摘要:

J. Chem. SOC., Faraday Trans. I, 1986, 82, 2577-2588 Ionic Solvation in Water-Cosolvent Mixtures? Part 12.-Free Energies of Transfer of Single Ions from Water into Water-Propan- 1-01 Mixtures Ibrahim M. Sidahmed and Cecil F. Wells* Department of Chemistry, University of Birmingharh, Edgbaston, P.O. Box 363, Birmingham B15 2TT The spectrophotometric solvent-sorting method for determining the free energy of transfer of the solvated proton, AG;(H+), between water and mixtures of water-cosolvent has been applied to mixtures of water with propan- l-ol. The assumptions underlying the method are examined critically and the consequences of varying the standard states of the species involved in the solvent sorting in the mixture are explored. The resulting values for AG,"(H+) are used to determine AG,"O(-) from AG;(HX) and these values for AG,"(X-) are used to determine AG:(M+) for other cations from AG,"(MX).The variation of AG,"(i) for individual ions in water-propan-1 -01 are compared with the variation of AG,"(i) in mixtures of water with other cosolvents. Values for AG,"(Ag+) and AG"(CNS-) are determined for other water-cosolvent mixtures. The spectrophotometric solvent sorting methodl7 for determining the free energy of transfer of the solvated proton from water into a water-cosolvent mixture has been applied to mixtures containing methan01,~ ethan01,~ propan-2-o13 or t-butyl alcohol5 as cosolvent as well as to mixtures containing non-alcoholic cosolvents.2t We now report its application to water-propan- l-ol mixtures. As with the other cosolvents, following the determination of the free energy of transfer of the proton, AG:(H+), values for AG,"(X-) are determined from values for AG,"(HX) and values for the free energies of transfer of cations M+ are determined from values for AG,"(MX).The positive structural contribution' to the change in the temperature of the maximum density of water by the addition of propan-1-01 suggests that propan-1-01 at low concentrations increases the amount of structure in water.8 This view is supported by the minimum found in the relative partial molar volume of propan-1-01 in water, v2 - V i , at a mole fraction of propan-1-01 x , z 0.05,9 the minimum in the excess volume of mixing Vg at x , x 0.05,1° the minimum in the excess enthalpy of mixing AHE at x, z 0.05,11 the minimum in the partial component of the compressibility for propan- l-ol at x , x 0.05,12 the maximum in the viscosity 'I at x, z 0.11 l3 and the maximum in the ultrasonic absorption at x , x 0.14.l4 In these properties, propan-1-01 in its mixtures with water behaves in a manner similar to the other alcohols mixed with 11, l5 Experimental A.R.propan-1-01 was used with the other materials as described earlier.lP6 The concentration of unprotonated 4-nitroaniline was determined spectrophotometrically at 383 nm as t This paper by Dr Wells should be read with the paper by Blandamer et al., J. Chem. SOC., Faraday Trans. 1, 1986, 82, 1471. It serves to clarify the distinctive approaches of these two workers. 25772578 Free Energies of Transfer of Ions Results and Discussion Determination of AG,"(H+) (a) Derivation of Relationships It has been suggested16 that the standard states employed in the derivation of the relationships used to calculate AG,"(H+) by the solvent-sorting procedure should be investigated. Before proceeding to a determination of AG,"(H+) for water-propan- 1-01 mixtures we therefore examine critically the method used in relation to other suggestions.The free energy of transfer of the proton between water and a water-cosolvent mixture consisting of n(H,O) moles of H,O and n(R0H) moles of the cosolvent is given by the difference in the standard chemical potentials : AG,"(H+) = pz(Hzolv) [ TPn(H,O) + n(ROH)] -pE(H&J (TPH,O). (1) By definition the standard state for p~(H&lv)[TPn(H20) +n(ROH)] must be in the mixture and that for pE(Hiq) (TPH20) must be in pure water, as is normal in considering the difference in the free energies of species between two 1iquids.l' As we are ultimately going to determine the concentration of species of the solvated proton spectrophoto- metrically on the molar scale, we adopt the molar scale (subscript c) here.Ify is the activity coefficient in the mixture, the standard state for p~(H~olv) [ TPn(H20) + n(ROH)] is y(H+) = 1 .O and [H+] = 1 .O with y -+ 1 .O as [H+] -+ zero; and ify' is the activity coefficient in pure water, the standard state for pz(H,+,)(TPH,O) is y'(H+) = 1.0 and [H+] = 1.0 with y' -+ 1.0 as [H+] -+ zero. AG:(H+) is divided into two parts for this determination. First, the solvated proton in water, H+(H,O)b, is transferred from water into the mixture using the Born expression for dielectric continua.In general in this treatment x is not specified except that it is assumed that b >, 5, the minimum being one sphere of H,O molecules surrounding H,O+ (only for the purposes of the Born calculation is b specified as 5 to provide a radius for the sphere transferred of 3rHz0, where rHzO is the radius of the water molecule). Ne2 AG(Born) = p~(H,+,)[TPn(H,O)+n(ROH)] --pz(H&)(TPH20) = ~ (D,1- D,1) (2) 6rHz" where Hiq = H+(H,O),, N is Avogadro's number, e is the electronic charge, D is dielectric constant and subscripts s and w indicate the mixture and pure water, respectively. The standard state for &(Hiq) [TPn(H,O) + n(ROH)] is defined in the mixture" and the standard state for p;(Hzq)(TPH20) is in pure water.As our investigations are restricted to mixtures which are largely aqueous in composition, with the mole fraction of ROH never exceeding x, M 0.2-0.3, it is assumed that other contributions to this transfer resulting from the departure of H2q from pure water and its reception into the water-rich mixture cancel out. As the contribution of AG(Born) to the total AG:(H+) is small, we consider that errors arising from deviations from these reasonable assumptions can be neglected. As shown elsewhere,, although the free energy of solvation of an ion i of charge ze and radius r derived from Born charging effects, AG(i)g0lv = (z2e2/2r)(Dg1 - l), is not on any concentration scale, the free energy of transfer of i between water w and the solvent s arising from Born effects, AG(Born) = AG(i)g0lV - AG(i)?lV, is on the molar scale., Therefore, eqn (2) is defined on the molar scale.Following this transfer in eqn (2), the solvent molecules around the proton relax to provide the stable situation in the mixture. This contribution to AG:(H+) is given by AG2 = P:(H:olv) [7-w320) +n(ROH)I -Pz(H,f,) ETWH20) + 4ROH)I (3) where the standard states for both chemical potentials must now both be defined in theI. M. Sidahmed and C. F. Wells 2579 mixture.17 This rearrangement of solvent molecules around the proton in the mixture is represented by the equilibrium : K where (ROH;),,, is a proton solvated by both H20 and ROH. It is assumed that x, is low enough in the water-rich conditions to restrict the composition of (ROHZ),,, to a ratio ROH/H+ = 1.0.As process (4) takes place entirely within the mixture, the standard states for all the species involved must be defined in the mixture1' and the standard free energy change for equilibrium (4) is given by AG"(5) = d(ROHi)mix + d(H2O)mix -&W2q)rnix -pz(ROH)rnix- ( 5 ) For the initial transfer of one mole of Hiq in eqn (2) between the two media, the free energy for the rearrangement of solvent molecules in the mixture is given by AG, = [ROHi] AG"(5) ( 6 ) (7) and the total free energy of transfer is given by AG,"(H+) = AG(Born) + AG2. AG"(8) = /4(ROH~)mix + P;(H~O)H~O -/G(Hiq)rnix -pZ(ROH),oH It has been suggested16 that eqn ( 5 ) should be (8) with the standard states for pi(H20) and pZ(R0H) being the so-called absolute rational states of pure water and pure ROH, respectively (subscript x).Although these two standard states are convenient for many processes involving the actual mixing of pure H,O and pure ROH, and especially so for the determination of the excess thermodynamic quantities of mixing, they have no absolute status.l8 In particular, they contravene the rule that the standard states for processes occurring entirely in a homogeneous liquid medium must be defined in that medium.l' Indeed, eqn (8) represents the standard free energy change for the fictitious equilibrium : (H:q)mix + (KoH)R.OH (RoHZ)rnix + (H20)H20 (9) which cannot occur in two miscible components H20 and ROH, and therefore, eqn (4) and ( 5 ) represent the equilibrium in the mixture.Following the normal procedure1' for determining the difference in free energies of species between two liquids, the standard states of all the species involved in the rearrangement (4) in the mixture n(H,O) + n(R0H) must be defined in the same mixture. For the solute species H$q and ROHZ on the molar scale this is y = 1.0 and [i] = 1.0 with y + 1 .O as [i] + zero. For the bulk components, H,O and ROH, in any particular mixture n(H,O) + n(ROH), their respective standard states, po(H,O) [ TPn(H,O) + n(ROH)] and p"(R0H) [TPn(H,O) + n(ROH)], are defined for each bulk component in that particular mixture, n(H,O) + n(ROH), without any solute species, e.g. HLq or ROH:, present. On the molar scale, the activity coefficient of each bulk component for that particular mixture, y" = 1.0 when the molar concentration of all solute species is zero.It should be noted that it is not assumed that p"(ROH)[TPn(H,O)+n(ROH)] = p"(H,O) [TPn(H,O) + n(ROH)] and neither, as has been suggested,16 does this assume that the chemical potentials of pure H,O and pure ROH are equal. Of course, in the normal way17 the standard states adopted for H,O and ROH in each particular mixture are related to standard states defined as activity = 1.0 for H20 in pure water and activity = 1.0 for ROH in pure ROH, even though these states canot be used for equilibrium (4) in n(H,O) +n(ROH) after transfer from H20. Iff(H,O) andf(R0H) are the activity coefficients on the mole-fraction scale of H,O and ROH in the complete2580 Free Energies of Transfer of Ions mixture of bulk and solute components related to the standard states of each respective pure bulk component defined as unity, f(H20) =fd(H20) y”(H20) Y”’(H20) and f(R0H) =fd(ROH)y”(ROH)y”’(ROH) where fd(H20) and f,(ROH) are degenerate activity coefficients17 on the mole fraction scale (subscript x) defined by p:(H,O)[TPn(H,O)+n(ROH)] = p34,O)(TPH2O)+RT lnfd(H,O) and p:(ROH)[TPn(H,O)+n(ROH)] = pg(ROH)(TPROH)+RT In fd(R0H) and y”’(H20) and y’”(R0H) in each case are factors converting y” from the molar to the mole fraction scale.From eqn (4) and (9, for any mixture n(H,O)+n(ROH) where for ROH; and H& the standard states are y = 1.0 and [i] = 1.0 with y -, 1.0 as [i] -+ zero and y” for H,O and ROH are as defined above arising from the presence of solutes in the mixture n(H,O) + n(R0H).This equation can be rewritten as AG, = - [ROH,] RT In Kc wR & 4 = Y(ROH;) Y”(H,O)l[Y(H:q) Y”(ROH)I. (12) where theconcentrationquotient Kc = [ROHz]/([H:,] [ROH]), wR = [H,O] in themixture and (1 3) For the transfer of one mole of protons between water and the mixture, i.e. [ROH$]+[H:,] = 1.0, all the quantities in eqn (12) can be determined. When a trace concentration of 4-nitroaniline B is added to aqueous acidic solutions, equilibrium (14) is set up in water K : B,, + H:q e BH;q + H20 and K; is given by where the standard state in water for BH+, B and H,+, is y’ = 1 .O and [i] = 1 .O withy’ -+ 1 .O as [i] -+ zero and y’(H,O) assumes pure water as the standard state. However, when B is added to acidic solutions in the mixture n(H,O) + n(ROH), equilibria (1 6) and (1 7) are set up in conjunction with equilibrium (4) Kl Bmix + W:q)mix * BHLix + H2Ornix (16) to which eqn (1 8) and (19) apply where the standard states in the mixture for B, BH+, H& and ROH; are y = 1.0 and [i] = 1 .O with y -+ 1 .O as [i] -+ zero and y”(H20) and y”(R0H) are as defined above for aI .M . Sidahmed and C. F. Wells 258 1 mixture containing dissolved species. If c and cR are the concentrations of B determined spectrophotometrically in acidic solutions in water and in the mixture, respectively, for a constant added total concentration of [B] = co for a constant temperature, eqn (20) can be deduced1-6 (20) where 4 = y(B) y(RoH;)/[y(BH+) y”(R0H)I and 4 = y(B) y(H,f,)/[y(BH+) y”(H,O)I, ccR K24 COCR wR cO ----- (cR - ‘> - Kl 4 (cO - cR) [ROHIT + K1 provided eqn (21) holds,? where F ; = y’(B)y’(H4q)/y’(BH+)y’(H20), w = [H,O] in pure water and [ROH], is the total molar concentration of ROH added to the mixture.It has been shown for a wide range of cosolvents in water-rich conditions that linear plots of cc,/(c, - c) against cR/(co - cR) are obtained experimentally for constant [ROH], and constant temperature at an ionic strength of 1 .OO, confirming the validity of assumption (21).lp6 From eqn (20), the slopes of these linear plots are given by where F, and K, are as defined for eqn (12) and (13). Moreover, for these linear plots, the ratio slope/intercept = K24, enabling the calculation of [ROH;] using yielding a range of values with the varying [HCl] used for each [ROH],.Experimentally, it has been found for a range of cosolvents in water-rich conditions that the latter K, values for varying [HCl] at constant [ROH], calculated using eqn (24) agree well amongst themselves for each [ROH], and also agree very well with the specific value for K , c1 calculated from the slope of the plot of CCR/(CR - c) against c,/(c, - c,) at the same [ROH],. We must conclude, therefore, that in general F, = 1.0. As Blandamer et al. desire,lG the y-values comprising F, can be related to the pure liquids H 2 0 and ROH using the degenerate activity coefficients. fd(H20) and f,(ROH) defined in eqn (10) and (1 1) on the mole-fraction scale can be used together with y”’(H20) and y”’(R0H) to relate y”(H20) and y”(R0H) to their respective pure liquids and similarly y values for solute species can be related to pure water y’ values via y’ = ydy, where yd is also a degenerate activity coefficient17 defined on the molar scale by ,uz( i) [ TPn( H20) + n( ROH)] = &( i) ( TPH ,O) + R T In yd( i).Rearranging eqn (13) for F, to relate y(i) and y”(H20) to pure water and y”(R0H) to To find [ROH;] in eqn (12), eqn (26) and (27) are used:1-6 [ROH;] = 0.5{A-(A2-4[ROH]r)~}. (26) (27) A = ([ROH], + 1 +&I) t Not w/wR = 1.0 as stated by Y. Marcus in Zon Solzlation (Wiley, Chichester, 1985), pp. 161 and 204.2582 As experimentally F, = 1.0 and wR is given by Free Energies of Transfer of Ions where d, is the density of the mixture and M,,, and M , are the respective molecular weights of ROH and H,O, all the quantities in eqn (12) are now known.(b) Evaluation of AG:(H+) for Water-Propan-1 -01 Mixtures Values of cR were determined spectrophotometrically at 383 nm19 and 25 "C for added concentrations of HC1 in the range 0.1-0.8 mol dm-3 for 5, 10, 15, 20, 25, 30, 35 and 40 vol % of propan-1-01 with co = 1.45 x lop4 mol dmp3 and with ionic strength made up to 1.00 mol dm-3 by adding NaCl, as before.1-63 l 9 Slight turbidity was found in solutions containing 5, 10 and 1 5 vol % propan- 1-01 and this was corrected for by using a suitable blank. Values of c for the same range of HCl concentrations in water with the ionic strength maintained at 1 mol dmp3 using NaCl were also determined spectrophotometrically. Owing to a separation into two layers for the mixture containing 40 vol % propan- 1-01 and I mol dmp3 NaCl with no added HCl, the extinction coefficient E of 4-nitroaniline could not be determined by the usual procedure19 for this mixture: E for 40 vol % propan-1-01 was therefore found by extrapolation of the values of E at the lower concentrations of propan-1-01.Good linear plots were obtained for ccR/(cR-c) against cR/(c,-cR) in 10, 15, 20, 25, 30, 35 and 40 vol "/o propan-1-01 with the intercept = wc,/K;I;;, confirming the validity of assumption (21) also for water- propan-1-01 mixtures. However, the scatter on the points for 5 vol % propan-1-01 was too great to draw such a plot for that concentration. The accuracy of the extrapolated value for E in 40 vol % propan-1-01 was tested by repeating the calculation of values for cR with slight variations of E either side of the extrapolated value.Only the plot of CCR/(CR-C) against cR/(co-cIt) using the values of cR derived from the extrapolated value of E gave a straight line; plots using slightly higher or lower values for E curved away below or above, respectively, from the latter plot. Values of K,C1 determined from the slopes of these linear plots using eqn (22) and corrected for the small contraction of volume on mixing water with propan-l-o11-6 are shown in table 1 . This table also contains values of K, calculated for each added acid concentration using eqn (23) and (24). The values of K,F, calculated from the ratio slope/intercept of the linear plots are also included in table 1 . For any particular mixture n(H,O) + n(R0H) good agreement is obtained between these latter values for Kc and for the value for K, C1 determined from the slope except, as found with all other cosolvents used,1-67 l9 at the higher concentrations of propan-1-01 where [ROH:] becomes high enough for ([Hiq] - [ROH;]) z zero in eqn (24), causing scatter in the values for K,.We conclude, therefore, that F, = 1 .O for water-propan-1 -01 mixtures in water-rich conditions, as found for all other water-cosolvent mixtures Values for AG, were calculated on the molar scale using eqn (12) with F, = 1 .O. Values for [ROH;] were calculated using eqn (26) and (27) with the values of K, in table 1 obtained from the slopes of the plots of CCR/(CR - c) against c,/(c, - cR). Values for wR were obtained using eqn (28) with the values of d, at 25 "C interpolated from the data of Chu and Thornpson2O and of Mikhail and Kimel,13 which are in good mutual agreement.The values of AG2 for water-propan-1-01 are plotted against solvent composition in fig. 1. Values for AG(Born) were calculated on the molar scale using eqn (2) with the dielectric constant interpolated from the data of Akerlof.21 As eqn (7) gives values of AG(H+) on the molar scale, these were corrected to the mole-fraction scale using the equation: AG,"(H+) = AG(Born) + AG, + RT In (d, M,/d, M,) (29)I. M. Sidahmed and C . F. Wells 2583 Table 1. Values of K , (dm3 mol-I) calculated from K , F, and of K, K1 (dm3 mol-l) derived from the slopes at ionic strength = 1.00 mol dm-3 and at 25 "C in water-propan-1-01 mixtures total added acidity 8.21 12.44 16.75 21.16 25.65 30.24 34.92 /mol dmP3 (0.0261) (0.0408) (0.0569) (0.0745) (0.0937) (0.1 15) (0.139) concentration of propan- 1-01 [wt % (mole fraction)] 0.096 0.37 0.60 1.15 1.6 1.8 1.9 2.1 0.153 0.35 0.57 1.07 1.6 1.7 1.8 1.9 0.192 0.35 0.58 1.04 1.5 1.4 1.7 1.7 0.383 0.34 0.57 1.07 1.5 1.3 1.9 1.6 0.766 0.34 0.56 0.87 2.0 2.1 3.2 3.6 K , C 1 0.337k0.004 0.56f0.01 0.97+0.01 1.30+0.01 1.47kO.01 1.54k0.03 1.66k0.02 (from slope) K2 4 45.7 27.8 15.9 11.8 10.5 9.9 9.5 2 0 0.02 0.04 0.06 0.08 0.10 0.12 0.lL X2 Fig.1. Variation of AG, for eqn (12) for water-propan-1-01 mixtures at 25 "C with mole fraction of propan- 1-01. where M, = lOO/[(wt % ROH/MR0,) + (wt % H20/M,)] and d, is the density of water at 25 "C. The resultant values for the free energy of transfer of H+ on the mole fraction scale are contained in table 2.Free Energies of Transfer of Anions Values for AG:(X-) can be calculated from values for AG:(HX) using the values of AG:(H+) in table 2 in the equation AG:(X-) = AG:(HX) - AG;(H+). H2(g) Pt I HC1, H 2 0 + propan-1 -01 I AgCl, Ag. (30) (31) Several sets of workers have determined E" values for the cell Claussen and French,22 Roy et and Elsemongy and F o ~ d a ~ ~ have determined E"2584 Free Energies of Transfer of Ions Table 2. Values for the free energy of transfer of individual ions from water into water-propan-1-01 mixtures at 25 "C concentration of propan- l-ol mole wt % fraction H+ Rb+ Agt c1 3.86 5.00 7.43 10.00 10.00 10.00 10.00 10.00 10.70 13.80 15.00 16.70 20.00 20.00 20.00 20.00 20.00 20.00 21.90 25.00 26.50 30.00 30.00 30.60 34.30 35.00 37.60 40.00 40.00 40.00 40.00 40.00 0.01 19 0.0155 0.0235 0.0322 0.0322 0.0322 0.0322 0.0322 0.0347 0.0458 0.0503 0.0567 0.0697 0.0697 0.0697 0.0697 0.0697 0.0697 0.0776 0.0909 0.0976 0.1 14 0.114 0.1 17 0.135 0.139 0.153 0.167 0.167 0.167 0.167 0.167 - 0.77 - 1.03 - 1.67 -2.65 - - - - - 3.02 -4.59 - 5.27 - 6.23 - 7.4 - - - - - - 7.8 - 8.2 - 8.3 -8.5 - - 8.6 - 8.7 - 8.7 - 8.8 - 8.8 - - - - OH- __ CNS- - 1.22" 3.09" 3-62" 3.13" 3.09d 3.09" _.- - 5.8" 8.2b 8.8" 8.1" 8.1d 8.0" 8. lf 9.1" 9.7b 9.4" - - - - - 9.8" 10.6" 11 .8" 10.2" 10.5" 10.5f - - - - E" data for HCl taken from: aref. (26), "ref. (24), "ref. (23), ref. (22), "ref. (25) and f ref. (27). on the mole-fraction scale for cell (31) for a range of solvent compositions and the free energy of transfer of HC1 on the mole-fraction scale is given directly by the equation: AG:(HCl) = 96.5(Ek -Ei)/kJ mol-l.(32) Gentile et al.25 have used cell (31) to provide values of E$ on the molality scale and values for AG,"(HCl), calculated from eqn (32) have to be corrected to the mole-fraction scale (kJ mol-l) using the equation: AG,"(HCl) = AG,"(HCl), + 1 1.41 log (Mw/Ms). glass electrode I HC1, H,O + propan- l-ol I AgC1, Ag (33) Smits et a1.26 have determined values for AG,"(HCl), on the molar scale using the cell: (34)I . M. Sidahmed and C . F. Wells 2585 and these values have been corrected to the mole-fraction scale (kJ mol-I) using the equation : AGi(HC1) = AGF(HCl), + 1 1.41 log ( M , dJM, d,). (35) Schwabe and Miiller2' have determined E L for the cell: H2(g), Pt I HCI, H 2 0 + propan- 1-01 I Hg,C12, Hg (36) and the values for AG,"(HCl), calculated from eqn (32) have been converted to the mole- fraction scale using eqn (33).All these values for AGi(HC1) have been combined with the values for AG,"(H+) in table 2 to produce values for AG,"(Cl-) on the mole-fraction scale using eqn (30). These latter values are collected in table 2. Good agreement is obtained between the values for AG,"(Cl-) from the various sources for the same solvent composition, except for some deviation of those derived from the E" measurements of Roy et a1.23 Dash and Padhi28 have determined E" on the mole-fraction scale for the cell: Ag, AgCNS AgCl, Ag (37) from which, after correction for the liquid junction potential,2s values for AG,"(HCNS) can be calculated using an equation analogous to eqn (32).Values for AG,"(CNS-) have been calculated using these values with the values of AGE)(H+) in table 2 in eqn (30). The values for AG,"(CNS-) are given in table 2. Values for Kip = [H+] [OH-]y2, have been determined for the ionization of water in water-propan-1-01 mixtures.29 These values for (Kip), on the molar scale were first converted to the molality scale (Kip)m using the equation: and the resulting values on the molality scale were used in eqn (39)Ip6 to determine the sum of the free energies of transfer of H+ and OH- on the molality scale. m, and m, are the molalities of water in pure water and in the mixture, respectively, and agzO is the activity of water in the mixture on the molality scale.Values for ahzO on the mole-fraction scale were calculated from the activity coefficient of water in the water-propan-1-01 mixtures relative to pure water determined by Butler et aL30 and these were converted to the molality scale using the equation:31 a",,,(molality) = 55.509a",,,(mole fraction). (40) Values for AG~(H+),+AG,"(OH-), on the molality scale were then converted to the mole-fraction scale using eqn (33) and values for AGi(OH-) were then calculated using eqn (30) and the values for AG:(H+) in table 2. The resultant values for AG,"(OH-) are shown in table 2. Free Energies of Transfer for Metal Cations Smits et al.32 have determined the free energy of transfer for RbCl on the molar scale from E" measurements on the cell: glass electrode I RbC1, H 2 0 + propan-1 -01 I AgCl, Ag using an ion-selective glass electrode.These values have been converted to the mole- fraction scale using an equation analogous to eqn (35) and values for AG,"(Rb+) have been calculated using the equation : AG,"(Rb+) = AG,"(RbCl) - AG,"(Cl-) (41)2586 Free Energies of Transfer of Ions ' Ag+ - l o t Fig. 2. Variation of the free energy of transfer of individual ions between water and water- propan-1-01 mixtures with the mole fraction of propan-1-01 at 25 "C. with the mean values for AG,"(Cl-) in table 2, excluding those derived from the E" measurements of Roy et al.,23 and are given in table 2. Values for the solubility product, Kip, for AgCl in H,O-propan-1-01 have been collated by Dash et al.33 and KYp in water has been determined by Gledhill and Malan.34 Values for the free energy of transfer for AgCl on the molar scale were calculated using the equation : (42) and these have been converted to the mole-fraction scale using an equation analogous to eqn (35).When combined with values for AG,"(Cl-) in an equation analogous to eqn (41), the values for AG,"(Ag+) which result are contained in table 2. AG:(AgCl), = RT In (cp/KZp) Comparison of Values for AG:(i) Fig. 2 shows that the distribution of values of AG,O(i) for varying i is similar to those found with most other cosolventsf-6 where the equilibrium OH- + RQH e RO- + H 2 0 (43) lies to the left. For these latter conditions AG:(OH-) > G,"(CI-), as found for ethan01,~ ethanonitrile6 and urea.6 When equilibrium (43) lies farther to the right, AG:(Cl-) > AGt(OH-), e.g.for with the latter becoming negative for ethane- 1,2-diol and 37 For low mole fractions of cosolvent, AGP for an alkali-metal ion like RbS is negative for propan-2-01,~? 3 9 acetone,,> 3 y dioxaq29 t-butyl DMSO,,? ethanonitrile6 and urea6 as cosolvents, but positive and ca. zero for methanol with AGt(Rb+),,? and negative values are found here for propan-1-01. For x, < 0.2, AG:(Ag+) is more negative than AG,"(Rb+) for methanol,,* 3 9 propan-2-01,~. t-butyl alcohol,2+ dioxan,2$ dimethyl sulphoxide,2T dioxan,27 acetone,2* 3 9I. M . Siduhmed and C. F. Wells 2587 I ,CNS:2- PrOH 5 4 I - 0 E ".._ 1 / 0.05 0.20 - x2 glycerol Fig. 3. Variation of the free energy of transfer of CNS- and Ag' ions between water and water+osolvent at 25 "C with mole fraction of cosolvent.t-butyl alcohol,23 DMSO29 and ethanonitrile,'j as found in fig. 2 for propan- 1-01, but the latter cosolvent is unusual in having AG,"(Ag+) more negative than AG:(H+), only observed previously for ethanonitrile,6 with AG,"(Ag+) = AG,"(H+) for DMS0.2> For other cosolvents, dioxan,2v 3 3 ti DMS0,2~ ethanol4 and urea,6 AG,"(CNS-) < AG,"(Cl-), as found here for propan-1-01. As E" values for cell (37)28 and Ksp values for AgC133 are now available for some other cosolvents for which AG,"(i) have been determined, it is appropriate here to determine AG,"(CNS-) and AGF(Ag+) for the mixtures of these cosolvents with water to see how they compare with the above discussion. AG,"(HCNS) has been calculated using eqn (32) from Eo values on the mole-fraction scale28 for methanol, propan-2-01 and glycerol as cosolvents and values for AG,"(CNS-) have been calculated using the appropriate values for AG,"(H+)2~3 in eqn (30).These values are plotted against solvent composition in fig. 3. When compared with the values for AG,"(C1-),2 AG:(CNS-) < AG,"(Cl-) for all these cosolvents, as found with the other cosolvents;2 moreover, AG,"(CNS-) with glycerol is negative, like AGZ'I-) for this cosolvent,2 with positive values for AGF(C1-).2 Using the values for Ksp for AgCl with cosolvents ethanol and propan-2-01 on the molar scale,33 values for AG:(AgC1), on the molar scale have been calculated using eqn (42) and, after correction to the mole-fraction scale using an equation analogous to eqn (35) and subtracting the appropriate values for AG,"(CI-) for these cosolvent~,~-~ values for AG;(Ag+) on the mole-fraction scale are obtained.These values plotted in fig. 3 show that AG:(Ag+) is more negative than AG,"(Rb+) with the same cosolvent,2$6 as found above for the other cosolvents. Moreover, when compared with the appropriate AG,"(H+)2$ and unlike many of the other cosolvents, AG,"(Ag+) z AG:(H+) for ethanol and propan-2-01, resembling DMSO in this respect. This analysis shows, therefore, using the values for AG,"(Ag+) calculated here for the cosolvents propan- 1-01, propan-2-01 and ethanol, that the earlier finding with other cosolvents of - AG,"(H+) > - AG,"(Ag+) is not necessarily the normal situation.References 1 C. F. Wells, Adu. Chem. Ser., 1979, 177, 53. 2 C. F. Wells, Aust. J . Chern., 1983, 36, 1739.2588 Free Energies of Transfer of Ions 3 C. F. Wells, J . Chem. SOC., Faraday Trans. 1. 1973, 69, 984; 1974, 70, 694; 1978, 74, 636. 4 C. F. Wells, 1. Chem. SOC., Faraday Trans. 1, 1984, 80, 2445. 5 C. F. Wells, J . Chem. SOC., Faraday Trans. 1, 1976, 72, 601. 6 C. F. Wells, J. Chem. SOC., Faraday Trans. 1, 1975, 71, 1868; 1978, 74, 1569; 1981, 77, 1515; Thermochim. Acta, 1982,53, 67; G. S. Groves and C. F. Wells, J. Chem. Soc., Faraday Trans. 1, 1985, 81, 1985, 3091; G. S. Groves, 1. M. Sidahmed and C. F. Wells, unpublished work. 7 G. Wada and S. Umeda, Bull. Chem. SOC. Jpn, 1962, 35, 646. 8 H. S. Frank and M. W. Evans, J . Chem. Phys., 1945, 13, 507; H.S. Frank and W-Y. Wen, Discuss. Faraday SOC., 1957, 24, 133; G. Nemethy and H. A. Sheraga, J. Chem. Phys., 1962, 36, 3382; 3401; W. Laiden and G. Nemethy, J. Phys. Chem., 1970, 74, 3501. 9 K. Nakanishi, Bull. Chem. SOC. Jpn, 1960, 33, 793. 10 C. Dethlefsen, P. G. Smensen and A. Hvidt, J . Solution Chem., 1984, 13, 191. 11 R. F. Lama and B. C-Y. Lu, J. Chem. Eng. Data, 1965, 10, 216. 12 M. Nakagawa, Y. Miyamoto and T. Morigoshi, J . Chem. Thermodyn., 1983, 15, 15. 13 S. Z . Mikhail and W. R. Kimel, J . Chem. Eng. Data, 1963, 8, 323. 14 S. Gasse and J. Emery, J. Chim. Phys., 1980, 77, 263. 15 F. Franks and D. J. G. Ives, Q. Rev. Chem. SOC., 1966, 20, 1; A. G. Mitchell and W. F. K. Wynne- Jones, Discuss. Faraday SOC., 1953,15, 161 ; J. Kenttamaa, E. Tommila and M.Martti, Ann. Acad. Sci. Fenn., 1959, No. 93; M. J. Blandamer, Introduction to Chemical Ultrasonics (Academic Press, London, 1973), chap. 11. 16 M. J. Blandamer, J. Burgess, B. Clark, A. W. Hakin, N. Gosal, S. Radulovic, P. Guardado, F. Sanchez, C. Hubbard and E-E. A. Abu-Gharib, J. Chem. Soc., Faraday Trans. 1, 1986,82, 1471. 17 H. S. Harned and B. Owen, The Physical Chemistry of Electrolytic Solutions (Reinhold, New York, 3rd edn, 1958), pp. 463 and 669-675; R. A. Robinson and R. H. Stokes, Electrolytic Solutions(Butterworths, London, 2nd edn, 1959), pp. 351-357; L. P. Hammett, Physical Organic Chemistry (McGraw-Hill, New York, 2nd edn, 1970), pp. 14-15. 18 H. L. Friedman and C. V. Krishnan in Water - a Comprehensive Treatise, ed. F. Franks (Plenum Press, New York, 1973), vol. 3, pp. 7, 8. 19 C. F. Wells, Trans. Faraday SOC., 1965,61, 2194; 1966,62,2815; 1967,63, 147; 1972,68, 993; J . Phys. Chem., 1973,77, 1994. 20 K-Y. Chu and A. R. Thompson, J. Chern. Eng. Data, 1962, 7, 358. 21 G. Akerlof, J . Am. Chem. SOC., 1932, 54, 4133. 22 B. H. Claussen and C. M. French, Trans. Faraday SOC., 1955, 51, 708. 23 R. N. Roy, W. Vernon and A. L. M. Bothwell, Electrochim. Acfa, 1973, 18, 81. 24 M. M. Elsemongy and A. S. Fouda, J . Chem. Thermodyn., 1981, 13, 1123. 25 P. S. Gentile, L. Eberle, M. Cefola and A. V. Celiano, J . Chem. Eng. Data, 1963, 8, 420. 26 R. Smits, D. L. Massart, J. Juillard and J-P. Morel, Electrochim. Acta, 1976, 21, 431. 27 K. Schwabe and R. Muller, Ber. Bunsenges. Phys. Chem., 1969, 74, 178. 28 U. N. Dash and M. C. Padhi, Thermochim. Acta, 1983,60, 243. 29 E. M. Woolley, D. G. Hurkot and L. G. Hepler, J . Phys. Chem., 1970, 74, 3908. 30 J. A. V. Butler, D. W. Thomson and W. H. MacLennan, J . Chem. Soc., 1933, 674. 31 C. H. Rochester, J . Chem. SOC., Dalton Trans., 1972, 5. 32 R. Smits, D. L. Massart, J. Juillard and J-P. Morel, Electrochim. Acta, 1976, 21, 425. 33 U. N. Dash, B. B. Das, U. K. Biswal, T. Panda, N. K. Purohit, D. K. Rath and S. Bhattacharya, 34 J. A. Gledhill and G. McP. Malan, Trans. Faraday SOC., 1952, 48, 258. Thermochim. Acta, 1983, 63, 261. Paper 5 / 18 1 2; Receiued 23rd Oclober, 1985

ISSN:0300-9599    

DOI:10.1039/F19868202577

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. I, 1986,82, 2589-2604 Isobaric and Isothermal Hysteresis in Metal Hydrides and Oxides Ted. B. Flanagan," J. Dean Clewley, Toshiro Kuji and Choong-Nyeon Park Department of Chemistry, University of Vermont, Burlington, Vermont 05405, U.S.A. and Douglas H. Everett Department of Physical Chemistry, University of Bristol, Bristol BS8 1 TS An analysis is presented of the thermodynamics of both isothermal and isobaric hysteresis, leading to equations for the calculation of the irreversible entropy production and the loss of free energy in hysteresis cycles of both kinds. The status of ' apparent' enthalpies derived from the temperature dependence of isothermal data is examined and two extreme types of behaviour are identified. An analysis of experimental data shows that the palladium-hydrogen system exhibits characteristics lying between these extremes.However, this does not seriously affect the use of either isothermal or isobaric data to derive the entropy production and free-energy loss. Existing published work on rare-earth metal-oxygen systems is also analysed, but no firm conclusions can be drawn. Many metal hydrides and oxides exist in two (or more) solid phases, conversions between which exhibit hysteresis. If the system is studied isothermally it is found that the pressure (pf) at which the phase richer in hydrogen (the hydride phase) or the higher oxide is formed is higher than that (Pd) at which the reverse process occurs on lowering the gas pressure. Alternatively, the gas pressure may be held constant at a value greater than p f at the lower experimental temperature.The temperature (Td) at which the hydride or oxide decomposes on raising the temperature is then higher than that ( T f ) at which the reverse change takes place on cooling. In this paper isothermal and isobaric hysteresis phenomena are considered, and the relationship between them is discussed. The conclusions are illustrated by experimental data for the palladium-hydrogen system, and compared with data on oxide systems from the literature. Two of the authors have previously presented a detailed model for isothermal hysteresis in metal hydrides,l3 and the work of another of the authors3 and McKinnon4 should also be referred to. We begin with a discussion of the fundamental thermodynamic nature of hysteresis phenomena.Isothermal and isobaric hysteresis are then analysed in thermodynamic terms. The present treatment applies to relatively low pressures when non-ideality of the gas and hydrostatic effects on the solid can be neglected. General Thermodynamic Analysis of Hysteresis Phenomena A thermodynamic interpretation of hysteresis phenomena may be based on the supposition that when an external (independent) variable ( x ) is changed through the hysteresis region, the system can persist in a metastable state beyond the true equilibrium point up to some critical transition point at which it transforms irreversibly into an equilibrium state; on reversing the direction of change of the external variable, the system again overshoots the equilibrium position and the reverse transition also occurs irreversibly from a metastable state.This sequence of events may be represented conveniently in terms of the variation of 25892590 Hysteresis in Metal Hydrides and Oxides G 2 X I X e X U Fig. 1. Schematic representation of free-energy curves for a systems exhibiting hysteresis in the interconversion of states a and j? brought about by variations in an external parameter x. X the free energy of the system G as a function of x, as indicated schematically in fig. 1.5 The curves representing the free energies of the system in states a and p intersect at E. In the absence of hysteresis the phase transition would occur reversibly at x,. However, for systems in which hysteresis occurs, when x varies from x, to xu the system remains in a metastable a state until at xu it changes irreversibly to state p.Similarly, on reducing x, the system is metastable between x, and xl, and returns irreversibly to state a at xl. In any process in a closed system the change in entropy (dS) is given by dS = d,S+diS (1) where d, S is the entropy transferred to or from the surroundings and is equal to dQ/T (where dQ is the amount of thermal energy transferred), and di S is the entropy produced in any internal irreversible processes.6 The production of entropy is associated with an irreversible dissipation of free energy : - Tdi S = di G. Thus in fig. 1 Ai S(2 + 3) = [G"(x,) - GP(x,)]/T (2 a) and Ai S(4 -+ 1) = [GB(xl) - G"(x,)]/T. (2b) If, after a cycle of hysteresis, the system returns to the same state, i.e.in Bridgman's terms7 the state is recoverabIe, then A S = 0 and r r r r fdiS=-$d,S=-$dQ/T=f(-diG/T). (3) The total entropy production is the sum of the contributions from the internal irreversible steps, in each of which a certain amount of free energy is dissipated. The irreversibly produced entropy in the cycle is transferred to the surroundings and appears as a net 'production of heat'. It is important to stress that, in general, it is not possible experimentally to identify the equilibrium state, so that only the total entropy production in a cycle can be obtained.? In most instances of hysteresis the transitions are not sharp, but are spread out over t In some special cases, e.g. supercooling of a liquid, it may be possible to show that one of the transitions takes place reversibly under equilibrium conditions, but in the systems considered here this is not the case.In other instances experimental observations may suggest the location of the equilibrium state, but the arguments employed are not firmly based on thermodynamic considerations. The relation between supercooling phenomena and hysteresis is discussed in more detail by Everett and Whitt0n.jT. B. Flanagan et al. 259 1 Fig. 2. Definition of system in discussing metal-hydrogen systems. The system contains 1 mol of iH, and 1 mol of metal (M). The solid hydride MH(s) coexists with gaseous hydrogen at a pressure p in a volume V . In a process in which an amount of work d Wis exchanged with the surroundings, a transfer dQ of thermal energy occurs.b r a G 2 /-- Fig. 3. Isothermal hysteresis. (a) Phase diagram for metal-hydrogen system which can exist in two states a and p. The hydrogen: metal ratio (r) in state a is a, and in state /I, b. Irreversible transition from a to /? occurs at pf(2 --+ 3), and from p to a at pa(4 -, 1); p e is the (hypothetical) equilibrium transition pressure. (b) Schematic representation of free energies of states a and /3 as function of logarithm of hydrogen pressure, showing irreversible fall in free energy in the steps 2 + 3 and 4 4 1 . a relatively narrow range of values of x. One of the authors and his coworkerss have interpreted this by suggesting that the system may be thought of formally as a mosaic of 'domains', the transition points xu and x1 varying from domain to domain.However, in the present discussion we shall begin by simplifying the problem by supposing that the transitions occur throughout the system at well defined values of xu and xl. Isothermal Hysteresis in Metal-Hydrogen Systems For definiteness we consider metal-hydrogen systems, although essentially the same arguments apply to metal-oxygen systems. The thermodynamic system under consider- ation is shown in fig. 2. Furthermore, we make the additional simplification of representing the composition-pressure isotherms as in fig. 3 (a). State a consists of (1 -a)2592 Hysteresis in Metal Hydrides and Oxides mol of iH2(g) and 1 mol of MHz(s), while state p contains (1 - b) mol of iH2(g) and 1 mol of MHg(s). (M denotes the metal). The free energy of the system when all of the metal is in the a-phase, i.e.along the line 1-2 (fig. 3), is given by Ga = &Ha +$( 1 -a) RT In ( p H , / p O ) (4) where the standard gaseous state i s p e and the gas is assumed to be ideal. Similarly, for the state p, i.e. along the line 3 4 (fig. 3), GB = pGHb + ;( 1 - b) RT In (pH,/pe). ( 5 ) These free-energy curves may be represented graphically as in fig. 3(b). As indicated above, the a and p states are in stable equilibrium with hydrogen gas in the regions 1-E and 3-E, and in metastable equilibrium with respect to the other phase in E-2 and E-4. Irreversible transitions from a to p and from to a occur via steps 2-3, at pf and 4-1, at pd, and are accompanied by the entropy productions (and losses of free energy) given by TA, S(2 + 3) = i(b - a) RT In (pf/pe) = - A, G(2 --+ 3) TA, S(4 --+ 1) = *(a - b) RT In (Pd/pe) = - Ai G(4 + 1) (6) (7) where p e is the equilibrium pressure. However, since p e is generally unknown, all that can be obtained experimentally is the total entropy production, and total loss of free energy in the cycle: the latter is equal to the net work done by the surroundings on the system. Thus - Ai G(cyc1e) = TA, S(cyc1e = T[Ai S(2 --+ 3) + Ai S(4 -+ l)] = $(b -a) RT In (pf/pd) = AW(cyc1e) (8) the work done in the step 2 --+ 3, (b - a) RT, being exactly cancelled by that done in 4-1, (a - b) RT.It is also instructive to follow an essentially equivalent procedure by calculating the entropy difference between states 2 and 3 (which are interconvertible experimentally only by the irreversible step 2 + 3) through the sequence of steps 2 -+ 5 , 5 + 6,6 + 3.Of these 2 -+ 5 and 6 + 3 are, respectively, the reversible expansion of (1 -a) mol of gas and the reversible compression of (1 - b ) mol of gas. Step 5 -+ 6 is not experimentally realisable, but consists of a hypothetical reversible absorption of (b -a) mol of H, at p,:? AS(2 + 5 ) = $( 1 -a) R In (Pf/pe) = AQ(2-5)/T AS(5 + 6) = (b-a) Af H/ T AS(6 -+ 3) = $(l - b) R In (pe/pf) = AQ(6-3)/T (9) where Af H is the molar enthalpy for hydride formation [i.e. for the absorption of 1 mol of iH,(g)]. AS(2-3) is given by the sum of the changes in eqn (9) (10) AS(2 + 3) = S(3)-S(2) = (b-a)A,H/T+i(b-a)R ln(pf/pe). When 2-3 occurs irreversibly AS(2-3) = A, S(2 + 3) + A, S(2 + 3). (1 1) t A question can be raised about the validity of the above procedure, which rests on the assumption that states 2 and 3 are recoverable in the Bridgman sense.' This seems to be justified experimentally by the observation that hysteresis cycles (sometimes omitting the first) are repeatable.In terms of one molecular interpretation,' in which hysteresis in these systems is attributed to the plastic deformation needed to accommodate the volume changes accompanying hydride formation and decomposition, it is suggested that the dislocation densities in the metal in states 2 and 3 are the same in successive cycles.T. B. Flanagan et al. 2593 r I I '12 Inp, 112 lnp, 31n P Fig. 4. General form of isothermal hysteresis loop for metal-hydrogen system showing diffuse transitions.The heat flow in the irreversible process at constant pressure is (b -a) Af H, so that Ae S(2 -+ 3) = (b -a) Af H/T, and comparing eqn (10) and (1 1) we may identify7 - Ai S(2 -+ 3) = i(b -a) R In ('pf/pe) Ai S(2 -+ 3) = AQ(2 -+ 5)/T+AQ(6 -+ 3)/T (12) (13) which is the same as eqn (6). Furthermore, from eqn (9) where AQ(2 -+ 5) and AQ(6 + 3) are positive and negative quantities, respectively. For the cycle 5 -+ 2 -+ 3 -+ 6 -+ 5 (fig. 3), A S = 0. Since the enthalpies of formation (2-3) and decomposition (6-5) cancel, the overall entropy exchange Ae S(cycle), which carries away the irreversibly produced entropy in step 2 -+ 3 is made up of the contributions from the reversible compression and expansion of the gas in steps 5 + 2 and 3 -+ 6. Of the amount of heat AQ(5 + 2) evolved during the compression p e -+pf, a lesser amount of heat AQ(3 -+ 6) has to be absorbed during the expansion p f + p e in order to compensate for the entropy production in the hydride formation step 2-3.By similar arguments Ai S(4 + 1) = AQ( 1 + 5)/T+ AQ(6 -+ 4)/T = i(b -a) R In (p,/pd). (14) As stressed above, the hypothetical steps 5-6 and 6-5 are not realizable in practice, so that one must consider the cycle around the whole hysteresis loop (or a closed scan from p f to Pd and back again or vice versa), when Ai S(cyc1e) = AQ( 1-2)/ T+ A Q ( 3 4 ) / T = i(b - a) R In (pf/pd). (15) The net heat change in the complete isothermal cycle now consists of the contributions from the reversible compression of the gas from 1 + 2 and the decompression 3 4 4 and this compensates for the irreversible changes in 2 -+ 3 and 4 --+ 1 so that AS(cyc1e) = 0. We stress that not only the entropy of the system, but also the enthalpy and free energy must return to the same values at the end of the cycle since the system is recoverable, at least for hysteresis cycles after the first, which are the ones of concern here.Thus for the simplified behaviour of fig. 3, the enthalpy of transition 2 + 3 is equal in magnitude to that of the reverse transition 4 + 1. The quantities which do not return to the same values (and are not functions of state) are the work done on the system and the heat exchanged with the surroundings. It is this fact which leads to the general thermodynamic concept that because of hysteresis the net work done on the system is dissipated as heat.t This involves the assumption that A, H at p e is the same as that at p,.2594 (see fig. 2) that in the more general case of fig. 4 that - Ai G(cyc1e) = AW(cyc1e) = p dV = +RT lnp dr Hysteresis in Metal Hydrides and Oxides So far we have discussed the simple case of a rectangular loop. It is readily showng ro+Ar f = iRT In (pf/pd) dr = TAi S(cyc1e) (1 6) where r = [H]/[M] and pf and P d are the pressures on the two branches of the hysteresis loop at a given r . Thus the entropy production in an isothermal cycle is given by the area of the loop plotted in R lnpi against r coordinates. The free-energy loss per unit quantity of H involved in the cycle is obtained by dividing the terms in eqn (16) by Ar. P ro Isobaric Hysteresis Here again it is instructive to consider the problem in terms of the free energies of states a and p.However, instead of maintaining constant temperature, the system is now in contact with a series of heat reservoirs covering a range of temperatures, while the applied pressure is constant. The composition-temperature diagram is taken as a simple rectangle [fig. 5(a)], while the free energies of the two states are sketched as functions of temperature in fig. 5(b). In general, for the reaction of 1 mol of $H2 converting MHE into MH!, denoted by Af, we have from the Gibbs-Holmholtz equation (assuming Af C,, the isobaric heat- capacity change of reaction, to be constant) The states p and a are thermodynamically stable in the regions 1 -+ E and 3 -+ E, respectively, and metastable in the regions E -+ 2 and E + 4.Irreversible entropy production occurs in the decomposition step 2 -+ 3 on raising the temperature to Td, and in 4 + 1 when state a is reformed at T,, the losses in free energy being, respectively, Ad G(Td) and Af G(T,). Hence Ai S(2 + 3 ) = - G(Td) = (b-a)(---- Af H( Td) Af H( Te) Af C, l n 2 ) , Td Td Te Te where A, H = -Ad H. In the cycle Ai S(cyc1e) = (b -a) 'f H(Td) 'f H(&) Af C, ln..>. ( Td T, T, The corresponding free-energy loss in the cycle is - Ai G(cyc1e) = Td Ai S(2 + 3) + Tf Ai S(4 + 1). Since both Ai S(2 + 3) and Ai S(4 -+ 1) involve Te it follows that Ai G(cycle), unlike Ai S(cycle), depends on T,. Thus while Ai S(cyc1e) can be calculated from experimental data, Ai G(cyc1e) for isobaric hysteresis is not amenable to direct evaluation in the absence of knowledge of the equilibrium temperature, or of an approximate method of locating the equilibrium state.T.B. Flanagan et al. 2595 b r U I 1 I I G Fig. 5. Isobaric hysteresis : (a) Phase diagram for metal-hydrogen system which transforms from the low temperature state /? to a at Td, and reforms /? at T f . T, is the (hypothetical) equilibrium temperature. (b) Schematic representation of free energies of states a and /? as function of temperature, showing irreversible fall in free energy in the steps 2 + 3 at Td and 4 -, 1 at Tf. Alternatively we may calculate the external entropy exchange in the separate steps 1-+2-+3-+4+1: c p ( M H D + ( y ) C,(W d T Td dQ Td Tf T Ae S( 1 -+ 2) = I,, = I = [C,(MH#)+ ( l i b ) ~ _ _ C,(H,) 1 In- : Ae S(cyc1e) = (b -a) +- = - Ai S(cyc1e) (26) since and where Ai S(cyc1e) + Ae S(cyc1e) = 0 The irreversible entropy production in the solid-phase reaction is partially compensated for by the fact that the calorimetric enthalpies of formation and decomposition are exchanged at different temperatures, and partly because the distribution of H, between gas and solid is different in the two reversible heating and cooling steps.Again it is important to remember that it is not possible to calculate the individual contributions Ai S(2 -+ 3) and Ai S(4 + 1) unless the equilibrium temperature is known. The above equations apply to a simple rectangular loop. A more general equation is Ai S(cyc1e) = $y dr (27)2596 Hysteresis in Metal Hydrides and Oxides Tf 7, T Fig.6. General form of isobaric hysteresis loop for metal-hydrogen system showing diffuse transitions. where Af H refers to the reaction in which 1 mol of $H,(g) is absorbed, and in some regions is a partial molar quantity reflecting the diffuseness of the transition (fig. 6). If A, C, z 0 so that Af H is constant this reduces to r,,+Ar Ai S(cyc1e) = - Af H i,. A ( l / r l d r (28) where A( 1 / T ) is the width of the loop, plotted as r against 1 / T , and ro and ro + Ar are the limits of the loop. To relate this to the entropy production per unit amount of H involved in the cycle, Ai S(cyc1e) obtained using eqn (28) must be divided by Ar. Approximate Location of the Equilibrium State It is not possible to demonstrate from thermodynamic arguments alone that the free-energy losses due to irreversibility should be equal for hydride formation and decomposition, and indeed they may not be generally equal.For the palladium-hydrogen case, however, it has been arguedl that the hysteresis is related to the formation of dislocations in the crystal lattice and that similar dislocation densities are associated with both the a + p and p + a transitions. Experimental support for this has been given.2 On this basis one might then postulate that Ai G(a -+ 8) = Ai G(P + a). In this case it follows that for isothermal hysteresis : In h l p e ) = In (PeIPd) (29) or Pe = (Pf P,)' (30) Te = (Td+ Tf)/2. (31) while for isobaric hysteresis, assuming ACp = 0 or (Td - T f ) is small, For small temperature differences the arithmetic and geometric mean are approximately equal so that Te % (Td &)i.On the other hand, if Ai S is the same for both transitions the same answer is obtained for isothermal hysteresis, but for isobaric hysteresis a slightly different condition emerges : which for Td = T f reduces to eqn (32).T. B. Flanagan et al. 2597 It is now possible to rewrite eqn (20) and (21) in the following approximate and more useful forms: Ai S(cyc1e) Af H( T,) AT - - - (b - 4 Td Tf Ai G(cycle) A, H( T,) AT - - ( b - a) (Td &)' where AT = Td- Tf. (34) (3 5 ) Alternatively, if one attempts to treat the problem in terms of a statistical theory which predicts the form of fig. 4 (or the equivalent pressuresomposition diagram exhibiting a van der Waals type loop) one could again predict the location of p,.In the isobaric case, the problem is rather more complicated, but is in principle soluble. Derivation of ' Apparent ' Thermodynamic Quantities It is a common practice to use values of pf or Pd at different temperatures to derive apparent enthalpies of hydride formation [A, H(app)] or decomposition [Ad H(app)] from the equations where A, H and Ad H refer to the transfer of 1 mol of $H,. Less commonly, the variations of the transition temperatures in isobaric measurements at a range of pressures have been used : If the quantities derived from eqn (36) and (37) were true enthalpies then AH(cyc1e) = AH(app)dr = 0. i This criterion has been shown not to be satisfied for the H,-Pd system,lo while a similar discrepancy exists for adsorption-desorption hysteresis.ll The problems arising in the use of the above equations were discussed tentatively by Everett and Whitton" and by La Mer.12 This discussion can be extended in the following way.We consider first the simple case of a rectangular hysteresis loop. From eqn (6) we have = (b - 4 [Af m P P ) - A, HI (41) where Af H is the true enthalpy of formation of the hydride. A similar set of equations relates to Af G(4 -+ 1). For a complete cycle it follows by summing the contributions from2598 steps' (2 3 3) and (4 3 1) that Hysteresis in Metal Hydrides and Oxides 1 d Ai G(cyc1e) d Ai S(cyc1e) Ai G(cyc1e) + - T( d(l/T) > = - d(l/T) = - (b - a) Pf W P P ) + Ad waPP)l = - (b - a) AH(app, cycle). (42) Two extreme cases can be identified: (i) If Ai S(cyc1e) is independent of T then AH(app) = AH and AH(app, cycle) = 0.(43) (ii) If Ai G(cyc1e) is independent of T. In each step A . G TA. S AH(app) = A H - 1 = A H i - i 6-a b-a (44) and (45) Case (ii) is that which Everett and Whitton postulated might apply to adsorption- desorption hysteresis. A H (app, cycle) = - Ai G(cycle)2 = iRT In kf/pd). In the more usual situation of diffuse transitions case (i) gives AH(app, cycle) = AH(app)dr = 0 P while for case (ii), eqn (45) becomes AH(app, cycle) = Ai G(cyc1e) = $RT (47) If we define an apparent standard entropy, corresponding to the change of gas at p e to the hydride phase at pressure p , by then case (ii) corresponds toll $AS* (app)dr = 0 (49) i.e. AS* (app) behaves as a function of state.It seems likely (see below) that the behaviour of real systems lies between these two extremes. In the general case it also follows from eqn (47) that Eqn (50) constitutes a thermodynamic consistency test of the analysis of experimental data. Previous discussions of the thermodynamics of metal-hydrogen systems have derived so-called standard free energies and ent~0pies.l~ It is important to stress that it is essential that the standard states be defined explicitly otherwise ambiguity and misunderstanding can arise. For example, the standard entropy of the equilibrium state with respect toT. B. Flanagan et al. 2599 Table 1. - Ai G(cyc1e) Ai S(cyc1e) d[Ai S(cycle)]/d( 1 / T ) AH(app, cycle) T / K J (mol H)-l J K-' (mol H)- J (mol H)-' J (mol H)-' Flanagan et al.14: annealed Pd strip :::} 1160 isothermal 200 980 273 865 383 810 2.1 present research: another sample of Pd strip (a) (b) (4 (b) (c) (4 (4 (4 isothermal 300.2 690 592 2.30 1.97 (Ar = 0.0665) isobaric 289-300 713 661 2.44 2.25 (Ar = 0.0685) Evans and Everett:lo Pd sponge (b) (b) ::a:) 2070 isothermal 353 958 (Ar = 0.56) 373 909 393 830 2.1 1 1350 1975 a Calculated by approximate eqn (8).(35). Calculated by exact eqn (16). Calculated by approximate eqn Calculated by exact eqn (28). Calculated by exact eqn (28)+approximate eqn (53). hydrogen at pressure p* (usually taken as atmospheric pressure) and pure metal is given by while for the system in state 3'(fig. 3), again starting from the same standard state, is Values of Af P ( E ) can only be calculated if p e is known.Although this is not generally possible, it may in some circumstances be adequate to estimate p e from eqn (30). Experimental and Results The above discussion may be illustrated using the data of Kishimoto (unpublished) and Flanagan,l* together with the work of Evans and EverettlO and data from the present investigation. In the former, thin, well annealed palladium strips were used in a conventional Sieverts apparatus. A series of measurements of plateau pressures were made in the temperature range 200-383 K and used to calculate AiG(cycle) and AiS(cycle) from eqn (8) (table 1). Since it was not possible to obtain complete hysteresis loops at lower temperatures, the alternative calculation through eqn (1 6) could not be applied to these data. Apparent enthalpies of formation and decomposition were calculated from the temperature dependence of the plateau pressures.In the present work another sample of palladium was used in an isothermal experiment at 300.2 K, and an isobaric experiment at p = 7.65 Torr (1.02 kPa). The results are presented in fig. 7 and 8. The hysteresis loops were not taken to complete conversion, but both the isobaric and isothermal experiments spanned approximately the same range of r (0.03-0.10). Table 1 includes values of Ai G(cyc1e) and Ai S(cyc1e) calculated for the2600 Hysteresis in Metal Hydrides and Oxides 2.6 3 .O 3.4 3.8 p&/(Torr)+ Fig. 7. Isothermal hysteresis loop at 300.2 K for palladium-hydrogen: r is shown as a function of pj/Torri (this work). r 2 80 29 0 300 T/K Fig.8. Isobaric hysteresis loop at 7.65 Torr for palladium-hydrogen : r is shown as a function of T (this work). isothermal experiment using eqn (8) and (16) and for the isobaric experiment using eqn (39, (28) and (53). In each case the approximate eqn (8) and (35) gave larger absolute values of both Ai G(cyc1e) and Ai S(cyc1e) than the exact equations, which take account of the diffuseness of the transitions. Evans and Everett, using the apparatus and Pd sponge sample described by Everett and N ~ r d o n , ~ reported hysteresis loops between complete conversion and recovery of the a-phase, i.e. r in the range 0.03-0.59, at temperatures in the range 353-393 K. ValuesT. B. Flanagan et al. 260 1 - I - 2 5 - v 2 g : 2 - 3 1 - 5 ;1 4 - 3 - '= n W I h 1 2 0 0 -1 0.2 0.3 0.4 0.5 0.6 Fig.9. [Ad H(app) + ALf H(app)]/kJ (mol H)-l as a function of r for the hydrogen-palladium system at 400 K (Evans and EverettlO). r of Ai G(cyc1e) and Ai S(cyc1e) obtained in this work and calculated using eqn (1 6) are given in table 1, while [AfH(app)-A,H(app)] calculated from their data is shown as a function of r in fig. 9. Discussion It has been postulated from earlier work1, that in isothermal hysteresis Ai G(a + a) = AiG(j?+ a) and a similar postulate for isobaric hysteresis is that AiG(B+ a) at Td = Ai G(a + a) at T,, in which case p p and Te can be calculated from eqn (30) and (32). This would imply that AiG(cycle) in isothermal hysteresis should be independent of temperature i.e. that the hysteresis phenomena conform to case (ii) above.The data presented in table 1 show, however, that both Ai G(cyc1e) and Ai S(cyc1e) depend on temperature, so that the systems fall into a class intermediate between (i) and (ii). The magnitudes of these quantities for one of the samples used by Flanagan et al. are broadly similar to those obtained from the work of Evans and Everett, although the temperature coefficients are very different. The other sample of Flanagan et al. leads to rather smaller values of both quantities, but this may not be significant because the measurements were made on different samples and over a much smaller range of r . Eqn (50) indicates a thermodynamic link between the temperature dependence of AiS(cycle) and AH(app, cycle). The data of Evans and Everett give d[Ai S(cycle)]/d(l/T) = 2070 J (mol H)-l while, from fig.9, AH(app, cycle) = 1975 J (mol H)-l, thus checking the internal consistency and the reliability of their calculations of the apparent enthalpy. A second check on the applicability of case (ii) is to compare AH(app, cycle) with -AiG(cycle): they should be equal. At 373 K-Ai G(cyc1e) = 909 J (mol H)-l, which is less than one half of AH(app, cycle). The work of Flanagan et al. gives d[Ai S(cycle)]/d( 1/T) = 1 150 J (mol H)-l, while the apparent enthalpies calculated from their data lead to AH(app, cycle) = 1350 J (mol H)-l. Although this differs from the value derived from Ai S(cycle), it is probable that it is within the experimental uncertainty of the enthalpy calculation which was based on approximating the hysteresis loop by a rectangular loop.Again both quantities differ significantly from Ai G(cyc1e) = 865 J (mol H)-l at 273 K, thus illustrating the inadequacy of case (ii). A direct comparison between isothermal and isobaric hysteresis follows from fig. 7 and 8. -AiG(cycle) at 300.2 K calculated from the approximate formula (8), 690 J (mol H)-l, is higher than that, 592 J (mol H)-l, obtained by integration [eqn (16)]. 86 FAR 12602 Hysteresis in Metal Hydrides and Oxides To apply eqn (35) to the isobaric experiment it is necessary to know Af H. Reported calorimetric values are - 19.2,15 - 19.216 and -20.1l7 kJ (mol H)-l. From fig. 8, A T = 10.9 K, T, z ( T f T'& = 293.4 K. Taking a value of - 19.2 kJ (mol H)-l for Af H gives -Ai G(cyc1e) = 713 J (mol H)-l at the mean temperature of 293.4 K.If the integration indicated by eqn (28) is used, together with the approximation - Ai G(cyc1e) = (Tf Td)i Ai S(cyc1e) (53) a lower figure [661 J (mol H)-l] results. Thus values of Ai G(cyc1e) and Ai S(cyc1e) calculated from isothermal and isobaric hysteresis are in reasonably close agreement. This is to be expected since the isobaric loop covers a range of only 11 K, over which Ai G(cyc1e) will not vary appreciably (cf. table 1): Ai G(a -+ /?) and Ai G(j3 -+ a) will be essentially the same in both types of experiment. It follows that because of this small temperature range these data cannot be used to distinguish between cases (i) and (ii). For this to be possible it would be necessary to seek conditions under which the isobaric loop covers a much wider range of temperature.It is of considerable practical importance to observe that, provided A T is not too large, Ai G(cyc1e) calculated from isobaric hysteresis is a reasonable approximation to Ai G(cyc1e) derived from isothermal hysteresis at the mean temperature. For many systems isobaric but not isothermal data are available, so that if A H for the change is known, the extent of isothermal hysteresis can be estimated; conversely A T for isobaric hysteresis can be calculated from a knowledge of the isothermal behaviour. Hysteresis in Metal Oxide Systems Data for metal oxide systems are less extensive and are probably of lower precision than those for the palladium-hydrogen system. Here we make use of the work of Eyring and his coworkers who have measured both isothermal and isobaric hysteresis loops for a series of terbium and praeseodymium oxides.18-20 The isothermal data have been analysed by Porter21 to obtain values of AiG(cycle) (which he denotes by Q).He used a different method of analysis in terms of the first equality of eqn (1 6), which is equivalent to that using the last equality, and expressed the results in terms of the conversion of one mole of metal. The values of AiG(cycle) were found to vary erratically with temperature : no temperature dependence can be discerned. Recalculation to correspond to the reaction of one mole of iO,(g) leads to the mean values given in table 2. In three of the four systems analysed by Porter Ai G(cyc1e) is close to 2.5 kJ (mol O)-l; the fourth gives a much higher but more uncertain value which is, however, not inconsistent with that for the other systems.Eyring's data for Pr,O,,/Pr,O,, which were not included by Porter lead to a value of 0.5 kJ (mol O)-l, although the results of a later study by Inaba and Naito22 give 1.21 kJ (mol O)-l. Comparison of isothermal and isobaric measurements is possible for two systems (see table 2). In both instances, in the absence of calorimetric data, it has been necessary to use values of AH(app) in the calculations. In view of the other uncertainties it is unlikely that this approximation will lead to serious errors. In the case of Tb,O,-Tb,O,, the value of Ai G(cyc1e) calculated from isobaric measurements is some 2.80 times higher than that from the isotherms. For Pr,0,,-Pr,016 a similarly large discrepancy is found if one adopts the value from isothermal data of Eyring et al., although the value of Inaba and Naito is close to the isobaric value.On the basis of the available evidence, therefore, one cannot draw any firm conclusions concerning the applicability of the equations developed in this paper to oxide systems. Because of the known sensitivity of the results to the pretreatment of the sample it is important that isothermal and isobaric experiments be carried out on the same sample and that the recoverability of the system be confirmed experimentally. It is not clear to what extent this condition was satisfied in the work on the metal-oxygen systems.T. B. Flanagan et al. 2603 Table 2. isobaric reaction isothermal : [for -AiG(cycle) AT (q Td)& AH - Ai G(cyc1e) W 2 ) l range ref.kJ (mol O)-l K K kJ (mol O)-l kJ (mol O)-l - _ _ _ addition of Tor T gTb203/$Tb7012 98 1-1 079 (TbOl. 5dTb0l. 71) ~Tb701,/~Tb,,0,, 76&804 (TbOl.7l/TbOl.8*) Wr7O 1 z/%Pr,O 16 973 ~ p r o l . 7 1 / p r o l . 78) 838 5Pr,0,,/9Pr50, 737-776 .78/pr01.80) 6Pr50,/5Pr,0,, 708-753 .80/Pr01. 83) ~ 78.3 1205.8 108 7.01 19, 21 2.51 k0.38 21 3.56k1.15 - 0.5 1 22 I 9.3a 854.7a 118.6a 1 .29a 21 2.20k0.30 ~~ a Ref. (18) Conclusions The analysis presented in this paper leads to both approximate and exact equations for the calculation of the loss of free energy and the production of entropy in cycles both at constant temperature and constant pressure. Provided that the temperature range involved in isobaric hysteresis is not too large and the enthalpy of reaction is known, the quantities calculated from such data are in good agreement (& 6%) for palladium- hydrogen with those obtained from isothermal measurements.The status of apparent enthalpies derived from the temperature dependence of isothermal measurements is examined. Two extreme cases are identified in which (i) the entropy production is independent of temperature, when the apparent enthalpies are measures of the true enthalpies; (ii) the loss in free energy is independent of temperature, when the apparent enthalpy, integrated round the cycle, is equal to the loss in free energy. The behaviour of the palladium hydrogen system appears to fall between these two limits. Available evidence for rare-earth metal-oxygen systems is inconclusive.T. B. F and his coworkers at the University of Vermont acknowledge financial support by the N.S.F. References T. B. Flanagan, B. S . Bowerman and G. E. Biehl, Scr. Metall., 1980, 14, 443. T. B. Flanagan and J. D. Clewley, J. Less-Common Met., 1982, 83, 127. D. H. Everett and P. Nordon, Proc. R. SOC. London, Ser. A , 1960, 259, 341. W. R. McKinnon, J . Less-Common Met., 1983, 91. 13 1. D. H. Everett and W. I . Whitton, Trans. Faraday Soc., 1952, 48, 749. E.g. I. Prigogine and R. Defay, Chemical Thermodynamics, transl. D. H. Everett (Longmans. London, 1954). P. W. Bridgman, Rev. Mod. Phys. 1950, 22, 56. D. H. Everett and F. W. Smith, Trans. Faruday SOC.. 1954,50, 187; D. H. Everett, Trans. Faraday Soc., 1954, 50, 1077; D. H. Everett, Trans. Faraday Soc., 1955, 51, 1551. 86-22604 Hysteresis in Metal Hydrides and Oxides 9 E.g. D. H. Everett, in The Solid-Gas Interface, ed. E. A. Flood (Dekker, New York, 1967), chap. 36, p. 1072. 10 D. H. Everett and M. J. B. Evans, J. Less-Common Met., 1976, 49, 123. 11 M. J. B. Evans and D. H. Everett, Proc. R. London, Ser. A , 1955, 230, 91. 12 V. K. La Mer, J. Colloid Interface Sci., 1967, 23, 297. 13 E.g. J. J. Murray, M. L. Post and J. B. Taylor, in Proc. Int. Symp. Metal-Hydrogen Systems, Miami Beach 1981, ed. T. N. Veziroglu, (Pergamon, Oxford, 1982), p. 445; F. Pourarian, V. K. Sinha, W. E. Wallace, A. T. Pesziwiztr and R. S. Craig, in Proc. Int. Symp. on Electronic Structure and Properties of Hydrogen in Metals, Richmond, Va. (Plenum Press, New York, 1983), p. 385. 14 S. Kishimoto and T. B. Flanagan, unpublished data. 15 T. Kuji, W. A. Oates, B. S. Bowerman and T. B. Flanagan, J. Phys. F, 1983, 13, 1785. 16 C. Picard, 0. J. Kleppa and G. Baureau, J. Chem. Phys., 1978,69, 5549. 17 D. M. Nace and J. G. Aston, J. Am. Chem. Soc., 1957, 79, 3619. 18 D. R. Knittel, S. P. Pack, S. H. Lin and L. Eyring, J. Chem. Phys., 1977, 67, 134. 19 J. Kordis and L. Eyring, J . Phys. Chem., 1968, 72, 2030, 2044. 20 A. T. Lowe and L. Eyring, J. Solid State Chem., 1975, 14, 383. 21 S. K. Porter, J. Chem. Soc., Faraday Trans. 1, 1983, 79, 2043. 22 H. Inaba and K. Naito, J. Solid State Chem., 1983, 50, 100. Paper 5/1814; Received 18th October, 1985

ISSN:0300-9599    

DOI:10.1039/F19868202589

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J . Chem. SOC., Faraday Trans. 1, 1986, 82, 2605-2614 Thermodynamics of the Adsorption from Aqueous Alcohol Solutions by Graphitised Carbon (Graphon) Douglas H. Everett* and Alistair J. P. Fletcher? Department of Physical Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 ITS Adsorption isotherms have been determined for the system [water (1)- methanol (2)] on graphitised carbon (Graphon) at five temperatures in the range 298.15-338.15 K, and for the system [water (l)-ethanol(2)]/Graphon at six temperatures from 298.15 to 348.15 K. The data have been subjected to a thermodynamic analysis to obtain values of the interfacial tension at the liquid/solid interface and for the enthalpy and entropy of immersion of Graphon into liquid solutions, relative to the corresponding quantities for one or other of the pure components.The condition for thermodynamic equilibrium at the three-phase line of contact in a system comprising liquid A, liquid B and a rigid solid S, where A and B are immiscible, is given by Young’s equation: where 8 is the contact angle measured through liquid A, aAS and oBs are the surface tensions of liquid A and B, respectively, at the A/S and B/S interfaces, and oAB is that at the AB interface. As is well known, it is not possible to measure uAS and aBS separately, so that no direct experimental confirmation of Young’s equation is possible. However, as pointed out previously,l if A and B are both miscible with C, then by measuring the adsorption from mixtures of A-C and B-C over the whole concentration range it is possible, by integration of the Gibbs adsorption isotherm, to obtain ( o ~ ~ - o ~ ~ ) and (ass - a,,).The difference (oBS - oAS) can thus be obtained and when aAB is known, the contact angle 8 can be calculated by a thermodynamic route. The present work is designed to test this procedure by calculating the contact angle for the system benzene/water/Graphon from measurements on (benzene+thanol)/ Graphon and (water-ethanol)/Graphon or from (benzene-methanol)/Graphon and (water-methanol)/Graphon; and for the system n-heptane/water/Graphon using ad sorption measurements for (n- hep tane-e t hanol)/Grap hon and (wa ter-e t hanol)/ Graphon. The methanol route is inapplicable for n-heptane since n-heptane and meth- anol are not completely miscible. The contact angles obtained in this way will then be compared with those measured directly, and published previously.2 This paper reports measurements on the systems (water-methanol)/Graphon and (water-ethanol)/Graphon.A reanalysis of our earlier work3 on (benzene-ethanol)/ Graphon and (n-heptane-ethanol)/Graphon together with new data on (benzene- methanol)/Graphon are presented in a second paper, while the third paper of this group considers the application of the data to the wetting characteristics of the systems benzene/water/Graphon and n-heptane/water/Graphon and comparison with direct observation. GBs - GAS = OAB cos 8 (1) t Present address: B.P. Research Centre, Sunbury. 26052606 Adsorption of Aqueous Alcohols on Carbon Experimental The apparatus and its mode of operation for non-aqueous systems has been described previ~usly.~ When used for aqueous solutions the phosphor-bronze bellows pumps tend to corrode and they were replaced by a mechanical piston pump oscillating a column of mercury (fig.I). The same sample of Graphon (rn = 19.665 g) was used throughout and was taken from the same batch (a gift from the Cabot Corporation) as that employed previo~sly.~-~ It was washed with 0.2 mol dmP3 HC1 to remove sulphide impurities, then several times with distilled water and dried. This was followed by soxhlet extraction with n-hexane, and by drying at 550 K and loP4 Torr for 24 h. The fraction sieved between 18 and 52 mesh per inch was used. The specific surface area determined by the B.E.T. method from N, adsorption at liquid nitrogen temperature was 84.5 m2 gP1.Between runs the absorbent was outgassed at 550 K, loP4 Torr for 24 h. Ethanol and methanol were AnalaR grade (B.D.H.) and were stored over 4A molecular sieve. The water was freshly double distilled in an all-glass still. The surface tension of typical batches was > 72 mN m-,, indicating the absence of surface active impurities. The purity of the components was further tested by passing each individually over the Graphon adsorbent: in no case did the refractometer register a significant change in composition between the reference and adsorption sides of the apparatus. Solutions were made up by weight, from degassed components, by distilling the liquids under vacuum into the preparation flask [fig. 2 of ref. (4)] : the total amount, no, of solution transferred to both the adsorption and reference circuits was obtained by weighing. The precision of the present technique is critically dependent on calibration of the refractometer which is needed to establish Ax:, the change in mole fraction resulting from adsorption.A particular problem arises with the water-alcohol systems since the refractive index passes through a maximum at a mole fraction of ca. 0.35 for methanol,8 u -\ =s+ G F!g. 1. Mercury operated circulating pump : A, precision bore glass tubing; B, stainless-steel piston; C, neoprene piston ring; D, cam operated by fractional HP electric motor; E, return spring; F, G, Youngs’ taps; H, I, glass non-return valves; J, mercury.D. H. Everett and A . J . P. Fletcher 2607 and 0.60 for ethan01.~ In the neighbourhood of the maximum the sensitivity of the refractive index method of analysis falls off so rapidly that adsorption measurements around these concentrations could not be made.The calibration was carried out at the end of each run by adding known amounts of alcohol to the reference side of the apparatus and plotting the refractometer output against the calculated change in mole fraction. At each mole fraction several additions of alcohol were made and the refractometer output plotted against the volume added. These graphs were accurately linear since the mole fraction change was small, and the slope gave the refractometer sensitivity at the mole fraction concerned. Three methods of adding alcohol were used. In the first a known volume of alcohol held in a bypass capillary between two Youngs’ needle valves was introduced into the main system by manipulating the taps; in the second, several small glass ampoules containing a weighed amount of alcohol were introduced into an enlarged section of the reference circuit.At an appropriate moment an ampoule was crushed using an externally controlled plunger. These methods, used for the water-ethanol system, were not entirely satisfactory and for the water-methanol system, degassed methanol was injected from an Agla syringe through a septum, one face of which was coated with PTFE. It was thus possible to make up to six injections covering the range 25-150 mm3. This enabled considerably greater precision to be achieved. Fig. 2 shows the sensitivity plotted as the reciprocal of the mole fraction change per chart recorder unit as a function of mole fraction for both ethanol-water and methanol-water.The form of these curves can be calculated from the known variation of refractive index with mole fraction. This was necessary in the case of the water+thanol system to overcome the scatter of points in the calibration. The refractive index ( n ) us. mole fraction (xi data of Scott9 were fitted to an eighth-order Chebyshev polynomial, 10 5 Is: \ I 2 0 - 5 0 Fig. 2. Refractometer calibration curves for water-methanol and water+thanol mixtures. 1 /R is shown as a function of xf, where R = recorder chart units for lop4 change in xi. The curve for ethanol was obtained by fitting points obtained by the first two methods described in the text to the refractive index against composition relati~nship.~ The calibration for methanol was carried out by the third method.0 , Interpolated points for ethanol-water; 0, experimental points for met hanol-wa ter .2608 Adsorption of Aqueous Alcohols on Carbon from which dn/dx was calculated and used to smooth the calibration curve. With water-methanol this procedure was unnecessary. A slow drift of refractometer sensitivity over several months meant that recalibration was needed from time to time. This problem may be overcome using the null method of measurement which was developed in later work.10 Results Specific surface excess isotherms (noAxi/m against xi) were determined at five temperatures in the range 298-338 K for the system [water (IFmethanol (2)]/Graphon and at the temperatures in the range 298-348 K for the system [water (l>-ethanol(2)]/Graphon (fig. 3 and 4).The isotherm data are given in tables 1 and 2. In both cases the alcohol is the preferentially adsorbed component. I I I I A I I I I 0-2 0 4 0.6 0.8 1 .o 4 Fig. 3. Adsorption isotherms for (water-methanol)/Graphon at various temperatures : n"Ax;/m as function ofx,. Points above xi = 0.4 at intermediate temperatures omitted for clarity. 0,298.15; 0, 308.15; A, 318.15; V, 328.15; a, 338.15 K. Analysis of Results Thermodynamic Analysis The thermodynamic analysis was carried out using the integrated form of the Gibbs adsomtion isotherm :I1 where 0 and a,* are, respectively, the surface tensions of a solution of mole fraction x i and of pure component 2 in contact with the solid, y i is the activity coefficient of component 2 in the bulk solution, and a, the specific surface area of the solid.If the integration is taken to xi = 0, the difference a: -0: is obtained.D. H. Everett and A . J . P. Fletcher 2609 I Fig. 4. Adsorption isotherms for (water+thanol)/Graphon at various temperatures : n"Axi/rn as function of xi. 0, 308.15; 9, 328.15; 0, 348.15 K. Curves for 298.15, 318.15 and 338.15 K omitted for clarity. Table 1. Values of (n"Ax~/m)/104 mol g-' for [water (1)- methanol (2)]/Graphon ~ __ ~ xk 298.15 K 308.15 K 318.15 K 328.15 K 338.15 K 0.034 0.078 0.090 0.127 0.193 0.249 0.277 0.302 0.441 0.51 1 0.599 0.646 0.669 0.858 1.327 2.746 2.8 19 3.319 3.586 3.952 4.128 4.083 2.749 2.344 1.913 1.126 0.648 0.335 1.286 2.607 2.692 3.165 3.393 3.699 3.763 3.749 2.749 2.382 1.890 1.106 0.622 0.343 1.258 2.474 2.564 2.998 3.208 3.446 3.480 3.412 2.742 2.4 14 1.863 1.083 0.594 0.350 1.217 2.340 2.436 2.83 1 3.022 3.192 3.140 3.075 2.742 2.449 1.836 1.01 1 0.571 0.357 1.183 2.20 1 2.309 2.67 1 2.837 2.939 2.909 2.737 2.763 2.434 1.808 1.060 0.548 0.364 The results of this analysis are critically dependent on the use of reliable activity coefficient data.For the water-methanol system we have used the data of McGlashan and Williamson,12 who report values of x,, y, (the mole fraction in the vapour) and p (the total pressure) at 35, 50 and 65 "C. The activity coefficients were calculated from In72 = WPY,/P,* 4 +(B,,+v,*)(P-P,*)/RT (3)2610 Adsorption of Aqueous Alcohols on Carbon Table 2.Values of (noAxf/m)/104 mol g-' for [water (lj+thanol (2j]/Graphon ~ x i 298.15 K 308.15 K 318.15 K 378.15 K 338.15 K 348.15 K ~~ -~ 0.004 0.910 0.861 0.8 13 0.766 0.720 0.674 0.022 4.343 4.229 4.107 3.924 3.673 3.406 0.029 4.646 4.576 4.440 4.292 4.141 3.902 0.051 4.776 4.736 3.663 4.536 4.369 4.169 0.145 4.128 4.0 16 3.880 3.768 3.588 3.385 0.195 3.477 3.31 1 3.233 3.010 2.860 2.724 0.221 2.980 2.852 2.741 2.641 2.513 2.425 0.305 1.994 1.844 1.749 1.618 1.443 1.365 0.359 1.300 1.247 1.171 1.088 1.03 1 0.970 0.433 0.691 0.623 0.579 0.456 0.384 0.304 0.601 0.318 0.405 0.579 0.738 0.882 1.013 0.772 0.259 0.315 0.382 0.436 0.483 0.517 0.05 1 0.928 0.031 0.033 0.036 0.042 0.048 0.106 4.607 4.53 1 4.434 4.289 4.I37 3.977 6 0 I I l I l l ~ ~ I 0.2 0.4 0.6 0.8 1.0 0 x:Y: Fig. 5. 0.2 0.4 0.6 0.8 1.0 4 r: Fig. 6. Fig, 5. Graphs of (n"Ax!Jrn)/(x: xf 7;) as functions of xf yf for (water-methanol)/Graphon at (a) 298.15; (b) 308.15; (c) 318.15; (6) 328.15; (e) 338.15 K. Above xi?: = 0.6 the curves are indistinguishable. Fig. 6. Graphs of (n"Axf/m)/(x; xi xf) as functions of x i y: for (water-ethanol)/Graphon at (a) 328.15; (b) 338.15; (c) 348.15 K.261 1 D. H. Everett and A . J . P. Fletcher Table 3. [Water (lkmethanol(2)]/Graphon : (a - a:), T(Aw - A, S:) and (A, h - Aw h,*) as functions of xi ~~ T(A, s^- A~ s:) (A, h -A, h:) (a - o,*)/mJ m-2 mJ m-2 mJ m-2 xi 25°C 35°C 45°C 55°C 65°C 25 "C 25 "C 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1 .oo 16.55 13.75 11.45 9.50 7.85 6.50 5.30 4.15 3.40 2.80 2.36 2.03 1.74 1.37 1 .oo 0.49 0.00 35.00 34.07 32.91 29.00 27.85 26.75 24.05 23.00 21.80 19.90 19.10 18.15 5.30 2.90 0.85 9.20 7.75 6.50 5.40 4.40 3.50 2.95 2.54 2.15 1.82 1.44 1.02 0.52 0.00 6.05 3.45 1.30 9.40 7.80 6.45 5.45 4.35 3.45 2.80 2.43 2.10 1.78 1.41 1.04 0.52 0.00 31.71 25.35 20.75 17.30 14.65 12.35 10.60 9.05 7.75 6.45 5.45 4.50 3.60 3.00 2.58 2.22 1.88 1.47 1.04 0.54 0.00 30.52 33.70 24.40 34.85 20.30 29.20 17.15 21.81 14.30 17.62 12.35 11.67 10.60 7.16 9.15 3.14 7.85 0.15 6.65 -0.95 5.60 - 1.87 4.65 - 3.49 3.75 -2.53 3.10 - 2.39 2.65 -2.18 2.39 - 2.50 I .94 - 1.48 1.53 - 1.07 1.06 -0.36 0.54 0.36 0.00 0.00 mean standard deviation : 68.70 63.85 53.24 41.71 34.17 25.42 18.01 12.64 8.00 5.55 3.47 0.66 0.85 0.41 0.18 0.26 0.30 0.64 0.85 0.00 & 0.93 - 0.47 where p ; and v z are, respectively, the saturation vapour pressure and molar volume of pure component 2 and B,, is the second virial coefficient of the pure vapour 2.Terms in B12, the cross-second virial coefficient, were ignored. Values of v; and B,, were taken from ref. (12). To obtain values of In y z at other temperatures, In y z was plotted against 1 / T and, assuming a linear relation, In y z at the required temperatures was obtained by interpolation or extrapolation. Values extrapolated to 25 "C agreed satisfactorily with the measurements of Butler et al.,13 but less well with the results reported by D~1itskaya.l~ For water-ethanol the values of In yz tabulated by Pemberton and Mash15 at 303, 323, 343 and 363 K were plotted against 1/T and interpolated to obtain values at our experimental temperatures.In this system these graphs are curved and the interpolations were made using a flexible spline. The curves of (n"Axf/rn)/(x: xf yf) against xf yf were constructed from the experimental points supplemented by points obtained by interpolation of the experimental isotherm. The form of this curve at low values of xi is important. Since experimental points for x i < 0.005 (for which xiyf < 0.03) were difficult to measure accurately, it has been assumed that the isotherm approaches linearity at sufficiently low values of x f . Values of the specific adsorption were interpolated on this assumption. There was some evidence that plots of Q1) (the relative adsorption of 2 with respect to 1) against x i 7: gave more consistent interpolated values. Typical curves of (n"Ax',/rn)/(x: x i 7;) against x i y i are shown in fig. 5 and 6.Integrations were made using either Simpson's rule or the trapezoidal rule with strip widths of 0.005 for xf increasing in steps of 0.05. Values of (0-0;) obtained in this way2612 Adsorption of Aqueous Alcohols on Carbon Table 4. [Water (l)-ethanol (2)]/Graphon : (a - a,*), T(Aw 6 - Aw 6:) and (Aw h - Aw h,*> as functions of x\ ~~~ -~ _ _ _ _ _ ~ ~ _ _ _ _ _ _ _ ~ -. (a - a,*)/mJ rnp2 T(Aw i- Aw S:) (Aw h - Aw h,*) mJ m-* mJ m-2 xi 25°C 35°C 45 "C 0.00 0.005 0.010 0.02 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1 .oo 42.3 39.0 36.0 30.25 18.2 9.30 5.10 3.48 2.51 2.05 1.64 1.39 1.23 1.11 1.02 0.92 0.80 0.67 0.525 0.37 0.21 0.08 0.004 0.000 41.33 38.5 35.2 29.1 17.4 8.95 5.30 3.73 2.84 2.36 1.98 1.75 1.58 1.46 1.35 1.23 1.08 0.92 0.72 0.51 0.3 1 0.13 0.03 0.00 40.21 37.3 33.6 28.25 16.85 8.85 5.50 3.85 3.10 2.58 2.46 2.02 1.87 1.74 1.60 1.41 1.20 0.95 0.71 0.47 0.36 0.12 0.03 0.00 39.36 36.6 33.3 27.0 16.30 8.6 5.55 4.22 3.60 2.92 2.63 2.44 2.30 2.16 1.97 I .73 1.44 1.13 0.82 0.53 0.28 0.1 1 0.03 0.00 55 "C 65 "C 38.24 35.6 32.5 26.80 16.20 9.10 6.10 4.7 1 3.96 3.47 3.17 2.99 2.86 2.72 2.48 2.18 1.85 1.45 1.07 0.73 0.42 0.19 0.04 0.00 75 "C 25 "C 25 "C 36.90 33.95 3 1.05 25.85 15.70 8.90 6.25 4.90 4.20 3.70 3.41 3.25 3.13 2.96 2.68 2.29 1.87 1.44 1.01 0.66 0.36 0.16 0.05 0.00 31.57 29.44 28.15 25.56 14.17 1.68 - 6.98 - 8.84 - 10.56 - 10.15 - 10.73 - 11.45 - 11.72 - 1 1.45 - 10.28 - 8.53 - 6.74 - 4.77 - 3.04 - 1.84 - 0.86 - 0.48 - 0.21 0.00 73.87 68.44 64.15 55.81 32.37 10.98 - 1.88 - 5.36 - 8.04 -8.10 - 9.09 - 10.06 - 10.49 - 10.34 - 9.26 - 7.61 - 5.94 -4.10 -2.51 - 1.48 - 0.65 - 0.40 - 0.20 0.00 mean standard deviation: k 0.77 are collected in tables 3 and 4.From these, enthalpy and entropy quantities were calculated from l1 = -(Aws"- A,.?,*) ( )$. (4) where Aw ,i: and Aw k are the entropy and enthalpy changes associated with the immersion of unit area of solid (denoted by the circumflex) in solution of mole fraction xi, while Aw j:; and Aw h,* refer to immersion in pure liquid 2. In all cases the relationships implied in eqn (4) and ( 5 ) were linear, and the slopes were obtained by linear regression analysis.Tables 3 and 4 present the resuits at 25 "C in the form of (Aw h - Aw h,*) and T(Aw s" - Aw s",*). In fig. 7 (a - a:), (Aw h - Aw h,*) and T(Aw s"- Aw j::) are shown plotted against xi; for purposes of discussiqn and for comparison with data for other systems it is convenient to plot (a - a:), (Aw h Aw h:) and - T(Aw j: - Aw j::) against xi (fig. 8). This figure also includes values of (Aw h - Aw h,*) calculated from preliminary measurements for (water- methanol)/Graphon obtained by Mr A. Jones by immersion calorimetry.D. H. Everett and A . J. P. Fletcher 2613 70 60 50 40 E 30 E Q N I h 5 20 s :< I 10 0 -10 c - r -201 -30 70 60 5 0 LO E c, 3 0 E <"," 20 Q I < - 10 9 h 0 -10 -20 - 3 0 N 1 n 0.5 x: 0.5 x: 0.5 4 Fig.7. Thermodynamic functions at 25 "C for (water-alcohol)/Graphon systems : (a) (0 -or), (b) (Awh-Awh,*), ( c ) T(AWi-Awi,*) as functions of xi. Open points: methanol; filled points: ethanol. 40 30 20 10 0 N E -10 h -20 % -30 * .3 -4 0 - 9 0 1 Fig. 8. Ther-modynamic functions at 25 "C for (water-alcohol)/Graphon systems: 0, (a -a:); A, (Aw h -Aw h:); 0, - T(Aw &-Aw 2:); Open symbols, methanol; filled symbols, ethanol. 0, (Aw h - Aw h:) from immersion calorimetry.2614 Adsorption of Aqueous Alcohols on Carbon Discussion Fig. 7 and 8 illustrate the broadly similar behaviour of these two systems. In the first place, the addition of water to ethanol has very little influence on the thermodynamic parameters for adsorption up to a mole fraction of ca.0.4 (fig. 8). Put another way, the addition of alcohol to water results in strong adsorption of alcohol, and a rapid change of the character of the interfacial layer towards that characteristic of the alcohol/Graphon interface. Consideration of the adsorption isotherms shows that ethanol is more strongly adsorbed than methanol, which is consistent with the view that adsorption arises mainly from dispersion forces between alkyl groups and the graphite surface. The secondary maximum at higher mole fractions which develops in the ethanol isotherms at higher temperatures, and which appears as a slight shoulder with methanol, is not readily interpreted. Its influence on the surface tensions is small, but leads to an inflection point in the (0-0;) against x', graphs which is, however, hardly seen on the scale of fig.7. It is also noteworthy that the adsorption isotherms for water-methanol are virtually independent of temperature above a mole fraction of methanol of 0.4, and that the graphs of T i n ) / x ; xi y i against x i y', are superposable above xi y', > 0.6, while for the water- ethanol system the corresponding graphs run closely parallel in the range 0.10-0.6. Fig. 8 also shows that the dominant factor which determines the sign of the preferential adsorption is the enthalpy of immersion, although the opposing entropy term is some 50% of the enthalpy term. A. J. P. F. is indebted to the S.E.R.C. and B.P. for the award of a CASE studentship. References 1 D. H. Everett, Pure Appl. Chem., 1981, 53, 2181. 2 I. Callaghan, D. H. Everett and A. J. P. Fletcher, J . Chem. Soc., Faraday Trans. 1, 1983, 79, 2723. 3 C. E. Brown, D. H. Everett and C. J. Morgan, J . Chem. Soc., Faraday Trans. I , 1975, 71, 838. 4 S. G. Ash, R. Bown and D. H. Everett, J . Chem. Thermodyn., 1973, 5, 239. 5 S. G. Ash, R. Bown and D. H. Everett, J . Chem. Soc., Faraday Trans. I , 1975, 71, 123. 6 D. H. Everett and R. T. Podoll, J. Colloid Interface Sci., 1981, 82, 14. 7 D. H. Everett, in Ahorption from Solution, ed. R. H. Ottewill, C. H. Rochester and A. L. Smith 8 Handbook of Chemistry and Physics, ed. R. C. Weast (C.R.C. Press, Cleveland, 57th edn, 197677). 9 T. A. Scott, J. Phys. Chem., 1946, 50, 406. (Academic Press, London, 1983). p. D-237. 10 D. H. Everett and C. Nunn, J . Chem. Soc., Faraday Trans. I , 1983, 79, 2953. 1 1 D. H. Everett and R. T. Podoll, in Specialist Periodical Report: Colloid Science (The Chemical Society, 12 M. L. McGlashan and A. G. Williamson, J . Chem. Eng. Data, 1976, 21, 196. 13 J. A. V. Butler, D. W. Thomson and W. H. McLennan, J . Chem. Soc., 1933, 674. 14 K. A. Dulitskaya, Zh. Obsch. Khim., 1945, 15, 9. 15 R. C. Pemberton and C. J. Mash, J . Chem. Thermodyn., 1978, 10, 867. London, 1979), vol. 3, chap. 2. Paper 5/ 18 15; Receii3ed 18th October, 1985

ISSN:0300-9599    

DOI:10.1039/F19868202605

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

J. Chem. SOC., Faraday Trans. I, 1986,82, 2615-2620 Studies of Alkylphenothiazinesulphonate Micellar Assemblies in Aqueous Solution Hisao Hidaka,*y Toshiaki Onai and Masahiko Murata Department of Chemistry, Faculty of Science and Engineering, Meisei University, 337 Hodokubo, Hino-shi, Tokyo 191, Japan Tadahiro Ishii Department of Chemistry, Faculty of Science, Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku 162, Japan Michael Gratzel Institut de Chimie Physique, Ecole Polytechnique Federale, Lausanne, Ecublens CH-1015, Switzerland The micellar properties and photochemical behaviour of sodium 9- alkylphenothiazinesulphonate and sodium cu-carbazol-9-ylalkanesulphonate (where alkyl = C,,H,, and C,,H,,) have been examined for the fundamental study of photoionization in micellar assemblies.A micellar system in which photosensitive probes are solubilized provides unique microenvironments for reactions and interactions.' In particular, the study of electron transfer in organized molecular assemblies is currently important for solar-energy conversion. Functionalized surfactants with a photoionized chromophore attached to the head group are employed to facilitate photoinduced charge Gratzel and coworkers showed that sodium 12-( 10'-phenothiaziny1)dodecyl- 1 - sulphonate was ionized monophotonically above the critical micelle concentration (c.m.c.) giving an excellent cooperative effect.6 In this paper we pursue the effects of photoionization and chain length with regard to phenothiazine incorporated either in the rim or in the core of the micelle.These effects have also been investigated by laser flash photolysis. Experiment a1 Two kinds of phenothiazine surfactant were prepared as follows. After conversion of phenothiazine (0.15 mol) into the N-sodium salt by treatment with sodium hydride (0.15 mol) in dimethyl sulphoxide (150 cm3) under a nitrogen atmosphere at 0 "C in a dark room, 1 -bromodecane or I -bromododecane (0.1 mol) was added and stirred for 24 h at ambient temperature. After extraction with cyclohexane, N-alkylphenothiazine was obtained via an active alumina c01umn.~ This was followed by sulphonation with chlorosulphonic acid in nitrobenzene and neutralization with sodium hydroxide to give sodium 9-alkylphenothiazinesulphonate (1) (where alkyl = C,,H,, or C,,H,,), or recrystallization from ethanol {i.r.(cm-l): 745 (benzene ring), 1190 (S=O), 11 50, 1330 (SO,), 2855, 2930, 2955 (CH alkyl); lH n.m.r. (D,O, 6 ppm): 0.80 (-CH,), 1.10 (-[CH,In+-), 1.32 (-CH,-C-N), 3.95 (-CH,-N), 6.80-7.60 (phenothiazine protons)). By a similar procedure, co-bromoalkylphenothiazine was derived from the sodium salt of phenothiazine (0.05 mol) and 1,lO-dibromodecane or 1,12-dibromododecane t Invited professor at the Ecole Polytechnique FCdCrale Lausanne, Institut de Chimie Physique. 261 52616 Alkylphenothiazinesulphonate Micelles S03Na (0.10 mol) in tetrahydrofuran. After evaporating tetrahydrofuran and extracting the reactant with cyclohexane, the crude product was chromatographed through an active alumina column using n-hexane to obtain cu-bromoalkylphenothiazine at ca.50 % yield. This was followed by sulphonation with sodium sulphite to give cu-phenothiazin- 9-ylalkanesulphonate (2). Purification was carried out with ethyl acetate using a Soxhlet extractor. {i.r. (cm-l): 750 (benzene ring), 1200 (S=O), 1335 (SO,), 2858, 2929 (CH alkyl); lH n.m.r. (D,O, 6 ppm): 1.10 (-[CH,Inp3-), 1.32 (-CH,-C-N), 3.95 (-CH,-N), 2.25 (-CH,-SO,Na), 6.80-7.60 (phenothiazine protons)}. Results and Discussion The relationship between surface tension and concentration is shown in fig. 1. The breakpoint allows for determination of the critical micelle concentration (c.m.c.) ; values were 0.15 mmol dm-3 for (1; n = lo), 0.09 mmol dmP3 for (1; n = 12), 0.3 mmol dm-, for (2; n = 10) and 0.1 mmol dm-3 for (2; n = 12). The C,,-derivative has a lower c.m.c. than the corresponding C,,-derivative.The surface tension of (1) is lower than that of (2). From the slope of the surface tension us. concentration plot below the c.m.c., the area occupied by one surfactant having a head group at the air/water interface can be calculated according to the Gibbs isotherm adsorption as follows: where r is the excess concentration per unit surface area, y is the surface tension, C is the concentration, and R is the gas constant. The slopes of the surface tension us. concentration curves for the homologues of (1) below each c.m.c. value exhibit a straight line. The occupied area per molecule was calculated from the slope near the c.m.c. as follows: s = 59.9 81, molecule-l for (1; n = 10) and s = 51.6 81, molecule-l (1; n = 12).The area is not affected by a change in the alkyl chain length. This comparatively large area may be attributable to the large size of the chromophore inhibiting any closer packing of the hydrophilic head group. On the other hand, the slopes below each c.m.c. of both (2; n = 10) and (2; n = 12) exhibit a convex curve. This implies a difference in packing for the hydrophilic head group in each case. Since in (2) the phenothiazine group in the tail is remote from the hydrophilic sulphonate, the packing at the air/water interface is very unstable. The flat slope of (2) in the concentration range more dilute than the c.m.c. indicates a horizontal orientation of the interface in comparison with that of (l), with the phenothiazine group in the head preventing a surface orientation.Molecules of (2) may not 'stand up' until close to the neighbourhood of the c.m.c. The area per molecule is 38.2 81, for (2; n = 10) and 38.2 81, for (2; n = 12) near the c.m.c. The area occupied per molecule of the homologues of (2) is less than that occupied by the homologues of (1). For a functional surfactant having a large chromophore head, a cylindrical micelle with globular ends was inferred from the literature data.8 The absorption band (A:;:) of 0.05 mmol dmP3 aqueous solution for (1; n = 10)H. Hidaka et al. 2617 -A 70 - Ah 60- 0. O.0 - 0 0-0- OLO- 0 o-o- 40 - O\ 30 - I I , I 1 I . I I 0.01 0.05 0.1 0.5 1.0 concentration/mol dm-3 Fig. 1. Relationship between surface tension and concentration at 20 "C. The surface tension was measured by the Wilhelmy vertical plate method with a Shimadzu ST-1 tensiometer.0 , (1 ; n = 10); 0, (I; n = 12); A, (2; iz = 10); a, (2; H = 12). concentration/ mmol dm-3 Fig. 2. Concentration dependence of the maximum wavelengths for (1) and (2). @, (1; n = 10); 0, (1; n = 12); A, (2; n = 10); A, (2; n = 12). consists of peaks at 265 and 314 nm and that for (2; n = 10) consists of peaks at 256 and 306 nm. The derivative of (1) resulted in a shift to longer wavelength than that of (2). The absorption band undergoes a small bathochromic shift which is attributed to the n-n* transition. The band is presumed to be composed of three large electronic transitions, as pointed out by Mantsch et ~ 1 . ~ Fig. 2 shows the concentration dependence of the shift in the absorption band2618 A lky lphen o t h iazinesulph on ate Micelles 400 450 500 550 600 wavelength/ nm Fig.3. Transient spectra of the triplet and cation radical generated by laser excitation at 347.1 nm for aqueous 0.05 mmol dmP3 solutions of (1; n = 10) (---) and (2; n = 10) (.--.) at (a) 1.1, (b) 20, (c) 1.2 and (d) 20 ,us after the laser pulse. The solutions were also saturated with N,O gas for 30 min. The excitation laser intensity was normalized at 300. maximum. Almost no shift in the maximum peak with concentration was observed for the homologues of (l), whereas the homologues of (2) exhibit a shift to larger wavelength with increasing concentration. In particular, at concentrations above the c.m.c. the maximum absorption band shifts markedly to longer wavelength.Therefore, it is concluded that on micelle formation the phenothiazinyl group is located in the micelle’s core. An electronic transition of n-n* character is facilitated because of the more hydrophobic environment inside the micelle. The bathochromic shift is coincident with the result for a system in which N-methylphenothiazine was solubilized in solvents of varying polarity. In contrast, the polar environment in which the phenothiazinyl group of (1) is located on or in the surface of the micelle or in which the surfactant formed by (2) below the c.m.c. lies in its monomer state does not cause such a bathochromic shift and gives a definite absorption band. The fluorescence spectrum of (1) gives a broad emission peak at 472 nm and that of (2) gives a peak at 452 nm.The fluorescence intensity of (1) was 30 times larger than that of (2) at the same concentration. This apparently larger bathochromic shift in the fluorescence spectra in comparison with the bathochromic shift of the U.V. absorption spectra is a product of the sulphonation of the carbocyclic part of the phenothiazine group of (l).9 Laser flash-photolysis experiments were performed with a JK-2000 frequency-doubled (347.1 nm) Q-switched ruby laser (10 ns duration) and transient species were monitored by fast kinetic spectrophotometry. The experimental arrangement has been described in detail elsewhere.6 The transient spectra of (1; n = 10) and (2; n = 10) in the presence of the electron scavenger N,O are illustrated in fig. 3. The dilute aqueous solution below each c.m.c.value exhibits two peaks at 460 and 510 nm. These were assigned to the triplet-triplet (T-T) absorption band and the cation radical band, respectively, from a quenching experiment with oxygen 6 l lo Although similar transient spectra were observed above the c.m.c., the intensity ratio of the peaks at 470 and 510 nm 1.1-1.2 ps after the laser flash is 1.8 for (1; n = 10) andH. Hidaka et al. 2619 0 2 4 6 8 10 12 14 16 time/ 1 Od6 second Fig. 4. Transient absorbance observed at ;1 = 460 nm of the solutions containing 1 mmol dmP3 of (1; n = 10) (a) and (2; rz = 10) (b). The solutions were degassed with Ar gas. Table 1. First-order rate constant and half-life for triplet-triplet absorption (460 nm) and cation-radical formation (510 nm)a ~- 460 nm 510 nm 1st order rate half-life 1st order rate half-life species constant, k, /w constant, k , h s ~ ~~~~~~ -___ (1; n = 10) 1.5 x 105 6.7 1.5 x 105 6.7 (2; n = 10) 2.7 x 105 3.7 1.1 x 105 8.9 a Solution concentration = loP3 mol dmU3 (above the c.n.c.) in the presence of N,O.~ 2.3 for (2; n = 10). This implies that the triplet species of the phenothiazinyl group located at the rim is more stable than that of those located at the core of the micelle. Furthermore, the feature of the temporal behaviour of the triplet absorption at 460 nm for (1; n = 10) and (2; n = 10) above the c.m.c. in an argon atmosphere changes drastically, as shown in fig. 4. The transient absorbance of (2; n = 10) at 460 nm rises more steeply compared with that of (1; n = 10).The slowly rising time course for (1; n = 10) may result from the rim location of hydrophilic sulphonated phenothiazinyl group. The first-order rate constants, k,, of the bands at 460 and 51 0 nm by quenching of N,O above the c.m.c. are evaluated and listed in table 1. The k, values of (1 ; n = 10) at 460 and 510 nm are almost the same, whilst the k , value of (2; n = 10) at 460 nm is more than twice that at 5 10 nm. The triplet species in the micelle is more easily changed to the cation-radical. The half-lives of the decay at 460 and 510 nm for (1; n = 10) and (2; n = 10) are also summarized in table 1. The half decay times at 460 and 510 nm gave almost the same lifetime (6.7 ps). However, with respect to (2; n = lo), that at 460 nm is smaller than that at 510 nm.The cation-radical of (2; n = 10) survives longer than that of (1; n = 10). The hydrophobic environment in the micelle contributes to the stabilization of the cation radical. In conclusion, on laser excitation, the phenothiazinyl chromophore in the micelle core produces a triplet species more rapidly, with the cation radical produced surviving longer,2620 Alky lphenoth iazinesulp hona te Micelles than is the case for the phenothiazinyl chromophore situated on the periphery of the micelle. H. H. thanks Dr P. Infelta for encouragement and hospitality when staying at the EPFL, Lausanne. H. H. also thanks Meisei University for leave of absence (1983-1985). References 1 Y. Moroi, A. Braun and M. Gratzel, J . Am. Chem. SOC., 1979, 101, 567; Y. Moroi, P. P. Infelta and M . Gratzel, J . Am. Chem. SOC., 1979, 101, 573. 2 T. W. Ebbesen, 0. Delgado, A. Valla, M. Girand, Y. Saito Tachibana and A. Wada, Photochem. Photobiol., 1982, 35, 665; T. Irie, M. Otagiri, K. Uekawa, F. Yoneda, F. Kusu and K . Takamura, Nippon Kagaku Kaishi, 1983, 219, 3 Y. Saeki, K. Maeda and K. Negoro, Nippon Kagaku Kaishi, 1979, 1740. 4 J. P. Cislo and A. Hopfinger, Tenside Deterg., 1976, 13, 253; J. P. Cislo, Yukaguku, 1985, 34, 61. 5 H. Hidaka, H. Kubota, S. Yoshizawa and T. Ishii, J . Chem. SOC., Chem. Commun., 1983, 99. 6 R. Humphry Baker, A. M. Braun and M. Gratzel, Helv. Chim. Acta, 1981, 64, 2036; M. A. Gilson, M. H. Abder Kader, P. Mauresecco, E. Oliveros, M. T. Maurette and A. M. Braun, Proc. 10th IUPAC Symp. Photochemistry (Interlaken, Switzerland, 1984), p. 41 1. 7 C. F. Hobbs, C. K. McMillan, E. P. Papadopoulos and C. M. Vanderwerf, J. Am. Chem. SOC., 1962, 84,43. 8 J. H. Israelachvili, D. J. Mitchell and B. W . Ninham, J . Chem. Soc., Faraday Trans. 2, 1976, 72, 1525. 9 H. H. Mantsch and J. Dehler, Can. J . Chem.. 1969, 47, 3173. 10 S. A. Alkaitis, G. Beck and M . Griitzel, J . Am. Chem. SOC., 1975, 97, 5723. Paper 6/242; Received 16th October, 1985

ISSN:0300-9599    

DOI:10.1039/F19868202615

出版商:RSC    

年代:1986

数据来源: RSC