criterion dx,, > 0, according to Ben-Naim,3 can also be used. Since V / x Z xp Q in a homogeneous solution is always positive, eqn (3) shows that solvent a is preferred whenever dAtr GP/dxa is positive and that otherwise solvent p is preferred.The same conclusion is obtained from eqn (23) [or the more exact eqn (9)], since V/V,,, is always a positive quantity. In the cases of infinitely dilute solutions of ions (or salts) in aqueous methanol and dimethyl sulphoxide, the quantity Q is > 7 kJ mol-1 over the entire composition range. For aqueous Me,SO this arises from the negative excess Gibbs free energy of mixing over the entire composition so that d2GFb/dxi is necessarily positive, and therefore also 100-23030 Preferential Solvation of Ions in Mixed Solvents 0.3 0.2 0.1 0.0 I I I I I I I I 1 I I I I I 1 I I I 1.2 1.1 1.0 0.1 0.3 0.5 0.7 0.9 X P Fig.6. The local excess of water (a) near (a) Cl- and (b) K' ions in aqueous ethanol, plotted against the mole fraction of the former. Continuous lines, QLQC approach with Z = 8; vertical lines, KB approach (with uncertainties), calculated for close-packed two layers of solvent with fij = 3.4. Calculation with fii = 2 produces values of ax,, > xp, that are physically impossible. is Q [eqn (4)) For aqueous MeOH, GfD is positive but small, and its curvature is such that the negative value of c together with the term RT/x,xD produce Q values > 7 kJ mol-l in spite of the positive value of a. For these two aqueous mixtures, therefore, both Gi, - G, and &via, having the same sign as dAtr GP/dx,, mean that solvent a (i.e.water) is preferred for those cases where Atr GP is positive and has a positive derivative as xD (i.e. the fraction of the co-solvent) increases. This happens with both cations and anions in aqueous methanol and with anions in aqueous dimethyl sulphoxide. On the other hand, the cations examined in aqueous Me,SO have negative AtrG: values and negative derivatives thereof with respect to xs, so that Gi, - G, and 6xin are both negative, and the co-solvent is preferred over water. The problem arises with aqueous acetonitrile and similar homogeneous solvent mixtures, which have large positive excess Gibbs free energies of mixing, giving rise to small Q values, where the negative d2G$/dx; nearly outweighs RT/x,xD. Thus Q being in the denominator [eqn (23)], any case of Q < 3 kJ mol-' over a wide range of compositions precludes the calculation of reliable G,, - G,, and Sxia values.Apart from this difficulty, which is not specific for acetonitrile (aqueous ethanol behaves similarly, with 4 6 Q/kJ mol-' 6 7), a further possible reason for failure of the KB approach as delineated here is its apparent consideration of the bulk of the solvent mixture, i.e. far away from the solute ion, as having the constant composition at the molecular level given by x, throughout. This ignores the fact that the two components in the mixture show their own preference for the nearest neighbours of their molecule^.'^ Thus, the assumption that gij of eqn (1) approaches unity at large r needs reconsideration. More work has to be done on this aspect of the problem, and will be the subject of a future report.Y.Marcus 303 1 This difficulty is not the result of the arbitrary choice of iij = 2 for eqn (7). The Gij function may be split as follows [cf. eqn ( 1 ') for the meaning of R, Gij here replacing Gi,] : The specification iij = 2 for eqn (7) in effect means that GY,-GYp is neglected beside GI, - Gib and that x, Gi, + xb G& is neglected beside x, Gl, + xp Gip which, in turn, is small compared with KO,.. The difference in G i cannot be more than a small fraction of the difference in GI, since the discrimination of the solvents near the solute ion must necessarily be strongest in the close vicinity of the ion.Neglect of the terms in GG. can therefore explain the quantitative discrepancies in &xi, noted, e.g. in fig. 2, 3 (6) or 5 (for the cations). It can explain values of dxin'> x8, indicating that values of iij > 2 are required for such cases, i.e. that substantial correlation [gij(r) > 11 occurs beyond the first solvation shell. A value of iij = 4 (two solvation shells) would increase c,or by a factor of nearly 8 and decrease dx, by nearly the same factor [of eqn (23)], see fig. 6. The QLQC approach also lets the mutual interaction of the two solvents play a role, through the specification of the parameter P in eqn (19) and (21), but it is not as decisive as in the KB approach. The sign of P is the opposilte of that of G$ (x, = 0.5) or of a of eqn (10).Whatever its sign, the effect on (Npb/NJ is no more than ca. f 10 YO when a changes from + 5 to - 5 kJ mol-', which represents its range for most aqueous solvent mixtures [ref. (9, pp. 190, 1911. This effect on (NDp/N,,)i is equivalent to an effect < f 0 . 0 2 in dxia, and will not result in the nomination of the wrong solvent as the one preferred near the solute ion. Therefore, whatever its quantitative inadequacies may be, the QLQC approach truly represents the preference for the right solvent near the ion. The Alexander von Humboldt Stiftung is thanked for partial support of the author while at the Institute of Radiochemistry in Munich and Profs F. Baumgartner and J. I. Kim are thanked for their hospitality there. Discussions with A. Ben-Naim are also acknowledged. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 A. Ben-Naim, Cell Biophys., 1988, 12, 255. K. E. Newman, J . Chem. Soc., Faraday Trans. I , 1988, 84, 1387. J. G. Kirkwood and F. P. Buff, J . Chem. Phys., 1951, 19, 774. D. G. Hall, J . Chem. Soc., Faraday Trans. I , 1972, 68, 25. Y. Marcus, Ion Solvation (Wiley, Chichester, 1985), pp. 188-191. Y. Marcus, Thermodynamics of Transfer of Single Ions from Water to Nonaqueous and Mixed Solvents, Part 5, Standard Molar Gibbs Energies of Transfer into Aqueous Alcohols, Report to IUPAC Commission V. 5, Electroanalytical Chemistry, 1987, to be published in Pure and Applied Chemistry. J. I. Kim and E. A. Gomaa, Bull. SOC. Chim. Belg., 1981, 90, 391. J. I. Kim, A. Cecal, H. J. Born and E. A. Gomaa, 2. Phys. Chern. N.F., 1978, 110, 209. B. G. Cox, A. J. Parker and W. E. Waghorne, J . Phys. Chem., 1974, 78, 1731. J. I. Kim, J . Phys. Chem., 1978, 82, 191. Y. Marcus, Pure Appl. Chem., 1986, 58, 1721. Y. Marcus, J . Chem. SOC., Faraday Trans. I , 1988, 84, 1465 (Part 2). J. I. Kim, Z . Phys. Chem. N.F., 1978, 113, 129. Y. Marcus, Aust. J. Chem., 1983, 36, 1719 (Part 1). Y. Marcus, J. Chem. SOC., Furuday Trans. I , 1989, 85, 381. D. Feakins and P. J. Voice, J . Chem. Soc., Faraday Trans. I , 1972, 68, 1390. B. G. Cox and W. E, Waghorne, Chem. SOC. Rev., 1980, 9, 381. 0. Popovych, J . Phys. Chem., 1984, 88, 4167. J. I. Kim and H. Duschner, Z . Phys. Chem. N.F., 1977, 106, 1.3032 20 H. T. French, J . Chem. Thermodyn., 1987, 19, 1155. 21 M. A. Villamaiian and H. C. Van Ness, J . Chem. Eng. Data, 1985, 30,445. 22 C. Treiner, P. Tzias, M. Chemla and G. M. Poltoratskii, J . Chem. Soc., Faraday Trans. I , 1976, 72, 2007. 23 B. G. Cox, R. Natarajan and W. E. Waghorne, J . Chem. Soc., Faraday Trans. 1, 1979, 75, 86. Preferential Solvation of Ions in Mixed Solvents Paper 8/05060K; Received 29th December, 1988

ISSN:0300-9599    

DOI:10.1039/F19898503019

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J . Chem. SOC., Furuduy Trans. I , 1989, 85(9), 3033-3044 Crystallochemical Characterization of Magnetic Spinels prepared from Aqueous Solution Stephen Mann," Nicholas H. C. Sparks, Suzanne B. Couling and Miranda C. Larcombe School of Chemistry, University of Bath, Bath BA2 7AY Richard B. Frankel Physics Department, California Polytechnic State University, Sun Luis Obispo, CA 93407. USA The crystallochemical characterization of magnetic spinels prepared from aqueous solution has been studied primarily by electron microscopy and 57Fe Mossbauer spectroscopy. Two synthetic routes have been investigated : method 1 ; partial oxidation of Fe" solutions in the presence of NO; at 100 O C , and method 2; reaction of hydrated Ferrr oxide (ferrihydrite) with Fe" ions at room temperature, pH = 7, 8 and 9.Both routes gave small (10-60 nm) irregular magnetite (Fe,O,) particles that were readily oxidised to maghemite (y-Fe,O,). The reaction proceeded via a green-rust intermediate and anions such as inorganic phosphate (Pi) and SO,,- reduced the rate of transformation. Spinel formation at room temperature was severely inhibited by Pi levels of 1 mol%, whereas 20-30 mol % Pi was required for retardation of crystallization at 100 "C. Intermediate levels (5-10 mol YO) resulted in morphological enhancement of the octahedral crystal habit. A similar effect was observed in the presence of SO:- and at neutral pH in method 2. The current interest in advanced materials is primarily directed towards the synthesis of novel solids. However, a further important aspect of this initiative is the crys- tallochemical tailoring of known substances with the aim of achieving functional specificity in solid-state applications. In this respect, we are involved in the elucidation of processes which modulate the crystallochemical properties of known magnetic materials.Ultimately, our objective is to synthesise structurally well defined magnetic spinels with homogeneous particle sizes and unique crystal morphologies as these properties are important in determining the catalytic and magnetic use of these materials. Magnetite (Fe,O,) has a cubic inverse spinel structure (space group, Fd3m, a = 8.396 A) with half of the FeIII ions in tetrahedral sites and both Fe" and FeII' cations randomly distributed in octahedral sites at temperatures above 119 K.The structure is related to the fully oxidised compound, maghemite (y-Fe,O,) which can be considered as an iron-geficient spinel of variable structure ranging from disordered cubic symmetry (a = !.34 A) to a Letragonal unit cell with ordered vacancies (space group, P4,2,, a = 8.34 A, c = 25.02 A). Conventional synthesis of magnetite, either by partial reduction of hematite (a-Fe,O,) or oxidation of Fe metal, is undertaken at high temperature (often 800 "C). Since these reactions occur under severe environmental conditions, the potential for crystallographic design of the products is limited. A more promising synthetic route for controlled crystallization is from the aqueous phase.' Here we report the characterization of magnetic spinels prepared by two independent methods based first on the partial oxidation of Fe" in the presence of NO, at 100 OC2 and 30333034 Crystallochemical Characterization of Magnetic Spinels secondly, on the reaction of hydrated FerI1 oxide (ferrihydrite) with Fe" ions at room temperature.Other routes from aqueous media at elevated and room temperature5, 7 ~ 1 " have been reported. Our objectives have been to investigate : (i) the influence of low molecular weight additives such as inorganic phosphate (Pi) on spinel formation, and (ii) the potential for spinel growth at room temperature and neutral pH. Preliminary studies of the former have been reported." The latter route offers the possibility of using a wide range of hydrophilic organic molecules (amino acids, peptides, proteins) or coordinating ligands that can be chemically tailored to induce a high degree of crystallochemical specificity in the products.In this respect, we note that biological magnetites are synthesized at ambient temperature and close to neutral pH with uniform particle sizes and novel species-specific morphologies. 12* l3 Experimental Preparation of Magnetic Spinels Method 1. Partial Oxidation of Aqueous Fe" by NO, at 100 "C Magnetite was prepared under N, at 100 "C by the slow addition (ca. 0.5 cm3 min-l) of a solution containing 0.1 mol KOH and 0.008 mol KNO, dissolved in 30 cm3 of deoxygenated distilled water to 70 cm3 of a boiling deoxygenated solution containing FeC1;4H2O (0.514 mol drn-,) at ca. pH 2.5. A green gelatinous precipitate was immediately formed which turned dark blue and then black on continued addition of the alkaline mixture.The suspension was boiled for a further 30 min and allowed to cool. The resulting black precipitate was washed several times with distilled water followed by two washings with acetone and left to dry at room temperature. Samples were removed at ten minute intervals during the course of the reaction, centrifuged, and the supernatent analysed for total dissolved Fe (by atomic absorption spectroscopy) and the pH measured. The FeIr1 : Fe'I ratio in the final product was calculated as follows. Fe" concentration was determined by dissolving a known weight of the spinel in conc. HC1 acid under N, and titrating against deoxygenated K,Cr,O,, total Fe was determined by atomic absorption spectroscopy, and FeIrr was calculated from the difference between total Fe and Fe" concentrations.The above synthesis was repeated with the following modifications ; ( a ) FeSO, - 7H,O in place of FeC1;4H2O and (6) in the presence of 5, 10, 15, 20 and 30 mol % KH,PO, added to the FeII solution prior to OH-/NO, addition. Method 2. Room-temperature Transformation of Hydrated Ferrr Oxide (Ferrihydrite) in the Presence of Fe" Ions Ferrihydrite was prepared by the addition of deoxygenated NaOH to 100 cm3 of a 19.6 mmol dm-3 deoxygenated solution of Fe(NO,), - 9 H,O. The resulting brown suspension was purged with N, overnight. 100 cm3 of a deoxygenated solution of 19.6 mmol dm-, FeSO;7 H,O was added to the stirred suspension under N, and the pH adjusted to a value of 7.0, 8.0 or 9.0 depending on the experiment. The reaction was accompanied by an immediate darkening of the ferrihydrite suspension and a continual decrease in pH which was buffered by the addition of deoxygenated NaOH such that the pH was kept within 0.2 units of the starting value.All experiments were run at room temperature under a stream of N, gas until no further change in pH was noted (3-26 h depending on the starting pH). The resulting black precipitate was collected by centrifugation, washed with deoxygenated distilled water followed by deoxygenated acetate buffer (pH 4.1, 0.5 mol dm-3) to remove any residual Fe" ions. Further washings with deoxygenated water and finally deoxygenated acetone were undertaken and the precipitate left to dry at room temperature under N,.S.Mann et al. 3035 The above procedure was modified at a reaction pH of 8.0 to include the presence of 1 and 5 mol O/O deoxygenated NaH,PO, - 2 H,O added to the ferrihydrite suspension prior to Fe" addition. Characterization of Products Electron Microscopy Samples for transmission electron microscopy were prepared by placing a droplet of the reaction suspension onto carbon-coated, nitrocellulose-covered copper electron microscope grids followed by blotting on filter paper and air drying. Changes in the crystallochemical properties of the precipitates formed during the phase transformation of hydrated ferric oxide (method 2 above) were determined by removing small aliquots of the suspension at different time intervals and mounting the material on electron microscope grids as above.Electron diffraction patterns were recorded on populations of particles and single crystals imaged in the selected area mode of the electron microscope. Compositional data on individual crystals as well as aggregates of particles were obtained using energy dispersive X-ray analysis (e.d.X) facilities coupled to the electron microscope. For conventional work a Jeol 1 OOCX analytical transmission electron microscope operating at 100 keV was used. Lattice imaging studies were undertaken on individual crystallites using a Jeol 2000FX transmission electron microscope operated at 200 keV and capable of a point-to-point resolution of 0.28 nm. X- Ray Diflraction, Infrared and "Fe Mossbuuer Spectroscopy and Magnetic Measurements Samples of the dried powders were examined by X-ray diffraction using a Debye- Scherrer camera and FeKr: radiation.Infrared spectra were recorded on a Perkin-Elmer 597 spectrometer. 57Fe Mossbauer spectra were recorded at variable temperature using a constant acceleration spectrometer with a "Co (Rh) source. Temperatures between 1.5 and 300 K were maintained and measured with a calibrated Si diode and a Lakeshore Cryotronics temperature controller. Spectra were analysed by a least-squares fitting program. Magnetic measurements were made with an S.H.E. Squid magnetometer. Results Method 1 (a) In the Absence of Phosphate Fig. 1 (a) shows the changes in pH and total dissolved Fe concentration accompanying the partial oxidation of a FeCl, solution in the presence of NO, at 100 "C.Addition of the OH-/NO, solution resulted in an initial rapid rise in pH with the dissolved Fe concentration remaining almost constant. After 10 min, the pH increase was reduced on continual addition of the alkali mixture although the Fe concentration decreased rapidly. Complete removal of soluble Fe after 50 min was accompanied by a rapid rise in pH and a black precipitate which showed a positive magnetic response to a small bar magnet. Chemical determination of the Fe" : Fe"' ratio in the product gave a value of 1 : 3 and X-ray diffraction data identified the material as a mixture of Fe,O, and y-Fe,O, spinels (table 1). These results were consistent with the Mossbauer spectrum of the sample recorded at 298 K [fig. 2(a)] which showed two overlapping subspectra corresponding to spinel-type tetrahedral Fe1Ir and octahedral Ferrr and Fe" sites (table 2).The intensity of the averaged (Fe" + Fe"') subspectrum was significantly reduced from that observed for stoichiometric magnetite', indicating substantial oxidation of Fe" ions in the octahedral sites. Magnetic moment measurements were also significantly smaller than3036 Crystallochemical Characterization of Magnetic Spinels - 12 -10 - ~ P H - 6 -4 - 2 0 20 40 60 rlmin - 14 - 12 - 10 - 8 PH - 6 -4 - 2 0 20 40 60 tlmin 0 20 40 60 t h i n 0 20 40 60 rlmin Fig. 1. Changes in soluble Fe concentration (mmol dm-3) (e), and pH (H), during the reaction of aqueous Fe" with NO;; (a) FeCI, solution; (6) FeSO, solution; (c) FeCl, with 10 mol YO P i , ( d ) FeCl, with 20 mol YO Pi.those of stoichiometric magnetite (table 2). However, infrared spectra showed only two bands at 570 and 360 cm-l [fig. 3(a)] characteristic of Fe,0,15 indicating that the bulk structure of the sample was primarily magnetite. This suggests that the maghemite phase was probably confined to an oxidised surface layer around the magnetite particles. Electron microscopic examination of the sample showed irregularly shaped particles in the size range 20-60 nm [plate 1 (a)]. E.d.X. analysis detected Fe and K (trace) (table 3 ) and powder electron diffraction patterns were consistent with the X-ray diffraction data. Magnetic spinels prepared from Fe" sulphate solutions were shown to be Fe,O, with some surface y-Fe,O, on the basis of X.r.d., infrared spectroscopy and chemical analysis (Fe"'/Fe" = 2.9) (Mossbauer data were not available).The pH and dissolved Fe" profiles were similar to those for Fe" chloride [fig. 1 (b)]. Electron microscopy showed that the spinel crystals formed from Fe" sulphate solution were generally larger, often up to 150 nm in length, and the particles exhibited a well defined cubo-octahedral morphology [plate 1 (b)] in contrast to the irregular crystals formed from the oxidation of Fe" chloride solution [plate 1 (a)].J . Chem. Soc., Faracial? Trans. I . Vnl. 85. Dart 9 (4 (h) PIutp 1 Plate 1. Transmission electron micrographs of spinel products from partial oxidation of Fe" solutions. (a) FeCI, solution; (b) FeSO, solution; (c) FeCI, with 5 mol O/O PI; (d) FcCl, with 30 mol YO P,.Needle-like particles in (4 are x-FeOOH. Scale bar in all micrographs is 100 nm. S. Mann et d.J . Clzern. SOC., Faraday Trans. I , Vol. 85, part 9 (4 (bl Plate 2 Plate 2. Transmission electron micrographs of precipitates from reaction of ferrihydrite with aqueous Fe"; ( a ) unreacted ferrihydrite, pH 8, 30 min; (6) green rust, pH 8 (or 9), 30 min; ( c ) green rust and Fe,O,, pH 8, 60 min and (6) magnetite (the needle-like crystal is a-FeOOH), pH 8, 22 h. Scale bars: ( a ) and (b) 500 nm; ( c ) and (6) 100 nm.J. Cheni. Soc., Furaduy Trans. I , Vol. 85, part 9 (4 (b) Pluto 3 Plate 3. Precipitates formed from the reaction of ferrihydrite with aqueous Fe" at pH 7 ; ( a ) green rust, 2 h ; (b) green rust and Fe,O,, 3 h ; (c.) Fe,O, and needle-like z-Fe00H and (6) lattice image of a Fe,O, single crystal showing {200) (4.2 A) fringes and well defined cubo-octahedral crystal edges.Scale bars: ( a ) and ( b ) 500 nm; (c.) 50 nm and (6) 10 nm.J . Clipm. Soc'., Faratla)! Trans. I , Vol. 85, part 9 Plute 4 Plate 4. Precipitates formed from the reaction of ferrihydrite with aqueous Fe" at pH 8 in the presence of 5 mol% Pi; (a) unreacted ferrihydrite and green rust, 4 h; (b) green rust and trace amounts of ferrihydrite, 50 h. Scale bars: (a) 500 nm and (b) 1 pm.S. Mann et a/. 3037 Table 1. Representative X-ray diffraction data (d-spacings/A) for spinel productsa d-spacing/A y-Fe,O,b Fe,O,' product 4.82 4.18 3.20 2.95 2.78 2.514 2.408 2.086 1.701 1.604 1.474 1.318 1.272 1.258 1.204 1.1 15 1.086 1.043 4.85 - 2.97 2.532 2.100 1.714 1.617 1.485 1.327 1.280 1.266 1.212 1.122 1.093 1.050 - - 4.84 4.18 3.26 2.96 2.78 2.525 2.41 6 2.090 1.708 1.614 1.479 1.324 1.277 1.263 1.209 1.1 19 1.090 1.047 a All samples gave similar diffraction spacings but the number of y-Fe,O, lines varied in different experiments depending on the extent of air oxidation of the materials.X.r.d. File 15-1402, X.r.d. File 19-629. (b) In the Presence of Inorganic Phosphate Addition of 5-30 mol YO KH,PO, (Pi) to Fe" chloride solutions prior to OH-/NO, addition resulted in structural and morphological changes in the spinel products. X.r.d. patterns, infrared spectra [fig. 3 (b)], room temperature Mossbauer spectra [fig. 2(b) and (c); table 21 and magnetic measurements (table 2) of crystals grown in the presence of 5 % and 10 YO Pi showed that the samples comprised surface oxidised Fe,O, similar to that formed in the undoped system.The infrared spectra showed an additional band at 950 cm-l [figure 3 (b)] corresponding to the P-0-Fe symmetric stretch." Particles examined by e.d.X analysis showed that some Pi was closely associated with the spinel crystals (table 3). The pH and dissolved Fe" profiles [fig. l(c)] were essentially unchanged from the non-phosphate containing systems. The crystals were 5S100 nm in size and had a well defined cubo-octahedral morphology [plate 1 (c)]. These results are similar to those described above for spinel formation from Fe" sulphate solutions and indicate the importance of anion charge in determining the crystallochemical nature of the magnetic products.Increasing the Pi concentration to 20-30 mol O/O resulted in marked changes in the structural and magnetic properties of the oxidation product. Addition of NO,/OH- first gave a dark blue-green product which turned dark brown towards the end of the reaction. The Fe concentration and pH profiles [fig. 1(4] showed a more rapid uptake of Fe from solution and a continual rise in pH throughout the reaction. X.r.d. patterns of the samples gave weak broad lines with d-spacings corresponding to Fe,O,/ y-Fe,O, indicating that the spinels were of low structural order. The degradation of structural3038 Crystallochemical Characterization of Magnetic Spinels -10 .o -5.0 0-0 5.0 10.0 velocity/mm s- ' Fig. 2. 57Fe Mossbauer spectra of samples from partial oxidation of FeCl, solutions; (a) 0; (b) 5 ; (c) 10; (6) 20 and (e) 30 mol% Pi.Spectra were recorded at 298 K. order was also apparent in the marked reduction in the saturation magnetic moment (table 2) and in the Mossbauer spectra [fig. 1 (d) and (e)] which showed that, although magnetic ordering was still present at 298 K, the lines were extensively broadened. Furthermore, the 30 mol% Pi product showed evidence of a weak high-spin FeI'I quadrupole doublet in the central region of the spectrum. Since no diffraction lines were observed for non-spinel crystalline iron oxides, this spectral component possibly corresponds to an amorphous or poorly crystalline Fell1 oxide of small particle size, for example, ferrihydrite. Infrared spectra of the samples showed only weak Fe,O, bands and a strong Pi band at 950 cm-l [fig.3(c)], consistent with the above results. Electron micrographs showed that whereas the particles formed in the presence of 20 mol % Pi were 40-120 nm octahedral crystals, those prepared in 30 mol YO Pi comprised ill defined grains of much lower size (1MO nm) [plate 1(4] E.d.X analysis showed Pi closely associated with all the particles (table 3). Some needle-like particles (100 nm in length) of goethite (a-FeOOH) were also occasionally observed in both samples [plate l(d)] although this material was not detected by X.r.d.S. Mann et al. Table 2. 57Fe Mossbauer parameters 3039 sample T/K 6/mm s-lU A/mm s-'* HF/kOec MM/emu g-ld 0 mol YO Pi 5 mol O/O Pi 10 mol% Pi 20 mol YO Pi 30 mol% Pi - - - PH 9 PH 8 PH 7 PH 8, 1 mol% Pi PH 8, 5 mol0/o Pi - 298 298 298 - - - - - 298 298 298 200 80 8 - - method I 0.34 - 0.58 0.34 0.55 0.33 0.55 - - - - - - - - - method 2 0.39 - 0.39 0.38 0.42 0.42 0.8 1 0.39 0.47 0.80 0.47 - - - - - 490 72% 76.5 450 28% 485 54% 76.8 445 46% - 485 56% 74.2 422 44% - 42.6 42.6 - - - _ _ - 502 - 503 - 503 - 450 - - 82% 470 18% - 482 - - - - - - _ - - "6, Isomer shift.* A, quadrupole splitting. 'HF, magnetic hyperfine field. d , MM, saturation magnetic moment per gram; for comparison, stoichiometric Fe,O, and y-Fe,O, have values of 92.0 and 56.0 emu g-l, respectively . 1400 1200 1000 800 600 400 wavenumber/cm- ' Fig. 3. Infrared spectra of samples from partial oxidation of FeCl, solutions; (a) 0; (6) 10 and (c) 30 mol O/O P,. Peak A', v(Fe0-P); peaks Y and Z , v(Fe0-Fe).Method 2 Reaction of ferrihydrite at room temperature in the presence of Fe" at pH 9 gave a magnetic product after 3 h which was identified as a mixture of Fe,O, and y-Fe,O, by X.r.d. and electron diffraction. Mossbauer spectra showed only a single hyperfine sextet [fig. 4(a), table 21 indicating that the major component was y-Fe,O,. The corresponding3040 Crystallochemical Characterization of Magnetic Spinels Table 3. E.d.X. analysis data (wt YO element) for spinel samples prepared by method 1 dopant level/atom YO Pia element 0 5 10 20 30 Fe 67.53 70.29 66.33 70.26 67.73 0 25.15 26.85 25.33 26.17 25.22 P - 0.95 2.08 1.14 2.06 "A1 (sample holder), Si (silicone grease) and K (residual KOH/KNO,) were also present in trace amounts giving a total wt O/O of 100 for each sample.* I, I v -10.0 0.0 5.0 10.0 veIocity/rnrn s-' Fig. 4. j7Fe Mossbauer spectra of samples from the reaction of ferrihydrite and aqueous Fe" at room temperature and at (a) pH 9; (b) pH 8; (c) pH 7. Spectra were recorded at 298 K. reaction at pH 8 was slower and a magnetic product was isolated after 12 h. X.r.d. data from a freshly prepared sample gave reflections corresponding to Fe,O, although the dried sample rapidly oxidised in air to y-Fe,O, as shown by the Mossbauer spectrum [fig. Changes in the crystallochemical properties of the reaction intermediates and spinel products were followed by electron microscopy. At both pH values the reaction proceeded via a pseudo-hexagonal plate-like precursor [plate 2 (b)] that gave single- crystal electron diffraction pattecns corresponding to a poorly-crystalline green rust IF7 [d-spacings ; 2.66 (101) and 1.52 A (1 12)].Whereas green rust (mean size ca. 450 nm) was predominant in samples taken after 30 min at pH 9, corresponding samples from the pH 8 5 mi.S. Mann et al. Fe c u Fe 304 1 Fig. 5. E.d.X. spectra of green rust prepared at pH 8 from the reaction of ferrihydrite and aqueous Fe"; (a) 0 and (b) 5 mol YO P,. Cu peaks originate from the sample holder and Si is a contaminant (from silicone grease). system contained much of the unreacted starting material [plate 2 (a)]. Subsequent transformation of green rust to magnetite appeared to take place at the surface of the intermediate and was associated with a concomitant corrosion of the pseudo-hexagonal platelets [plate 2 (c)].The magnetic crystals were irregular in shape during the early stages of the transformation but an octahedral or cubo-octahedral morphology was apparent in the mature crystals [plate 2(d)]. Particle size distributions and mean diameters for spinel crystals at different stages of growth were similar indicating that ripening of the early crystals was not a predominant mechanism of formation. Furthermore, the mean diameter, range and standard deviation (32, 1040 and 9.5 nm, respectively, at pH 9) of the spinel crystals were not significantly different in the two systems even though the reaction was substantially slower at pH 8. Similar values were also obtained from particles grown at pH 7 (see below). This suggests that the particle size of the magnetic products is independent of the rate of formation and is possibly constrained by other factors such as the local supersaturation levels and structural disorder in the growing crystals.E.d.X. spectra showed the presence of S [from Fe" sulphate] in both the ferrihydrite and green rust materials [fig. 5(a)]. No S was observed in the corresponding analysis of the spinel crystals. The above reaction, when carried out at pH 7, resulted in a mixture of magnetic and3042 Crystallochemical Characterization of Magnetic Spinels fc) 1.00 0.99 0.98 0.97 0.96 * -10 0 -5.0 5.0 10.0 velocity/mm s-' Fig. 6. 57Fe Mossbauer spectra of samples from the reaction of ferrihydrite and aqueous Fe" at room temperature, pH 8; (a) 1 mol YO Pi 200 K; (b) 5 mol YO Pi, 80 K and (cj 5 mol YO Pi, 8 K.non-magnetic oxides. Green rust was formed during the first 2 h of the reaction followed by slow transformation (26 h to completion) to Fe,O,/y-Fe,O, and a-FeOOH (goethite) (plate 3). Mossbauer spectra were consistent with the diffraction data and showed hyperfine split components corresponding to y-Fe,O, and a-FeOOH [fig. 4(c), table 21. Whereas the Fe,O, particles formed in close proximity to the green rust platelets [plate 3 (c)], the a-FeOOH needle-like crystals were spatially separated. The spinel crystals had a size range 1&60 nm and mean diameter of 33 nm, which were not significantly different from spinels formed at higher pH values. There appeared, however, to be an increased morphological resolution when compared to the higher pH products, with many crystals exhibiting a well defined cubo-octahedral habit [plate 3 (c)].High-S. Mann et al. 3043 resolution electron micrographs showed lattice fringes running continuously and coherently across the total width of the individual spinel particles [plate 3(d)]. These results indicated that the spinel particles are well ordered single-domain crystallites. Addition of 1-5 mol YO Pi prior to Fe" addition to ferrihydrite inhibited spinel formation. The rate of green rust formation was significantly reduced and although green rust was present after 4 h, unreacted ferrihydrite was present throughout the reaction (plate 4). The initial green rust particles were irregular and associated with an amorphous gel of ferrihydrite [plate 4(a)].At 50 h, well developed pseudo-hexagonal plate-like crystals were observed [plate 4(h)]. No spinel phases were detected by X.r.d. or electron diffraction. E.d.X spectra of both the ferrihydrite and green rust particles showed the presence of P and S (from sulphate) in these solids (fig. 5). Mossbauer spectra of the above sampIes showed no evidence of spinel phases. The spectra recorded at 200 K consisted of a high-spin Fe"' quadrupole doublet [fig. 6(a), table 21. A minor component, corresponding to a hyperfine split sextet, was also observed in the sample prepared in the presence of 1 mol% Pi [fig. 6(a)]. A similar component was only observed at temperatures below 80 K in the sample prepared in the presence of 5 mol% Pi [fig. 6(b) and ( c ) , table 21.Lowering the temperature to 8 K resulted in the loss of the central doublet and the concomitant increase in the sextet component. The relatively low hyperfine field value (table 2) and the broad lines of the sextet suggest that the material is not y-Fe,O, of small particle size. On the basis of the electron microscopy results, the spectral data can be interpreted as arising from a mixture of disordered Fe"' oxides, possibly formed by air oxidation of green rust in combination with unreacted ferrihydrite. The temperature dependence of the spectra is therefore characteristic of magnetically ordered small particles ( < 10 nm) exhibiting superpa ramagne t ism. Genera1 Comments The results presented in this paper show that magnetic spinels can be formed from aqueous media and that the crystallochemical properties of these materials are readily influenced by changes in pH, temperature and anionic species present in the reaction.Although Fe,O, is the initial product formed by partial oxidation of Fe" at 100 "C and by the reaction of ferrihydrite with Fe" at room temperature, the material formed in the latter system rapidly oxidises to y-Fe,O, during sample isolation and storage. Since the particle sizes were similar in both systems, the low temperature product is possibly more disordered. Both synthetic routes involved green rust intermediates which are hydrated mixed valence comp~unds,'~ and the subsequent dehydration and transformation to Fe,O, will be favoured at higher temperature. Furthermore, the high final pH of method 1 compared with the lower buffered pH values of method 2, favours the formation of 0x0- rather than oxy-bridges in the product. Although we have been successful in preparing spinels at ambient temperature and neutral pH, we have not attained the degree of specificity characteristic of the biologically controlled synthesis of stoichiometric magnetite, as found, for example, in magnetotactic bacteria.13, Future work will focus on achieving greater chemicaI control over spinel formation through the use of gel media and micellar compartments which may limit the rate of reaction and provide increased regulation of nucleation and crystal growth. Since ferrihydrite has been shown to be a precursor to magnetite formation in bacteria,". l9 method 2 has potential as a model system for the biomineralization of iron oxides. We note, however, that no green rust intermediates have been observed in the bacterial systems.Interestingly, magnetite formation in the teeth of marine molluscs (chitons) also involves the transformation of ferrihydrite but green rust intermediates have been observed;20 the subsequent reaction products include both Fe,O, and a- FeOOH and the system appears to be chemically similar to the inorganic preparation at3044 Crystallochemical Characterization of Magnetic Spinels p~ 7 reported in this paper. Furthermore, the chiton Fe30,, like the inorganic products described here, does not show the crystallochemical specificity of bacterial magnetite. Thus a future strategy will be to eliminate green rust intermediates from the ferrihydrite to spinel reaction pathway.Previous workers3.* have proposed that the reaction of Fe" with Fell' oxides results in Fe,O, by a mechanism involving the formation of soluble mixed valence complexes. The rate limiting step appears to be the transformation of green rust and this reaction step is profoundly influenced by the pH, temperature and nature of anionic additives present in the reaction medium. Both Pi and SO:- stabilize the intermediate presumably through surface adsorption, and reduce the rate of spinel formation. At high temperature ( I 00 "C), relatively large concentrations of additive can be tolerated, whereas at room temperature concentrations as low as mol % Pi result in complete inhibition of Fe30, crystallization. The consequent reduction \ rate at intermediate additive concentrations results in morphological enhancement of the octahedral habit of spinel crystals grown from partial Fe" oxidation at 100 "C.A s i m i h effect is observed with SO:- and with a reduction in the pH to 7 in method 2. Since the (1 11) octahedral faces of Fe30, are intrinsically stable, the increased resolution in morphology is unlikely to be due to specific surface interactions between these crystal faces and PO:- and SO:- anions, although P was detected in the Fe,O, crystals analysed by e.d.X analysis. Bacterial magnetites, on the other hand, show a range of species-specific morphologies that have not yet been replicated in inorganic preparations, and this must be a priority of future work since such speciality materials may have important technological application. This work was supported by SERC grant GR/D30754. R. B. F. was supported by the US National Science Foundation. We thank Dr G. C . Papaefthymiou for help with Mossbauer spectroscopy and discussions. References 1 E. Matijevic, Langmuir, 1988, 2, 12. 2 P. S. Sidhu, R. J. Gilkes and A. M. Posner, 1. Inorg. Nucl. Chem., 1978, 40, 429. 3 Y. Tamaura, K. Ito and T. Katsura, J. Chem. SOC., Dalton Trans., 1983, 189. 4 T. Sugimoto and E. Matijevic, J. Colloid Interface Sci., 1980, 74, 227. 5 R. M. Taylor and U. Schwertmann, Clay Minerals, 1974, 10, 299. 6 K. Kaneko and T. Katsura, Bull. Chem. SOC. Jpn., 1979, 52, 747. 7 R. M. Taylor, Clays Clay Min., 1984, 32, 167. 8 T. Misawa, K. Hashimoto and S . Shimodaira, Corros. Sci., 1974, 14, 13 1. 9 S. Mann, A. J. Skarnulis and R. J. P. Williams, J. Chem. Soc., Chem. Commun., 1979, 1067. 10 S. Mann and J. P. Hannington, J. Colloid Interface Sci., 1988, 122, 326. 1 1 S. B. Couling and S . Mann, J. Chem. Soc., Chem. Commun., 1985, 1713. 12 S. Mann, Chem. Br., 1987, 23, 137. 13 S. Mann, N. H. C. Sparks and R. P. Blakemore, Proc. R. SOC. London, B, 1987, 231, 477. 14 W. Kundig and R. S . Hargrove, Solid State Commun., 1969, 7, 223. 15 B. Gillot, F. Bouton, J. F. Ferriot, F. Chassagneux and A. Rousset, J . Solid State Chem., 1977,21,375. 16 R. L. Parfitt, J. D. Russell and V. C. Farmer, J. Chem. SOC., Faraday Trans. I , 1976, 72, 1082. 17 J. D. Bernal, D. R. Dasgupta and A. L. Mackay, Clay Min. Bull., 1959, 4, 15. 18 S. Mann, R. B. Frankel and R. P. Blakemore, Nature, 1984 310, 405. 19 R. B. Frankel, G. C. Papaethymiou, R. P. Blakemore and W. O'Brien, Biochim. Biophys. Acta, 1983, 20 K. S. Kim, D. J. Macey. J. Webb and S. Mann, Proc. R. SOC. London. B, 1989, 237, in press. 763, 147. Puper 9/00260J ; Receiued 14th January, 1989

ISSN:0300-9599    

DOI:10.1039/F19898503033

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J . Chem. SOC., Faradaj! Trans. I , 1989, 85(9), 3045-3057 Dielectric Studies of the Switch-over Mechanism in the Principal Relaxation Process of Alkan- 1-01s Humayun Mandal and David G. Frood Department of Physics, Lakehead University, Thunder Bay, Ontario, Canada P7B 5El Mohammad Habibullah, Linda Humeniuk and Stanley Walker* Department of Chemistry, Lakehead Unicersity, Thunder Bay, Ontario, Canada P7B 5EI Dielectric absorption studies have been made on the alkan-1-01s in inert and weakly interacting solvents over a wide range of concentration at various temperatures and in the frequency range 106-109 Hz. Some representative alcohols have also been studied in the strongly hydrogen bonding solvents, diethyl ether and di-n-butyl ether. It has been found that not only does the flexible chain of the alkan-1-01 influence the enthalpy of activation on its dilution with a dialkyl ether, but the chain length of the latter also exerts an influence.Altogether the work strongly supports a switch-over type of mechanism as being involved in the principal relaxation process of the alkan-1-01s. The data for the alkan-1-01s in n-heptane and toluene solutions have been employed to test more quantitatively a switch-over theory, and for the shorter-chain alkan-1-01s this has been found to yield reasonable agreement between the measured and estimated principal relaxation time ( T ~ ) over a wide range of concentration and temperature. The lowest-frequency dispersion exhibited by the pure alkan- 1-01s and their solutions has received innumerable studies in the past 40 years.' This dispersion is known to exhibit Debye behaviour.' Many models have been developed to account for this principal dispersion' characterized by the principal relaxation time (zl), the mechanism of which may still be regarded as a controversial subject.There is an abundance of spectroscopic evidence to demonstrate that the alkan- 1-01s are highly multimerized2-* even at the lowest concentrations at which dielectric measurements are carried out, and this is commonly acknowledged in the models proposed to account for the principal dispersion. One fairly common feature in proposed mechanisms is that hydrogen- bond breaking must take place for dielectric absorption to ensue. Four examples of this are the following. (I) Brot and Magat5 proposed that alcohol multimers of variable hydrogen-bonded chain length exist in the liquid together with free molecules all in dynamic equilibrium.The lifetime, z,, of a hydrogen-bond is shorter than the time necessary for all but the smallest multimers to reorient themselves as a whole in the applied field. Brot and Magat5 then visualized that the breaking of a hydrogen-bond makes possible the orientation of the liberated dipole. (2) Garg and Smyth' proposed a mechanism for which they describe the process as the breaking of a hydrogen-bond immediately followed by molecular rotation of the then partially liberated ROH. (3) On the basis of the dielectric study of some isomeric octanols, Dannhauser and co- w o r k e r ~ ~ - ~ proposed that hydrogen-bond rupture is a prerequisite of rather than a rate- determining step for the z, process.(4) Higasi and co-workers1° formulated a cooperative mechanism which consists of 30453046 Relaxation of Alkan-1-01s breaking the 0-H . . .O bond at the end of the chain; this 0-H group then rotates through 180", and the switch occurs cooperatively all along the multimer chain. The net outcome is that the large vectorially added dipole moment (p) is reversed, leading to a large loss factor which is, in fact, observed. The process may be represented as follows : R 1 0 / '.. H, .:H 0 R I I R R I 0 R 0 I \ H H '.. / 0 I R I 1 I I 4 P P The Higasi model is termed a switch-over mechanism and places emphasis on the enthalpy of activation, AHE, which may be defined as the barrier to be surmounted in order to achieve the 0-H dipole reorientations in the rl process (see Results).Earlier a switch-over type of mechanism had been proposed by Sagal" to account for the increase of AHE on dilution of ethanol with cyclohexane. He postulated that 'the hydrogen bond will break when another (alcohol) molecule approaches with the oxygen atom oriented favourably for a switch. It is reasonable to assume that the presence of this third oxygen atom will lower the energy barrier for breaking the hydrogen bond'. Thus, when an alcohol molecule (RO'H) approaches the intermolecularly hydrogen- bonded species R R R I I I H-0' 0-Ha ... bO-H ... I then the hydrogen bond ab breaks, and 0-Ha switches and becomes hydrogen bonded with 0'. The dilution of ethanol with cyclohexane leads to a reduced probability of an RO'H molecule approaching the multimerized unit, and as a consequence the barrier increases with progressive dilution.Neither the Higasi theory nor the Sagal postulate takes into account directly the possibility that the flexible alkyl chain in the alkan-1-01 may influence AHE. To establish firmly that the energy barrier is lowered on dilution of the alkan-1-01, a considerable amount of work is required on an alkan-1-01, preferably with a rigid chain, that is on methanol, in a variety of solvents. Emphasis has been placed on examination of methanol in diethyl ether and di-n-butyl ether, where the chain length of the solvent is varied. Close examination of the infrared data for alkan- 1-01 hydrogen bonding intermolecularly and with normal ethers would suggest that the strengths of the intermolecular hydrogen bonds R R R 0 - H ...0-H and 0-H ... 0, I I I /R1 R1 are of a similar order of magnit~de.~-~ This led us to test the Sagal postulate'' by studying methanol not only in weakly interacting solvents but in the stronglyH . Mandal et al. 3047 intermolecular hydrogen-bonding dialkyl ethers as well. Some of the types of associated species, when an ether is the solvent, may well be : (a) at high alkan- 1-01 concentrations : R / O\ (b) at low alkan- 1-01 concentrations : R I / \ O 0 - H ... 0, / R R I I / >o 0- H ... 0-H _.. 0, etc. From the point of view of testing the Sagal theory in these types of solutions, the prominent species involve a case such as: R \ I ,O 0 - H ...0 which, from the switch-over postulate of Sagal, would have a lower energy barrier than the case: R I inert solvent 0 - H ... 0 . Thus, there is a possibility that if the Sagal postulate is correct, the enthalpy of activation may remain roughly constant or even exhibit a small decrease or increase on dilution with the ether. There appears to be little in the literature on this, with the exception of a specific study by Higasi and co-workers,12 where they examined propan-1-01 in pyridine and also 1,4-dioxane and found that AHE falls with dilution. Propan-1-01, however, has a flexible alkyl chain. Our major aims in this paper are: (a) to test the Sagal postulate for methanol in a variety of solvents, (b) to examine the influence of the length of the alkyl chain of both the alkan-1-01 and the solvent diethyl ethers on r1 and AHE, and ( c ) to test any appropriate model with the experimental data.Experimental The dielectric measurements were carried out with a Hewlett Packard 4191A RF impedance analyser in the frequency range 106-1 O9 Hz. The operational temperature3048 Relaxation of Alkan-1-01s 45 r O A 0.2 0.4 0.6 0.8 1 mole fraction alkan - 1 - 01 Fig. 1. Enthalpy of activation A H , (kJ mol-l) uersus mole fraction of alkan-1-01s in diethyl ether. A, Methanol; V, ethanol; A, propan-1-01; ., butan-1-01; 0, hexan-1-01; +, octan-1-01; 0, decan- 1-01 ; V, undecan- 1 -01. 1 I 1 0.4 0.6 0.8 1 mole fraction alkan - 1 - 01 Fig. 2. Enthalpy of activation AH, (kJ mol-’) uersus mole fraction of alkan-1-01s in di-n-butyl ether.Symbols as for fig. 1. limit of the cell was from 77 to 363 K and was controlled to within kO.1 K as has been described previously. l3 All the alcohols and solvents were obtained commercially and were purified by refluxing with a suitable drying agent and distilling over 4 A molecular sieves. Results The experimental loss data ( E ” ) as a function of frequency (v/Hz) produced dielectric absorption curves. Analysis of such curves by a computer program for a best linear fit to the Fuoss-Kirkwood relation~hipl~. l5 cosh-’ ( E ~ , , / E ” ) = P(ln vmaX -In 17)H. Mandal et al. 3049 I ? i’l 0.2 0 I mole fraction alkan - 1 - 01 Fig. 3. Relaxation times r1 (s) uersus mole fraction of alkan- 1-01s in diethyl ether at 293 K. Symbols as for fig. 1. 24 r n 0.4 0.6 0.8 1 mole fraction alkan - 1 - 01 Fig.4. Relaxation times z, (s) uersus mole fraction of alkan-1-01s in di-n-butyl ether at 293 K. Symbols as for fig. 1.3050 Relaxation of Alkan-1-01s 0.3 0.5 0.7 0.9 1.0 mole fraction methanol Fig. 5. Relaxation times T, (s) versus mole fraction of methanol in toluene 0, 293 K. (-) T, values calculated using eqn (4). 0 , 2 0 0 K ; 0 , 2 2 5 K ; mole fraction alkan - 1 - 01 Fig. 6. Relaxation times T~ (s) uersus mole fraction of 1-alkanol in n-heptane solution at 200 K. A, butan-1-01; V, hexan-1-01; 0, octan-1-01; 0, decan-1-01, (-) z1 values calculated using eqn (4). yielded three parameters : maximum loss factor of the absorption, z,( 1 /271vma,>, the mean relaxation time which is the value of z, from the frequency maximum of the dielectric absorption curve, and p, the distribution parameter which ranges between 0 and 1, with 16 = 1 corresponding to a single Debye process and p < 1 to a broad distribution of relaxation times.The Eyring parameters were evaluated from the equation :H. Mandal et al. 305 1 0.3 0.5 0.7 0 . 9 1.0 mole fraction alkan- 1-01 Fig. 7. Relaxation times T~ (s) r ~ r s u s mole fraction ofalkan- 1-01 in n-heptane at 293 K . (-) t, values calculated using eqn (4). Symbols as for fig. 6. 0 0.3 0.5 0.7 0.8 1.0 mole fraction alkan - 1-01 Fig. 8. Relaxation time 7, (s) uerws mole fraction of alkan- 1-01 in toluene at 200 K. (-) t, values calculated using eqn (4). Symbols as for fig. 6. AHE and ASE were determined from a weighted least-squares fit of the In (Tz,) versus T-' data, and the free energy of activation from: AGE = AHE- TAS,.(3) The results are presented in fig. 1-9. For a dipole relaxation process AHE is sometimes referred to as the excess enthalpy. For the alkan-1-ols, Bottcher and Bordewijk' have interpreted AHE as being the activation energy for the z, process as expressed in the Eyring equation, while Higasi and co-workers10 have employed essentially the same approach. For the multimerized pure3052 Relaxation of Alkan-l-ols 1 8 9 I I I 1 0.3 0.5 0.7 0.9 1.0 mole fraction alkan - 1-01 Fig. 9. Relaxation times z, (s) uersus mole fraction of alkan- 1-01 in toluene at 293 K. (-) z, values calculated using eqn (4). Symbols as for fig. 6 . methanol, the AHE value of 14 kJ mol-1 (see later) virtually corresponds with the energy required to break one mole of intermolecular hydrogen bonds.However, for the flexible chain alkan-1-01s the length of the chain also exerts considerable influence on AHE.16 Discussion (A) Methanol in Weakly Interacting Solvents Examination of methanol in toluene reveals that AHE increases on dilution.16 Thus: AHJkJmol-l: 14 15 17 17 18 17 19 22 and in p-cymene (a slightly better n-electron donating solvent) we found essentially the same result :16 AH,/kJmol-l: 14 14 14 17 18 18 19 22 mole fraction: 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 mole fraction: 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Methylene dichloride, which is a very weakly hydrogen bonding solvent, gave :16 mole fraction: 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 AH,/kJmol-': 14 14 14 15 15 15 16 17 The results for methanol in all three of these solvents bear out the Sagal postulate. The increment in AHE, when methylene dichloride is the solvent, is definite but minimal.In this case, the interaction between the solute and the solvent is extremely weak, and it may be worth noting that both the solute and the solvent are of a similar size and both spherical in shape. These results may be compared with those of Sagal for ethanol in the inert solvent, cyclohexane :11 AH,/kJmol-l: 21 23 23 28 28 For the more dilute solutions of the n-electron-donating solvents, toluene and p-cymene, the barrier may be higher than that for the corresponding methylene dichloride concentration because of the intermolecular hydrogen bond between the OH and the n-electrons of the solvent molecule. Thus, an approaching RO'H molecule, as visualized in the switch mechanism, would first have to displace the hydrogen- bonded solvent molecule.mole fraction: 1.0 0.90 0.75 0.50 0.25H . Mandal et al. 3053 (B) Methanol in a Strongly Intermolecularly Hydrogen Bonding Solvent Infrared evidence readily establishes that methanol forms a strong intermolecular hydrogen bond with pyridine :2 I I 0- H ... (0-H), ... N< where rn falls on considerable dilution. Thus, when the pyridine approaches the end of the alcohol chain, we have: I I // tN\ 0 - H ... 0 - H The influence on the barrier of dilution of methanol by pyridine is as follows: AH,/kJmol-': 14 15 18 18 19 20 20 All these data conform with the Sagal postulate. In the case of pyridine, an additional switch mechanism is possible involving : mole fraction: 1.0 0.9 0.8 0.7 0.6 0.4 0.3 I I ... 0 - H ...0 - H ... N < Thus, for methanol the Sagal postulate holds for a very weakly hydrogen bonding solvent (methylene dichloride), x-electron-donating solvents (toluene and y-cymene) and a strongly electron-donating solvent (pyridine). However, when a flexible chain is introduced, as in the study of propan-1-01 in pyridine and also in 1,4-dioxan,12 then AHE falls appreciably on dilution of the propan-1-01. This is in direct opposition to what occurs for methanol in pyridine and suggests that the alkyl chain of the alkan-1-01 is a factor to be taken into account when the switch-over mechanism is being studied. (C) Methanol and some other Alkan-1-01s in Dialkyl Ethers Our aim is now to test not only the switch mechanism, but also to assess how the alkyl chains of both the solute and the solvent influence the principal relaxation time and the enthalpy of activation.In fig. 1 for butan-1-01, hexan-1-01, octan-1-01 and decan-1-01, AH, is plotted against the mole fraction of alkan- 1-01 in diethyl ether. In all cases, the energy barrier decreases with dilution. However, for methanol (fig. l), the change in AHE on dilution from the pure alcohol to 0.4 mole fraction is not significant, whereas for hexan- 1-01 and decan- 1-01 AHE is approximately halved. These plots suggest that: (a) in the absence of a flexible chain (i.e. methanol) the 0-H intermolecular hydrogen bond can scarcely distinguish between an oxygen atom in the ether and one in the alcohol since the barrier barely changes by replacement of one by the other; (b) for the other four alkan- 1-01s for a given concentration the barrier increases appreciably with chain length, and A H , decreases noticeably on dilution of the alkan- 1-01 with diethyl ether; (c) AH, values extrapolated to ca.0.15 mole fraction are very similar and are of about the same magnitude as the intermolecular hydrogen bond strength. We also studied methanol, ethanol, propan- 1-01, butan- 1-01, hexan- 1-01 and octan- 1 - 01, decan-1-01 and undecan-1-01 in di-n-butyl ether where the number of flexible groups in the solvent molecule chain has increased from four in diethyl ether to eight. The3054 Relaxation of Alkan-1-01s results are presented in fig.2. For octan- 1-01, hexan- 1-01, butan- l-ol and propan- 1-01, AHE decreases consistently as the alcohol is diluted, but the change is appreciably less than in the parallel case in fig. 1, whereas for methanol and ethanol there is a small increment in AHE on dilution with di-n-butyl ether, which again differs from the behaviour in fig. 1. In fig. 2 extrapolation of AHE to 0.15 mole fraction does not produce a similar value for all the alkan-1-ols, and in most cases is well above the strength of the intermolecular hydrogen bond. From the data in fig. 1 and 2 we conclude that: (1) for alkan-1-01s with n > 2, where n is the number of carbon atoms, both the chain length of the alkan-1-01 and the solvent dialkyl ether influence AHE, which for a given concentration tends to increase with chain length; (2) for methanol the results appear in harmony with the Sagal postulate.The main question remaining is why, in general, the energy barrier of the alkan-1-01 decreases on dilution with the ether. Some appreciation of this may be gained from the behaviour of methanol in the two dialkyl ethers. In each case the barrier exhibits little change on dilution, and this is the only case of an alkan-1-01 with a non-flexible chain, where, if we have: and CH3 CH3 R1 \ I I R*’ 0 0 - H ... 0 - H CH3 CH3 CH3 I I I H - 0 0 - H ... 0-H the barriers are quite similar. Therefore, this is a clear case which fits the Sagal model where little or no variation in AHE would be expected on dilution. For example, when diethyl ether is the solvent, AHE exhibits no significant decrease on dilution of methanol to 0.5 mole fraction, and when a similar experiment is carried out with di-n-butyl ether as solvent, there is a small increase in AH, on dilution.Perhaps the small difference in behaviour may be attributed to the influence of the longer chain in the di-n-butyl ether case. However, the main point is that for methanol in both solvents, there is little change in AH, on dilution, which is to be contrasted with the butan-1-01, hexan-1-01 and octan- l-ol cases where AHE decreases significantly on dilution with ether. For these cases, we have to take into account both the flexible chain of the alkan-1-01s and the dialkyl ethers which may interact with each other and also become entangled. Very likely the Sagal postulate has its limitations in this more complex situation. The effect of dilution on the principal relaxation time of the following alcohols: methanol, butan- 1-01, hexan- 1-01, octan- 1-01 and decan- 1-01 in diethyl ether is given in the z, us.concentration plot in fig. 3 where the temperature is 293 K. In the case of methanol, very little change in z, occurs on dilution. This is to be contrasted with the other alkan-1-01s where on dilution from the pure alkanol to 0.4 mole fraction the relaxation time is shortened by a factor of ca. 5. At an extrapolated 0.15 mole fraction, with the possible exception of methanol, they all tend to a similar value of ca. 100 ps. The behaviour of the z, 293 K values of eight alkan-1-01s in di-n-butyl ether is represented in fig.4, On the whole, they exhibit similar behaviour to the alkan-1-01s in diethyl ether as given in fig. 3 and even extrapolate to a similar limiting value at ca. 0.05 mole fraction. The fact that at ca. 0.15 mole fraction both systems have a similar z, value for these various sized alkan-1-01s complexed with two different sized ethers, rules out the relaxation process at low concentrations from being entirely the molecular relaxationH. Mandal et al. 3055 of 1 : 1 and 1 : 2 complexes. The process itself, at these lower concentrations, as judged solely from z, considerations, may first be thought of as being independent of chain length. However, when AHE values are also taken into account, this interpretation would seem too simple. (D) Test of a Relaxation Mechanism for the 7, Process Above we have seen that, in the main, the experimental data for methanol in a variety of solvents are consistent with the switching mechanism advanced by Sagal." The closest theoretical treatment is one proposed by Higasi and co-workers" where they deduced an equation which relates the principal relaxation time to the mole fraction of the solvent (x& the absolute temperature, the energy of activation and some other parameters.The equation applies to alkan- 1-01s in inert and weakly interacting solvents. Higasi and co-workers1° tested their equation by comparing the measured and estimated z, values for ethanol/cyclohexane, hexan- 1 -ol-cyclohexane, and propan- 1 - 01-benzene solutions in the temperature ranges 268-323, 288-308 and 283-3 13 K, respectively, and found that the measured and estimated values agreed quite well.The data we have obtained enabled us to extend the test of their key equations over a wider temperature range and to a wider variety of alkan- 1 -01s, especially to methanol and those with long chain length. The theory itself does not directly take into account the chain length of the alkan-1-01, and with our findings under (C) in mind, further testing of the theory for longer chain lengths seems essential. For details of the Higasi model the initial papers should be consulted.'0 This model, of which we gave a pictorial account in our introduction, is essentially a dipole-inversion process arising from the cooperative rotation of the -OH group of the multimers.The key equation obtained by Higasi and co-workers, which may be employed to calculate TI, 1s: where a and p are constants characteristic of the solution being examined, E,(O) is the energy of activation of the pure alkan-1-01 where and E,(O) and a are obtained from the straight-line plot of Ea(xB) against x,. When In Tz, is plotted against 1/T, a straight line ensues, which at a given mole fraction of solvent (x,) has a slope E,(x,)/R while the point of intersection with the ordinate axis yields a term In [A(xB)] which enables A ( 0 ) and p to be obtained from the equation : A plot of the left-hand side of eqn (6) against x, gives a straight line where p is obtained from the slope and ln[A(O)] from the intercept. From these data it is then feasible to calculate z, at various concentrations by means of eqn 4, and in fig.5-9 this has been carried out. This approach has been applied to the systems: (a) methanol in toluene at 200, 225 and 293 K (methanol is insufficiently soluble in the inert solvent, n-heptane); (b) butan- 1-01, hexan- 1-01, octan- 1-01 and decan- 1-01 in n-heptane and toluene at 200 and 293 K. Comparisons between the experimental z1 values and the ones from eqn (4) are made in fig. 5-9 from which we conclude that: (1) in fig. 5 it is apparent that at all three temperatures for methanol in toluene, the agreement between the experimental and estimated values is good; (2) on the whole, butan-1-01 also exhibits good agreement between the experimental and estimated z, values for both temperatures and both3056 Relaxation of Alkan-1-01s solvents.The agreement is not so good for hexan-1-01, particularly in toluene. For octan-1-01 some definite deviations are noted (see fig. 6 and 9), while for decan-1-01 serious deviations are apparent (see fig. 6 and 8); (3) on the whole, the deviation between the experimental and estimated t, values increases with increasing chain length. Conclusions I . For all the alkan-1-01s examined, except ethanol, AHE decreases appreciably on dilution with diethyl ether and di-n-butyl ether, the change being more appreciable in the former than in the latter. At a particular concentration the length of both types of chains appears to influence AHE. When diethyl ether is the solvent, at 0.15 mole fraction the extrapolated AHE value of each alkanol is of the order of the strength of the intermolecular hydrogen bond, whereas, when di-n-butyl-ether is the solvent, the extrapolated value is almost double this.2. A detailed study of methanol in weakly and strongly hydrogen bonding solvents gives strong support for the switch-over type of mechanism first proposed by Sagalll and later developed by Higasi and co-workers" on a more theoretical level. A recent dielectric study by Huque and Walker13 on 2,6- and 2,4,6-halogenophenols lends further support to the lowering of the energy barrier in a switch-over mechanism. They found that relaxation of the OH group between two identical intramolecular hydrogen- bonding sites significantly lowers the energy barrier. This result is in harmony with the switch-over mechanism as conceived by Sagal.However, it must be stressed that very different geometric constraints exist for OH group relaxation in the intramolecularly hydrogen-bonded 2,6-disubstituted phenols and the intermolecularly hydrogen-bonded alkanols. 3. A suitable theory on which to test the switch-over mechanism is one developed by Higasi and co-w0rkers.l' However, the theory does not involve directly the alkyl chain length of the alkan-1-01, and, as a consequence, we have examined this aspect by employing five representative alkan- 1-01s ranging from methanol to decan- 1-01 in solution over a wide temperature range. Good agreement between the experimental and estimated t, values is obtained for the methanol and butan-1-01 solutions, but, in general, deviations between these values increase with the lengthening of the chain while the most appreciable deviations occur for decan- 1-01 solutions. We conclude that for the alkan- 1-01s in solutions of inert and weakly interacting solvents the switch-over mechanism seems a satisfactory one to account for the principal relaxation process, while the treatment of Higasi and co-workers1' for this is more than adequate for the shorter-chain alkan- 1-01s.4. In principle, it would be desirable to make dielectric measurements at much lower concentrations than we have employed. However, as Cro~sley'~ pointed out from his dielectric studies, the t, process, which dominates the absorption of pure liquids is notably absent in dilute solution but becomes evident at intermediate concentrations.It must remain a matter for conjecture as to whether more sensitive relaxation methods than the dielectric absorption techniques would detect the phenomenon at lower concentrations. From a mechanistic behaviour point of view this would be a most interesting type of study. S. W. expresses his gratitude to the National Research Council of Canada for financial support of this work and to Mr B. K. Morgan for invaluable technical support of this work over the four years in which it was carried out.H. Mandal et al. 3057 References 1 C. J. F. Bottcher and P. Bordewijk, Theory ofElectric Polarizafion (Elsevier, Amsterdam, 1978), vol. 11. 2 L. J. Bellamy, Infrared Spectra of Complex Molecules (Chapman and Hall, London, 1975). 3 G. C. Pimentel and A. L. McClellan, The Hydrogen Bond (W. H. Freeman, San Francisco, 1960). 4 S. N. Vinogradov and R. H. Linnell, Hydrogen Bonding (Van Nostrand Reinhold Company, New 5 C. Brot, M. Magat and L. Reizisch, Kolloid Z . , 1953, 134, 101. 6 S. K. Garg and C. P. Smyth, J. Phys. Chem., 1965, 69, 129. 7 W. Dannhauser, J . Chem. Phys., 1968, 48, 191 I ; 1918. 8 W. Dannhauser and A. F. Fleuckinger, Phys. Chem. Liquids, 1970, 2. 37. 9 G. P. Johari and W. Dannhauser, Phys. Chem. Liquids, 1972, 3, 1. York, 1971). 10 R. Minami, K. Itoh, H. Sato, H. Takahashi and K. Higasi, Bull. Chem. SOC. Jpn, 1981,54, 1320; 3684. 1 1 M. W. Sagal, J. Chem. Phys., 1962, 36, 9. 12 T. Koshii, H. Takahashi and K. Higasi, Bull. Chem. Soc. Jpn, 1975, 48, 993. 13 M. E. Huque and S. Walker, Chem. Phys., 1989, 130, 345. 14 M. E. Huque and S. Walker, J. Chem. Soc., Faraday Trans. 2, 1986, 82, 51 1. 15 S. R. Gough and A. H. Price, Trans. Faraday SOC., 1965, 61, 2435. 16 H. Mandal, D. G. Frood, M. A. Saleh, B. K. Morgan and S. Walker, Chem. Phys., in press. 17 J. Crossley, J. Phys. Chem., 1971, 75, 1790. Paper 9/00280D; Received 17th January, 1989

ISSN:0300-9599    

DOI:10.1039/F19898503045

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

J . Chem. SOC., Fclraduy Trans. I, 1989, 85(9). 3059-3069 Numerical Interpretation of Oscillatory Glow and Ignition during Carbon Monoxide Oxidation in a well-stirred Flow Reactor John F. Griffiths" and Anne F. Sykes School of Chemistry and Centre for Non-Linear Studies, The Uniuersity, Leeds LS2 9JT Numerical results are presented which give very satisfactory simulations of the oscillatory glow and ignition phenomena that accompany the thermal oxidation of carbon monoxide in a well-stirred flow vessel, when small proportions of hydrogen are present in the reactants. Quantitative comparisons are made with experimental results not only in relation to the amplitudes of oscillations but also the p-T, regimes in which the different phenomena exist. The origins of oscillatory ignition are traced to the competition between the elementary reactions H + 0, + OH + 0 and H +0,+M + HO,+M, as occurs in the oxidation of hydrogen itself. A change in overall third body efficiencies, that results from changes in composition as reaction proceeds, controls the switch from branching to non-branching reaction.The oscillatory glow originates in a different kinetic competition namely 0 + H, + OH + H and 0 + CO + M CO, + M. In this case the switch from a branching to non-branching reaction is governed by the change in ratio of [H,]/[CO] as reaction proceeds. The prediction of the oscillatory phenomenon is sensitive to the magnitude of the rate constant for termination. From the earliest developments of branching chain reaction theory'*2 there have been very close links between experimental and theoretical studies of the spontaneous oxidation of carbon monoxide and of hydrogen, and the two systems are commonly discussed simultaneously.3-6 The reason behind this, and the widely accepted kinetic view, is that the chain branching of hydrogen oxidation (involving H and 0) is invariably imposed on the oxidation of carbon monoxide : it seems to be impossible to free the experimental CO + 0, system sufficiently from hydrogenous compounds to avoid this interference. Indeed, we do not need very high concentrations of hydrogen in the CO + 0, system (> 1 mol YO per mole of CO, say)' for the overall features to be dominated by those of H, + 0, itself. One very interesting feature of carbon monoxide oxidation that distinguishes it from that of hydrogen is the occurrence, under certain conditions, of an isothermal oscillatory glow (CO;).The oscillatory reaction takes places in mixtures that contain less than ca. 1 mol YO of hydrogen-containing compounds. It was first detected and studied in closed '-12 The corresponding oscillatory glow associated with reaction under well- stirred flowing conditions was investigated in detail subsequently by Gray et al.13 using equimolar mixtures of CO + 0, to which controlled proportions of hydrogen were added. The purpose of the present numerical study is to correlate the simulations of oscillatory ignition and glow phenomena under well stirred flowing conditions with the experimental observations, and from this to identify the principal kinetic features that control events.An established kinetic mechanism is exploited in the numerical study. 101 3059 F A R I3060 Numerical Simulation of Carbon Monoxide Oxidation Experimental, kinetic and numerical background Experimental Methods and Principal Results Carbon monoxide was oxidized in a mechanically stirred, flow reactor (Pyrex glass, 0.5 dm3) located in a recirculating air f ~ r n a c e . ' ~ ' ~ ~ Reactant pressures and flow rates were controlled by a high pressure supply upstream, and a pumped outlet downstream of the vessel. Reactant temperatures were measured by thermocouple, reactant and product concentrations by mass spectrometer and light output by photomultiplier. Total reactant pressures of up to 100 Torr'f were studied at a mean residence time of 8.5+ 1.0 s. A range of reactant compositions was studied comprising CO (99.950%) and 0, (99.985 YO) in equimolar proportions, supplied directly from cylinders without further purification, to which were then added 0, 150, 1500 and 7500 ppm H, (99.999%) in successive experiments.In each case the most prominent features of the (pQ ignition diagrams were the regions in which a steady glow and an oscillatory glow were observed. However, as the proportion of hydrogen present was raised (1 50 -+ 7500 ppm), an ignition peninsula, characteristic of that of hydrogen oxidation, encroaches on the glow regions of the ignition diagram (fig. 1). Supplementary studies of the composition 0.2H2 + 0.8CO + 0, gave ignition characteristics that could be accounted for quan- titatively as those of hydrogen oxidation in the presence of CO acting principally as a third body on the formation of H0,.15 The oscillatory glow was no longer seen and the steady glow was virtually completely masked by the ignition region of this particular mixture. Kinetic Model and Background to Oscillatory Ignition The present work is linked to a recent analytical, numerical and experimental study of the oscillatory combustion of hydrogen in a jet-stirred, flow react~r.'~-'~ The kinetic mechanism developed in that work constitutes the foundation to this numerical study.Four elementary reactions were added to account for the oxidation of carbon monoxide (table 1). To account for the differences in behaviour observed at the first limit due to the presence of the stainless steel rotor in the vessel used for the CO s t ~ d i e s , ' ~ ~ ' ~ the kinetic parameters for the rates of termination of radicals at the wall under low pressure conditions were increased for the present analysis from the values used previo~sly.'~ A correction for the diminishing effect of surface termination at higher reactant pressures was incorporated in these rate constants as an inverse pressure dependence. The existence of oscillatory ignition and its frequency in hydrogen combustion in a well stirred flow reactor are linked to the competition between the chain branching and non-branching elementary steps H+O,-+OH+O (3)l H+O,+M+HO,+M. ( 5 ) Which of these two steps dominates at a given vessel temperature and reactant pressure within the ignition region is governed by the overall, third body efficiency of M (table I ) in the non-branching route ( 9 , as determined by the composition of the reactants and products in the vessel at a particular time.16-19 A change of efficiency is brought about by the displacement of the reaction products from the vessel by inflowing reactants.t 1 Torr = 133.322 Pa. Equation numbering is consistent with the order in table 1.J . F. Grifiths and A . F, Sykes 306 1 1 - 1 I 1 I I r- 725 750 775 800 825 T, /K Fig. 1. Experimental (pT,) ignition diagram for CO + 0, containing amounts of added hydrogen (indicated on each ignition boundary as ppm of the total mixture). The regions marked dark reaction, steady glow and oscillatory glow (broken line boundaries) are revealed provided that they have not been engulfed by the encroaching ignition boundary.The ignition limit for 0.8CO + 0.2H2 + 0, is also shown. Numerical Methods The numerical program, PJSPRINT,~~ permits the interactive simulation of well-stirred flow experiments. The first-order differential expressions representing spatially-uniform temperature and the concentrations of the 11 species in the kinetic scheme are integrated simultaneously using the LSODE Reactant compositions, pressure and mean residence time, and the vessel temperature define the control parameters. Normally an initial condition is set which represents the displacement of a non-reactive gas from the vessel by the reactants at the operating pressure and temperature, although a variety of other procedures may be exploited to accommodate different experimental methods.An important facility of PJSPRINT is the ability to change the simulated vessel temperature during the course of the calculations in just the way that changes are made experimentally to map out the main features of the (pT,) ignition diagram. Our principal interest lies in the stationary-state behaviour rather than the dynamics leading to its attainment. Thus, integration is continued until a stationary-state is attained or an unstable oscillatory mode is sustained reproducibly. Numerical Predictions Four different reaction modes from the numerical analysis may be distinguished, as follows : (i) stable (non-oscillatory) reaction, (ii) small amplitude oscillations, as measured by the proportion of CO consumed, (iii) large amplitude oscillations in which all of the CO and H, are consumed, (iv) biperiodic sequences comprising small amplitude oscillations interpersed by the large amplitude event.101-23062 Numerical Simulation of Carbon Monoxide Oxidation Table 1. Reaction mechanism, kinetic and thermochemical data for simulation of carbon monoxide reaction A/[(mol-l m3)11-1 s-'1 ( E / R ) / K - 1 H,+O,+HO,+H H,+OH -, H,O+H H + 0 , + OH +O H,+O + OH +H H+O,+M +HO,+M "H -+ inert at wall "0 + inert at wall "OH + inert at wall HO, + inert at wall HO, + HO, + H,O, + 0, HO,+H + H,O+O HO,+H,+H,O,+H HO,+H, + H,O+OH HO,+H+H,+O, H,O,+M +OH+OH+M H20+H-+H,+H0, H,O,+H+H,O+OH H,O, +OH + H,O + HO, H,02+O+OH+H02 H,O+H + H,+OH OH +O + 0, + H OH+H + H,+O OH+OH + H,O+O H+OH+M+H,O+M H+O+M+OH+M H+H+M+H,+M OH+OH+M +H,O,+M O+O+M+O,+M 31 HO,+OH --* H,O+0, 11 HO,+H -+ 20H 21 H,O+O + 20H H,O+M+H+OH+M H,+M+H+H+M O,+M-+O+O+M CO+O+M+CO,*+M CO+OH+CO,+H CO + HO, + CO, +OH co; -+ co, 3.10 x 107 1.95 x 107 6.56 x 107 7.00 x 103 1.15 x lo8 500 50 50 0 2.00 x lo6 1.50 x 10' 3.00 x lo8 7.30 x 105 6.50 x 105 2.50 x 107 1.00 x 107 2.80 x 107 8 .5 7 ~ 107 1.80 x 107 2.80 x 105 1.26 x 104 1.03 x 103 1.20 x 10" 1.70 x lo6 7.13 x lo6 8.86 x lo7 4.00 x lo6 6.30 x lo6 9.10 x 10, 5.00 x 10, 6.00 x lo6 2.20 x 1O'O 2.20 x 10' 1.20 x 10' 1.20 x 103 3.00 x 105 2.00 x 103 1.00 x lo6 28 700 2 850 7 619 5 337 - 605 0 0 0 0 0 506 2 000 9 400 9 400 3 50 20 000 1 900 1810 736 3 224 9 509 10 526 0 3 500 550 0 0 0 -2 500 0 0 52 920 48 350 54 250 2 184 500 10 000 0 238 651 70 660 8 247 - 199 451 0 0 0 0 -177 163 - 159 707 -236 170 -64 000 61 488 223 200 217 288 - 238 65 1 -61 488 -285 257 - 125 549 -53 271 72 279 64 000 -70 660 - 8 247 -72 279 -502 544 -430 266 -438 483 -217 587 - 503 026 -303 576 505 682 441 475 503 026 533 640 103 342 265 265 0 Third-body efficiencies relative to that of hydrogen reaction 5 0.4 6.4 0.2 1.5 reaction 35 12.0 3 .O 7.0 - a Values at p = 10 Torr.J .F. Grifiths and A . F. Sykes r 15-1 3063 -7 - E“ 10- \ N 3 z m 5- 2 0 I I 1 1 I I I I 40 45 50 55 60 65 70 75 ao tlS Fig. 2. The predicted changes of reactant concentration and [CO:] during oscillatory glow in CO + 0, containing 0.4 mol O/O H, (4000 ppm) at = 780 K and p = 45 Torr. These oscillatory modes are exemplified below. The compositions assumed for these simulations correspond to an equimolar CO + 0, mixture containing 0.4 mol % H,.The small amplitude oscillations simulate the oscillatory glow observed experimentally (fig. 2 and 3). Only a small proportion of the carbon monoxide is consumed during each cycle, and even some of the hydrogen remains. The predicted ‘quantum yield’, determined from the moles of CO,* produced per mole of CO consumed in each cycle, is ca. 1 quantum per 1.5 x lo5 molecules of CO reacted. The CO,* profile follows a rather slow rise and decay, changing in concentration by up to an order of magnitude between the minimum and maximum of each cycle and matching the rather lazy waxing and waning of the feeble light pulses observed experimentally, especially at the lowest pressures (fig. 3).Only very small temperature changes are predicted to occur. By contrast, all of the carbon monoxide and all of the hydrogen is consumed during ‘oscillatory ignition’ (fig. 4) and, at a given vessel temperature, the frequency of oscillations is related to the supply rate of inflowing reactants. The reactant temperature is predicted to reach the adiabatic limit during each excursion. This is not obtained experimentally because the measuring thermocouple has a finite response time of ca. 130 ms. (Baulch et a1.l’ made corrections for the thermocouple response in their numerical simulation of oscillatory ignition in H, + 0, and produced a very satisfactory correlation between numerical and experimental results.) The third, biperiodic, oscillatory mode is represented in fig.5. A change of conditions, such as raising the vessel temperature, increases the number of successive ‘glows’ that occur between each ‘ignition ’. Only feeble extents of reaction accompany the non-oscillatory reaction mode. However, we are unable to distinguish readily any discontinuity of the dependence of the calculated CO,* or 0 atom concentrations on the reaction conditions that could be construed as a distinction between the experimentally observed steady glow or dark reaction modes.3064 \ - Numerical Simulation of Carbon Monoxide Oxidation - o*221 P 0 1 - 10 15 20 25 30 35 40 45 50 tls Fig. 3. The predicted changes of reactant concentration, [CO:] and AT during oscillatory glow in CO + 0, containing 0.4 mol % H, at T, = 750 K and p = 20 Torr.The Predicted (pT,) Ignition Diagram The (pT,) regions in which the above reaction modes exist are shown in fig. 6. Also imposed on this figure is the experimental ignition diagram for the equimolar mixture CO+O, to which 0.15 mol O h H, has been added. These results show extremely satisfactory accord between the location of the lower, oscillatory glow limit and of the upper (or second) oscillatory ignition limit. The location of the biperiodic oscillatory mode coincides with the experimental division between the oscillatory glow and ignition. These phenomena were observed experimentally by Scott22 at the interface between oscillatory glow and ignition. The region for the existence of the mixed oscillations was not characterised completely in the experimental study.Dependence on Proportions of Hydrogen If the proportion of hydrogen in the reactant composition is increased beyond 1 mol O/O the predicted oscillatory ignition limit moves towards the left hand side of fig. 6, its lower pressure limit is reduced and the oscillatory glow region is engulfed within the ignition peninsula. A reduction of the proportion of hydrogen in the reactant composition expelsJ . F. Grijiths and A . F. Sykes 3065 0.3 m ‘E z 0.2 E 1 - 0.1 0.0 25 YE 20 & 0 -% - 15 N 2 i p 10 5 0 I 15 20 i 1 I 30 35 t l S I 40 45 50 Fig. 4. The predicted reactant concentration changes during oscillatory ignition in CO + 0, containing 0.4 rnol % H, at T, = 760 K and p = 45 Torr. the oscillatory ignition region towards the right hand side of fig.6 exposing a region of non-oscillatory reaction. The (p-T,) region which simulates oscillatory glows does not vary much. Calculations on compositions containing less than 0.05 mol YO H, did not exhibit oscillatory glow under any conditions. Simulations of the ignition phenomena did not occur in compositions containing < 0.1 mol YO H,. Discussion We believe that the oscillatory reaction modes shown in fig. 2-5 are appropriate numerical sumulations of the phenomena observed experimentally by Gray et aZ.13 Moreover, apart from the absence of a distinction between the steady ‘dark’ and steady ‘glow’ reaction modes, there is satisfactory quantitative accord between the numerical and experimental ignition diagrams (fig. 6). That we are able to predict the existence of the oscillatory glow in the presence of hydrogen at concentrations down to 0.05 mol YO (500 ppm) is broadly consistent with experiments in the absence of added hydrogen when research grade, cylinder CO is supplied to the flow system without further purification.The difference in fig. 6 between our computation at 0.4 mol O/O H, and the experimental measurement made at 0.15 mol O h (1500 ppm) added hydrogen must relate, in part, to the unknown amount of hydrogenous components already present in the cylinder CO used in the experiments.3066 Numerical Simulation of Carbon Monoxide Oxidation 4, 5 10 15 20 r I 25 30 35 40 tls Fig. 5. The predicted changes of reactant concentration and [CO:] during biperiodic oscillations in CO+O, containing 0.4 mol % H, at T, = 765 K and p = 45 Torr.The number of ‘glows’ interspersing each ‘ignition’ is modified by changes of the control temperature. Kinetic Sensitivity and the Existence of Oscillations Two extremely important kinetic competitions occur in the oxidation of carbon monoxide in the presence of hydrogen. The first, already discussed in the Kinetic Background, and now termed C l for convenience, is H+O,+OH+O ( 3 ) H+O,+M+HO,+M. ( 5 ) The second, to be called C2, involves 0 atoms, as follows: O+H,-+OH+H (4) O+CO+M +CO,+M. (3 5 ) In each of these pairs a bimolecular branching step competes with a termolecular non- branching reaction (which is a termination step in the case of C2). Notwithstanding this common form, each pair of reactions operates in a different way and plays a different role in carbon monoxide oxidation. Flowing conditions are a prerequisite for the existence of oscillations.Temperature change is not essential, but it is an inevitable accompaniment; the extent to which it occurs is governed by the rate and extent of reaction that takes place.J . F. Griflths and A . F. Sykes 3067 100 I2 4 s 50 dic ions 0 725 750 775 800 825 K, /K Fig. 6. The (p-T,) regions for the existence of the simulated oscillatory phenomena in CO+O, containing 0.4 mol O h H,. The experimental results from CO + 0, containing 0.15 mol % H, are marked in as the broken lines. The region exhibiting biperiodic oscillations was not characterised by Gray et a1.,13 although events of this kind were observed by them.2g Oscillatory Ignition The existence of oscillatory ignition is controlled by C l in exactly the same way as in all of the CO is consumed, mainly via (36), considerable amounts of heat are produced and the adiabatic temperature is reached.There is an excess of 0, in equimolar mixtures with respect to the complete oxidation of carbon monoxide, so that co + 0.50, = CO,, from which AXga = -286 kJ per mol CO reacted. The contribution to the overall exothermicity due to the formation of water, namely H, + 0.50, = H,O; AZg8 = - 242 kJ mol-’ H,, is determined by the proportion of hydrogen present relative to the carbon monoxide and by the relative exothermicities at complete oxidation. Enough water is formed at ignition that the rate constant for (9, governed by the third-body efficiencies of the molecular components (see table l), is enhanced sufficiently for the termolecular reaction to dominate in C1.A period follows ignition during which overall ‘slow’ reaction takes place. The switch back to domination by chain branching and a subsequent ignition is controlled by the diminution of A , as the composition within the reactor reverts to predominantly hydrogen and oxygen by inflow of fresh reactants. 16-19 Although the existence of oscillatory ignition itself is not dependent upon the relative proportions of hydrogen and carbon monoxide present, the (p-T,) location of the second ignition limit is controlled by the ratio of reactant concentrations. Gray et have set out analytical expressions based on simplified kinetics which show the relationship between the location of the ignition boundary and the reactant composition ; the computed results based on the present reaction scheme (table 1) are to be reported elsewhere.An increase of the pressure at the first limit is also predicted in the analytical3068 Numerical Simulation of Carbon Monoxide Oxidation deri~ation,'~ although the simplifications involved mean that the effect is not as pronounced as that measured experimentally, as shown in fig. 1. Oscillatory Glow Cl remains in its non-branching mode (5) throughout the course of oscillatory glow. Thus the glow occurs outside the ignition peninsula, and is below the first limit. By contrast, C2 switches from the predominance of branching (4) to the predominance of termination (35). The 'switching off' of the branching mode as reaction proceeds results from a shift in the [H,]/[CO] ratio from typically 4.5 x at the peak in the [CO] amplitude to typically 3.0 x lo-, at the minimum in [CO] (see figure 3, for example).This is due to a considerable change in the proportion of H, present (ca. 30 YO consumption) relative to the very small change in CO (ca. 1 % consumption). The [H,]/[CO] ratio reverts to the higher value as fresh reactants flow into the vessel. Some features of carbon monoxide oxidation in closed vessels23 were shown to be accounted for similarly by changes of the [H,]/[CO] ratio. The oscillatory glow is not controlled by any aspect of the changing overall third body efficiencies in either of the termolecular reactions (5) or (35). The oscillatory glow is predicted to exist only in a very small range of values for the termination rate constant (35).At 50 Torr and 780 K with the current data set. the range of values of A,, within which oscillatory glow is predicted, is ca. (0.5-50) x lo3 mol-, mP6 s-l. The range can be extended or modified by change of vessel temperature or proportion of hydrogen present. Biperiodic Oscillations Oscillatory phenomena which comprise ignitions interspersed by glows are possible because conditions are accessible in which C2 is able to switch from branching to termination even during the non-branching phase of C1, in the interval between the ignitions. The authors thank the S.E.R.C. for financial support. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 N. N. Semenov, Chemical Kinetics and Chain Reactions (Clarendon Press, Oxford, 1935).C. N. Hinshelwood, The Kinetics of Chemical Change (Clarendon Press, Oxford, 1940). J. G. Minkoff and C. F. H. Tipper, The Chemistry of Combustion Reactions (Elsevier, Amsterdam, 1962). G. Dixon-Lewis and D. J. Williams, in Comprehensive Chemical Kinetics, ed. C. H. Bamford and C. F. H. Tipper (Elsevier, New York, 1977), vol. 17, p. 1. C. K. Westbrook and F. L. Dryer, Prog. Energy Combust. Sci., 1984, 10, 1. P. Gray and S. K. Scott, in Oscillations and Traveling Waves in Chemical Systems, ed. R . J. Field and M. Burger (Wiley, New York, 1985), p. 493. P. Gray, J. F. Griffiths and S . K. Scott, 20th Int. Symp. Combustion (Combustion Institute, Pittsburgh, 1984), p. 1809. P. G. Ashmore and R. G. W. Norrish, Nature (London), 1951, 167, 390. P. G. Dickens, J. E. Dove and J. W. Linnett, Trans. Faraday SOC., 1964, 60, 559. B. J. McCaffery and A. L. Berlad, Combust. Flame, 1976, 26, 77. J. R. Bond, P. Gray and J. F. Griffiths, Proc. R . SOC. London, Ser. A , 1981, 375, 43. J. R. Bond, P. Gray and J. F. Griffiths, Proc. R. SOC. London, Ser. A , 1982, 381, 293. P. Gray, J. F. Griffiths and S . K. Scott, Proc. R. Soc. London, Ser. A , 1985, 397, 21. P. Gray, J. F. Griffiths and S . K. Scott, Proc. R. SOC. London, Ser. A , 1984, 394, 243. P. Gray, J. F. Griffiths and S. K. Scott, Proc. R. SOC. London, Ser. A , 1985, 402, 187. K. J. Chinnick, C. Gibson, J. F. Griffiths and W. Kordylewski, Proc. R. SOC. London, Ser. A , 1986,405, 117. K. J. Chinnick, C. Gibson and J. F. Griffiths, Proc. R . SOC. London, Ser. A , 1986, 405, 129. D. L. Baulch, J. F. Griffiths, A. J. Pappin and A. F. Sykes, J . Chem. SOC., Faraday Trans. I , 1988, 84, 1575.J. F. Grifiths and A . F. Sykes 3069 19 D. L. Baulch. J. F. Griffiths, A. J . Pappin and A. F. Sykes, Combusr. Flume, 1988, 73, 163. 20 p. Jacoby, unpublished work, developed from M. Berzins and R. M. Furzeland, T.N.E.R. 85058, 1985, 21 C. M. Lund. HCT, UCRL-52504 (Livermore, University of California, 1978). 72 S. K . Scott, Ph. D. Thesis (University of Leeds, 1982). 23 K. J. Chinnick and J. F. Griffiths, J. Chem. SOC., Faradap Trans. 2, 1986, 82, 881. Shell Research Ltd. Puper 91007 191 ; Received 15th February, 1989

ISSN:0300-9599    

DOI:10.1039/F19898503059

出版商:RSC    

年代:1989

数据来源: RSC

摘要:

Reviews of Books Impedance Spectroscopy. Emphasizing Solid Materials and Systems. J . R. Macdonald. (Wiley, Chichester, 1987.) Pp. xvi + 346. Price E41.25. This is an interesting and timely book, covering an area that has grown enormously in importance in the last ten years. The primary thrust of the book is in the area of solid-state electrochemistry, and it is here that the reader will find it most useful. Other areas of application are dealt with, although the authors prove appreciably less sure-footed once they stray from the mainstream of solid electrolytes. The book is a collection of articles written by a number of well known authorities on impedance analysis and solid-electrolyte studies. These articles are preceded by an introduction, written by J. R. Macdonald and W.B. Johnson, which describes the nature of the techniques used in the analysis of the ax. response of solid and liquid electrolytes and electrolyte/electrode interfaces. The introduction also contains some important caveats to the would-be user of impedance spectroscopy (IS), and introduces one of the central problems in analysis: the use and interpretation of circuit elements in equivalent-circuit analysis. Probably the most significant difficulty encountered in this type of analysis, a difficulty emphasised throughout the book, is the existence of ‘distributed’ circuit elements. These have played an increasingly important role as the inadequacy of finite combinations of ideal resistors, capacitors and inductances in the fitting of experimental data has been demonstrated. Characteristic of these elements is the fact that the impedance is related to the frequency through a power law.Owing to the mathematical properties of the Kramers-Kronig transform, a power law in the imaginary part of the impedance of an element will lead to a power law in the real part, and the ratio of the two, which determines the phase angle of the element, is then independent of the frequency. Such elements are said to possess a constant phase angle (CPA), and the origin of this behaviour and its ubiquity has been the subject of lively debate. This debate is fundamental to the subject since different models attach quite different significance to the parameters derived from a least-squares fit; the only common point is that such power laws are associated with a distribution, either in space or time, of the microscopic quantities underlying a particular theory.A second difficulty, emphasised in chap. 2 (on theory) is that for all but the simplest equivalent circuits, there is an ambiguity associated with the particular choice of circuit, and this can only be resolved by appeal to a physical model. Additional difficulties and problems include the incorporation of adsorption effects, which can lead to negative capacitances, and fitting problems associated with complex non-linear least-squares fitting. This latter problem is reviewed in depth and some very valuable comments are made. A computer program is also available from the authors incorporating the caveats made in the text, and the computational approach is described in chap.3. The third chapter also reviews measurement techniques and can be recommended unreservedly, particularly to those who may believe that the acquisition of expensive frequency-response analysers is a substitute for careful design of cell, leads and electronics. The serious problems associated with inherent precision are fully dealt with, and the use of Kramers-Kronig integrals and the coherence function as indispensible tests for long-term stability are also treated clearly. The final chapter reviews applications of impedance spectroscopy to three areas. The first, on characterisation of materials, pays particular attention to the microstructural information to be gleaned in ceramic research. It describes both the basic theoretical understanding of the a.c. response of inhomogeneous media and experimental data on a number of selected fast-ion conductors.Particularly helpful in this section was the incorporation of results from electron microscopy: combination of this with conductivity data for p-alumina has permitted the development of a coherent picture of this material. The second section covers ‘Solid State Devices’ and here the touch is less sure, with a rather eclectic coverage of examples. The final section is an interesting account of the application of IS to corrosion research. A variety of approaches are 307 13072 Reviews of Books discussed and simulations of a wide range of impedance plots given; a discussion of some recent work on crack propagation and growth is also provided.The main impression given by the book is very positive. Inevitably, as with all multiple-author texts, some repetition of material has occurred. Each author has tended to develop independently the theory needed to describe a given area and this has some unforeseen effects. For example, the Kramers-Kronig relationships appear in every chapter save the one on theory, with the result that the physical basis of these relationships is never discussed, and they are introduced ex cathedra. There is also a plethora of unfamiliar acronyms to digest, especially in the theory chapter. It is important to recognise that such acronyms detract appreciably from the value of any reference text unless, as was not done here, the authors are prepared to supply a key. Nevertheless, the superficial flaws do not fundamentally alter the great usefulness and timeliness of this text; it will be an indispensible handbook for electrochemists, particularly those concerned with solid electrolytes, for a long time to come.A. Hamnett Received 14th April, 1988 Physical Chemistry of Inorganic Crystalline Solids. H. F. Franzen. (Springer-Verlag, Berlin, 1986.) Pp. ix+ 158. Price DM 92. This is an eclectic text that contains much of interest to anyone active in the field of solid-state chemistry. Nevertheless, it will not be a particularly popular text, nor one that encourages reference. In some ways, this is a pity: in a book that is, by modern standards, commendably short, Franzen covers an enormous amount of ground. In the course of the book, however, the author evolves a style more reminiscent of a grammatical primer, with proofs reduced to rather less than the bare essentials, and with a level of treatment that makes widely different demands on the reader in different chapters.There is, in addition, a surprising number of misprints and solecisms in an otherwise beautifully printed text; there are also some errors. e.g. VO, is described, on p. 47, as possessing the CaF, structure. The author is at his surest in his discussions of the structural features of solid-state chemistry. Chap. IV contains a good account, at an elementary level, of the structural chemistry of a wide range of inorganic materials, including many that would not normally feature in a textbook at this level. Chaps. VIII and IX cover diffraction methods and orderdisorder phenomena.The former is unusual in treating orderdisorder and superstructure lines, including those derived from incommensurate ordering. In chap. IX, the Landau theory of symmetry and phase transitions is applied to a number of examples of order-disorder processes in inorganic materials, treating first the classic CsC1-type to b.c.c.-type transition in CuZn, and extending the discussion to vacancy ordering in Sc,.,S (NaCI to CdCl, type) and Cr,.,S (NiAs to CdI, type). These considerations are extended, in the final part of the chapter, to more complex ordered structures, where the details of the site occupancy are, as yet, not fully understood. These three chapters are of considerable interest, covering material that is difficult to locate at the textbook level, and employing a theory that is still unfamiliar to the vast majority of physical and inorganic chemists. The earlier chapters are concerned with symmetry and here the touch is less sure.The introductory material, in chap. I, reviews traditional solid-state concepts and discusses their applicability to the wide range of inorganic solids. The author emphasises throughout this chapter the important, though to most chemists now familiar point that models which only consider metal-non-metal interactions cannot account for the bonding in metal-rich solids such as Ti0 or Zr,S. The author also introduces the Engel-Brewer model for the rationalisation of the structures of simple metals. Like the celebrated VSEPR model for rationalising molecular structures, to which it bears some relation, the Engel-Brewer model has been the subject of considerable recent computational investigation. The root causes of the undoubted success of these models remain uncertain, although it does appear that a rationale in terms of d-band occupancy is equally successful in predicting metallic structure.Rather unfortunately, the author does not give any references to more recent work on models for rationalising metal structures, and indeed, the book is not well referenced in general. The second and third chapters are concerned with symmetry. The approach is to introduce many of the concepts in two dimensions, prior to an extension in chap. I11 to three dimensions. These chapters will not prove useful to those unfamiliar with the symmetry operations associatedReciews of Books 3073 with a crystalline lattice.The treatment is far too cursory to have any pedagogical value and I could not find a single reference to any of the more specialised monographs on symmetry in solids, or indeed a single literature reference of any sort in chap. I1 and 111 together. Symmetry considerations are also taken up in chap. VI, which covers the concept of reciprocal space and the deduction of the irreducible representations of the space groups. The whole of this topic is dealt with in nine pages, and once more there are no references to any further, more thoroughgoing texts. I believe that this is a great pity: an overview, such as that provided by the author, can only be of value if the student is given careful guidance in the pursuit of points of difficulty, of which there is no shortage in this area.Prior to this chapter, there is a discussion of the thermodynamics of solids, the main thrust of which is a treatment of non-stoichiometry. The theoretical development is reasonably clear, although the introduction provided to the theory of regular solutions in V.11 is, again, really too cursory to be of value. The final chapter considers some aspects of band theory. The point made in chap. I about the electronic structure of metal-rich solids is amplified by a consideration of the band structure of ZrS, and various interpretations of the calculation are provided. Probably the most important, if rather depressing conclusion, is that ‘the success of the simple models for the rock-salt structure is highly dependent upon [its] high symmetry, which provides very few alternatives for first approximation to the electronic configurations of the atoms ’.The overriding impression left by this chapter is just how far there is yet to go in the interpretation of even very simple band- structure calculations in terms of concepts familiar to chemists. A. Hamnett Receiiled 8th April, 1988 The Elements of Solid State Physics. By H. Y . Fan. (John Wiley, New York, 1987.) Pp. x +211. Price E30.50. Solid State Physics is not so much a topic as a constellation of topics. Within it the student will discover many phenomena of subtlety and interest, but what is surely so remarkable is not the occurrence of say superconductivity, semiconductivity or ferromagnetism, but that such a spectacular variety of physical properties of condensed matter can stem from the common roots of quantum and statistical mechanics.The author of a prospective textbook in such a broad and highly developed field has an unenviable task. He must be selective yet present a balance in the choice of material, he is required to give a mathematical development without failing to provide physical insight but, above all, he must justify the inclusion of this constellation of topics within the general title of Solid State Physics, by demonstrating the existence of an overall coherence. Judged by these standards I do not believe that Professor Fan’s book will resonate strongly with the needs of students. The genesis of the book, as explained in the Preface, consists of organized lecture notes which were used many times for a one-year graduate course on solid-state physics.The book is conceived as an introduction to the subject and, for this reason, the development of the subject matter is limited to basic problems. Within it there are topics, such as for example Introductory Transport Theory, Symmetry in Solids, Superconductivity or Optical Properties, that are rather fully developed for a book which addresses itself to the Elements of the subject. Elsewhere the discussion seems all too brief, as with Energy Bands or the Kondo effect and at times quite cursory as with for example, Brillouin zones, biexcitons, quasiparticles or the de Haas-van Alphen effect, which receive less than half a page each.Perhaps the most surprising feature of Professor Fan’s book is the almost total absence of pictorial or graphical material. Solid-state physics is richly endowed with topics where diagrams aid our understanding, and yet the book contains only a single figure; the first Brillouin zone of a face-centred cubic structure. The absence of figures also highlights the decision by the author to largely omit making connections with experiment. This, together with the absence of problems or exercises and only the briefest of bibliographies, is unlikely to commend this book to other lecturers. In its anodyne and rather formal approach this book may, however, find friends with those seeking a book to aid revision, a compact book of reference, indeed a mini-encyclopaedia of the elements of solid-state physics.M. Springford Receiced 10th March, 19883074 Reviews of Books UV-VIS-Spektroskopie und ihre Anwendungen. By H-H. Perkampus. (Springer-Verlag, Berlin, 1986.) Pp. viii + 208. Price DM 148. What is there to be said of u.v.-visible spectroscopy which is not already well established (as common parlance has it) in the public domain? Not a lot, is the message of this monograph, but what there is is important, and what is not has evoked quite a nice collated presentation. The book was clearly intended to serve as a successor to the Kortum tones of the 1960s and it is adequately up to date on many related developments. It has not covered them all, however, and contains curiously eclectic references to specific makes and models of spectrophotometer.In this connection, a thorough ‘ Which’-hunt of models currently available would be invaluable, although the logistics of such a survey could prove daunting. Starting from the absorption laws and the mechanistic consequences of photon absorption, the author outlines spectrophotometer geometry and construction with an allusion to microcomputer- driven assemblies. In real life this is one of the most important areas of technical innovation. Analytical applications feature in some detail regarding both basic algebra and amenability of system ; lists are provided of complexing agents for most elements together with extinction coefficients and maxima. Quantitative determination of sundry organics, photometry of enzymes including kinetic studies, multicomponent analyses, and identification and structural analysis follow.More recent developments include multiple-wavelength analysis, especially good for systems with wandering baselines, derivative techniques examining second-order derivatives, reflectance observations (though I myself would still go back here to Kortum’s original text), photoacoustic spectroscopy and fluorescence and phosphorescence techniques. Calculations of equilibrium constants for a number of kinds of fluid-phase equilibria are elaborated in some detail. These here ultimately depend on the use of a linear plot, involving approximation. Such a procedure does indeed provide a useful preliminary treatment of data, but in this era when ‘micros’ seem a dime a dozen and mainframe access widespread, quite unsophisticated programs can often deal with the statistics associated with fitting to unapproximated equilibrium equations and absorbance observations.Spectrophotometric kinetics are presented with even more algebraic detail. Although again eschewing statistical computer methods, the usefulness of the survey should not be understated. Stopped flow, relaxation and photochemical methods are also treated in some detail. The book has a concluding chapter on oscillator strengths, transition moments and band analysis. The author has diligently cited the origins and given equations with the appropriate constants made explicit, avoiding those infuriating expressions containing apparently magic numbers x 10” to be found almost universally when such topics are broached in texts.The impression so far to be gained is that what has been done has been done well. The omissions are, however, important. Most of the systems considered are dilute liquid solutions. There was thus the possibility of dealing with solvent effects on spectra; a brief section on solvent effects in complexdye adducts is certainly relevant, but only tangentially. There is scope for solid-state (compacted disc or single crystal) studies, including thin-film measurements and their associated optical hazards. Furthermore, the brief mention made of polarisation could perhaps have been elaborated, and techniques involving ellipsometry, circular dichroism and magnetic effects generally, would be of interest. New methods are omitted, such as that involving wide-wavelength instantaneous repetitive scanning employing photodiode detectors - an essential for up to date spectrophotometric kinetics of any sort.These have been available since 1979. Microspectrophotometry is neglected. Methods such as fibre-optics input and output, to inaccessible samples, may not have been available in commercial instruments during the gestation of the book, but they were in view and do merit mention. Each of the seven substantive chapters has 50-200 references, largely to the mid 1970s. The book as it stands will be of practical use in general spectrophotometry by advanced undergraduates or research people and will provide some updating for the more mature amongst us. Study of particular monographs cited would probably be necessary to put into use the specialist techniques.There is a dimensional error on p. 3 and table 22 cited on p. 134 appears to be actually table 18. The diagrams are nice, in the Springer style, but the page aspect is in my view quite austerely mittel-Europaisch, with uncentred equations lacking italicisation of symbols. The German text is accessible to survivors, like your reviewer, of courses on German for Scientists (but do such courses still exist?) D. R. Rosseinsky Received 3rd March, 1988Retiiews of Books 3075 The Art of Scientific Writing. By H. F. Ebel, C. Bliefert and W. E. Russey. (VCH, Weinheim, 1987.) Pp. xix+493. Price E39.25, DM 98 (Hard cover); E19.25, DM 48 (soft cover). It must take great courage to write a ‘how to write’ book: such authors inevitably set themselves up as targets for literary snipers.The authors of this book, no doubt recognizing through their choice of title that writing is not an exact science, are to be commended for their thoroughness and scholarly approach: every aspect of the writing and publishing process treated is dealt with meticulously, though there are flaws that a second edition could address. The book discusses both the causes and the consequences of scientific writing, giving the ‘why’ as well as the ‘how’, and has much to say to the experienced author as well as to the novice. The style of writing is naturally heavily didactic, but is permeated with common sense. As two of the authors work in Germany and one in the United States, the orthography and phraseology (including the perennial ‘is comprised of’) are American English, but this in no way affects the book’s generality.Although the subtitle (‘ From student reports to professional publications in chemistry and related fields ’) alludes to chemistry, the authors, two of whom are chemists, have produced a book of broad scientific relevance. The text is divided into two major parts: the first discusses the basic types of scientific writing and their organization ; the second details the practicalities and conventions connected with converting a manuscript into a document. There are also I 1 appendices, occupying one-third of the book’s length, and a 43-page index. In chap. 1 the authors explain how to write a report, giving useful details on keeping a laboratory notebook.Even guidelines for preparing grant applications are not overlooked. Chap. 2 deals with the nature, components and preparation of a thesis, with a note on the purpose of, and tactics for, the oral examination. These chapters should be of interest to established scientists with postgraduate students of their own, as well as to the students themselves. The commonest type of scientific writing, the journal article, is covered in chap. 3, from a discourse on the nature of journals and the choice of which to publish in, through to the publication process itself. The different needs (those of authors, publishers and readers) served by journals are kept in the forefront of the discussion. Whenever mention is made of the sometimes onerous requirements laid down by publishers for the preparation of typescripts - no doubt a source of mingled puzzlement and impatient annoyance to authors - an explanation is given of the reasons for them; this chapter also gives a helpful insight into the workings of an editorial office. The differences between preparing a typescript to be typeset and preparing a typescript to be used as camera-ready copy are made clear.Chap. 4 deals with writing a book, starting with the justification for doing so and the approach to the publisher, and taking it through the organizational and writing phases to the completion tasks : indexes, preliminary pages, cover and promotional material. Chap. 5 begins the second part of the book by examining the process of converting the manuscript of a report or thesis into a polished document suitable for distribution.The relative merits of typewriters and word processors are addressed, and then matters of format, proofreading and duplication. The only section of the book that is explicitly chemical in nature is chap. 6 , which in 31 pages deals concisely with chemical nomenclature. It starts with a brief historical section, goes on to outline IUPAC rules for inorganic and organic nomenclature, and concludes with a note on CAS registry numbers. Chap. 7, on quantities, units and numbers, picks its way carefully and largely successfully through the minefield of frequently misused concepts and symbolism. As ever the exposition is clear and authoritative (although it came as a surprise that ‘m’ for metre should be placed last: m s-’ is often mistyped ms-’, but s-’ m seems unlikely).In chap. 8 the presentation of equations and formulae, both chemical and mathematical, is examined. Chap. 9 and 10 discuss the effective use and preparation of line and half-tone figures (chap. 9) and tables (chap. lo). These three chapters provide a wealth of useful practical details. Concluding the text, chap. 11 deals with collecting and citing the literature, with hints on how to organize a personal source collection. The eleven appendices include items on oral presentations, use of English, copyright and contracts, preparing indexes, and proof marks (a discussion of American and ‘ Continental ’ systems only, ignoring the international standard IS0 5776).3076 Reviews of Books The index, although extensive, does not seem to have been prepared with the reader always in mind: for instance, the entry ‘triad’ conveyed nothing to me, and a single reference under ‘and’ is faintly ludicrous.Quibbles aside, this book has been prepared to a high standard, and its publication in both hard and soft covers will widen its readership: it deserves to be read. M. B. Goatly Received 20th April, 1988 The Technology of Pressure-driven Crossflow Processes. By R. G. Gutman. (Adam Hilgar, Bristol, 1987.) Pp. xiii+210. Price f35.00. This is a very timely book since pressure-driven membrane separation processes have emerged in the last two decades as important unit operations. This book is confined to reverse osmosis (RO), ultrafiltration (UF) and microfiltration (MF) and does not deal extensively with other important membrane separations driven by concentration, electrical potential or temperature driving forces.Nevertheless, the subject matter is relevant to a wide range of modern process applications. The book is divided into six chapters dealing with membrane manufacture and properties, membrane equipment and plant design as well as some specific process applications. The mechanism of membrane filtration is concisely presented and should suffice for those readers requiring an introduction to the theoretical treatment of solute and solution diffusion across semi- permeable membranes. Researchers will have to read more widely for a complete understanding of the underlying principles. There is a well structured presentation of process plant and equipment design, which gives mechanical details and illustrations of industrial membranes in modular construction, especially hollow fibre, spiral wound, tubular and flat-sheet configuration.The theoretical treatment of module performance is based on the concept of mass transfer at a stagnant liquid film at the membrane surface. Convective mass-transfer theory is well explained in simple terms and the reader is provided with some simple example calculations to assist in determining parameters such as solute flux, salt retention and pressure drop. Fouling of membranes is a major problem and tends to restrict the efficiency of the process in most practical applications. The concept of concentration polarisation is carefully explained, and useful theoretical guidance is provided to account for this effect and practical ways of alleviating the problem of membrane fouling are suggested.This section of the book draws heavily on the author’s experience in the field. The book also contains a useful survey of the applications of membrane filtration in such diverse areas as desalination, production of ultra-pure water, industrial effluent treatment, food and dairy industries and as a downstream process in biotechnology. Useful appendices give a brief description of other membrane separation processes, a list of membrane and equipment manufacturers and a glossary of selected terms. This is a concise, easy-to-read, comprehensive handbook of membrane filtration technology and I commend it to students with a first-time interest in the subject material, to practitioners who might encounter these processes as part of their daily work and to the process engineer who requires helpful guidance in the formative preparation of a project design.M. Streat Received 9th March. 1988 Microemulsion Systems. Surfactant Science Series Vol. 24. Ed. H. L. Rosano and M. Clausse. (Marcel Dekker, New York, 1987.) Pp. xix+433. Price $1 19.50. This book is a report of the proceedings concerned with ‘Microemulsion Systems’ which formed part of the 59th Colloid and Surface Science Symposium and the 5th International Conference on Surface and Colloid Science held in Potsdam, New York in June 1985. It contains 25 papers concerned mainly with the phase behaviour, structural characterisation and dynamic properties of a range of microemulsion systems.The book forms a collection of specialised articles and as such represents a cross-section through the state of microemulsion research in 1985. The content is inappropriate for people seeking an introduction to the formulation, general properties and range of potential and realised practical applications of microemulsions. The clarity of certain articles would be greatly improved if more attention had been given to theReuiews of Books 3077 quality of the English and the presentation of results. For example, in the introduction (p. xvii), Rosano states that stability is not dependent on the value of the interfacial tension. This is followed, in the next sentence, by the contradictory assertion that ‘low interfacial tension appears to be required for stability to occur at any degree’.Chap. 12 contains six graphs illustrating constant values of the surface tension versus composition variables. A rather small table would have been sufficient for these data. Furthermore, it would have been helpful to the reader had the different chapters been arranged under sub-headings rather than the apparently random arrangement used. It is interesting to note an example of the same lack of editorial control in the publicity pamphlet accompanying the book. In this, the list of chapter titles includes one by Magid et al. concerned with small-angle neutron scattering (SANS) entitled ‘Static SANS Measurements.. . ’. This has been helpfully ‘ translated ’ as ‘ Static Without Measurements.. . ’ ! In spite of the editorial shortcomings, the book does contain a number of very readable articles by leaders in their respective fields which provide useful background and insight into the general microemulsion literature. Most noteworthy of these are the contributions by Kahlweit et al. on non-ionic amphiphile systems, the review of molecular self-diffusion in microemulsions by Lindman et al. and the discussion of dynamic processes in water-in-oil systems by Langevin et al. More specialised articles on the interpretations of n.m.r. and e.s.r. spectra by Soderman et al. and Taupin et al., and the advances in theoretical treatments of microemulsions described by Safran et al. and Widom et al., are interesting. Structural studies of microemulsions by neutron scattering are well represented in the book by the articles of Ravey et al., Taupin et al. and Magid et al. The major part of the book is taken up with less fundamental, largely descriptive accounts of the effects of changing composition variables (including the substitution of various apolar solvents for water) and the mechanism of formation of microemulsions. Of the remaining chapters, the papers concerned with the non-homogeneity of middle-phase microemulsions (Li et al.), the properties of glass-forming systems (MacFarlane et al.) and the use of oxygen as an electrochemical probe in microemulsions (Berthod) proved interesting reading. This book does not ‘review and synthesise all work in this area since 1982’ as claimed on the back cover. Rather, it is a poorly edited collection of specialist papers ranging in quality from authoritative and readable to mediocre. As such, these conference proceedings might have been better published in a special issue of an appropriate journal. P. D. I. Fletcher Received 27th April, 1988

ISSN:0300-9599    

DOI:10.1039/F19898503071

出版商:RSC    

年代:1989

数据来源: RSC