3801
J . Phys. Chem. 1991,95,3801-3804
Diaphragm Cell Determination of the InterdMuslon Coefflclents for Aqueous Solutions of Copper Sulfate, Cobalt Sulfate, and Nickel Sulfamate Norman L. Bums, John C. Clunie, and James K. Baird* Department of Chemistry, University of Alabama in Huntsville, Huntsville, Alabama 35899 (Received: June 4, 1990) Using diaphragm cells, we have measured the differential interdiffusion coefficients for the systems CuSO, + H20, CoSO, H 2 0 , and Ni(S03NH2)2+ H 2 0 as a function of concentration at 25 C f 0.01 OC. In each system, the interdiffusion coefficient, D(E), decreases monotonically with concentration, E. For CuSO,, D(E)varies from 0.734 X lV5 cm2/s at E = 0.0188 M to 0.382 X lV5cm2/s at E = 1.17 M; for CoSO,, the range is 0.895 X to 0.342 X lV5 cm2/s between 0.0124 and 1.465 M; whereas, for Ni(S0,NH2)2, the range is 0.922 X to 0.616 X cm2/s between 0.0251 and 1.785 M. Throughout this concentration range, the Ni(S03NH2)2interdiffusion coefficient values lie on a single straight line when plotted as a function of ( @ ' I 2 . Extrapolation of that line to E = 0 yields D(0) = 0.965 X lo-* cm2/s.
+
1. Introduction The diaphragm cell consists of two well-stirred solution compartments on opposite sides of a membrane, which is usually a sintered glass disk.'-' Once the geometric cell constant for the devices has been determined by calibration, the interdiffusion coefficient for a two-component system can be determined by following the time dependence of the concentration difference, Ac(r), (of either solute or solvent) appearing across the frit. Recently, we have found an exact solution to the equation of motion governing Ac(t) for a diaphragm ell.^.^ Given that Vl and V2are the volumes of chemical solution below and above the frit, respectively, and that cl(0), c2(0) and cl(t), c2(t) are the concentrations at time zero and time t, respectively, we have demonstrated that the volume-averaged mean concentration defined by E = VICl(0) + V2c2(0) VlCl(0 + V2c2W (1.1) VI + V2 VI + V2 is a constant of the motion, while, in addition, the time t is related to AC(t) = cl(t) - ~ 2 ( t ) (1.2) through the infinite series f = Bo + BL In (Ac) + Bl(Ac) + B2(Ac)2 + ... (1.3) where BI, B2, ..., etc. are coefficients which depend upon the differential interdiffusion coefficient, D(E),and its derivatives with respect to concentration, D(')(E),D(2)(E),..., etc. evaluated at E, The coefficient Bo is determined by the initial values, cl(0) and c2(0), while
-
-[ - + 4
and the cell constant, j3, is given by j3 = A
1
(1.5) 1 VI where A and 1 are the effective cross-sectional area and thickness of the frit, respectively. In principle, D@) and all its derivatives may be determined when eq 1.3 is fitted to t vs Ac data. In practice, only a finite set of t vs Ac points can ever be available, and the infinite series represented by eq 1.3 must be truncated at some order. If the values ~
~
TABLE I: Diaphragm Cell Parameters cell no. V,,cm3 1 65.8 2 76.3 3 100.3
0.219 0.132 0.126
of the remaining B coefficients are adjusted by the method of least squares, so as to provide the best statistical representation of the data, D(P) and a finite number of its derivatives may be evaluated. For the general case where VI # V2,we have successfully applied this truncated series-least-squares method to aqueous solutions of HCl at 25 OC and have determined D(E), D(l)(E),and D ( 2 ) ( E ) at P = 1 M.6 When Vl = V,, however, all odd order coefficients, B, (j= 1, 3,5, etc.) are identically ~ e r o . Under ~ . ~ this simplifying condition, combination of the initial conditions and eqs 1.2 and 1.4 with eq 1.3 truncated starting at the term, B2(Ac)2, gives
which is the usual diaphragm cell result except that on the lefthand side D(E) replaces the integral diffusion coefficient, b.5 Experiments on the electrodeposition of the elements, copper, cobalt, and nickel at high rates in reduced gravity have made it desirable to determine the interdiffusion coefficients of the systems CuSO, + H 2 0 , CoSO, + H 2 0 , and Ni(S03NH2)2 H 2 0 at 25 OC over as wide a concentration range as possible.' In the case of CuSO, H 2 0 , this occasion has also provided us with an opportunity to test eq 1.6 against the Rayleigh interferometric method! the Hamed conductimetric method? and three previous diaphragm cell experiments."I2 In section 2, we describe the diaphragm cells, the materials used in the experiment, and the analytical methods employed to determine the concentrations of Cu2+,Co2+,and Ni2+. In section 3, we report in both tabular and graphical form our values of D@) for the systems, CuSO, + H20, COSO, + H20, and Ni(S03NHd2 + H 2 0 at 25 OC for concentrations, E, ranging from dilute to near the solubility limit.
+
+
2. Experiment 2.1. Materials. We used without further purification Aldrich Ni(S03NH2)2and Malinckrodt AR crystal grade CuS04.5H20
~~~
(1) Northrop, J. H.; Anson. M. L. J . Gen. Physiol. 1929, 12, 543. (2) McBain, J. W.; Liu, T. H. J . Am. Chem. Soc. 1931, 53. 59. (3) Stokes, R. H. J . Am. Chem. Soc. 1950, 72, 2243. (4) Mills, R.; Woolf, L. A. The Diaphrugm Cell; Australian National University Prtss: Canberra, 1968. (5) Baird, J. K.; Frieden, R. W. J . Phys. Chem. 1987.91.3920. (6) Clunie, J. C.; Li, N.; Emerson. M.T.; Baird, J. K. J . Phys. Chem. 1990, 94, 6099.
,9, om-*
~~
~~
(7) Riley, C.; Coble. H. D.; Loo, B.; Benson, B.; Abi-Akar, H.; Maybee, G. Polym. Prepr. (Am. Chem. Soc., Diu. Polym. Chem.) 1987, 28, 2. (8) Miller, D. G.; Rad, J. A.; Epptein, L. B.; Robinson, R. A. J. Solution Chem. 1980, 9,467. (9) Noutly, R. A,; Leaist, D. G. J . Solution Chem. 1987, 16, 813. (10) Emanuel, A.; Olander, D. R. J . Chem. Eng. Datu 1963.8, 31. (11) Woolf, L. A.; Hoveling, A. W. J . Phys. Chem. 1970, 74. 2406 (12) Awakura, Y.; Doi, T.; Majima, H. Metall. Truns. 8 1988, 198, 5.
0022-3654/91/2095-3801$02.50/00 1991 American Chemical Society
3802 The Journal of Physical Chemistry, Vol. 95, No.9, 1991 TABLE II: Diffusion Coefficient of Aqueous CUSO, at 25 oc“
* 0.01
cell no.
cl(0), M
c2(0), M
E, M
D(z), 10-5 cm2 s-l
1 1 and 3 3 3 2 3 2
0.0376 0.0505 0.1261 0.2017 0.2523 0.3764 0.5045 0.73 13 0.9078 1.261 1.323 1.323 1.323 1.323 1.273
0 0 0 0 0 0 0 0 0 0 0.200 0.449 0.606 0.898 1.058
0 0.0188 0.0252 0.06305 0.1008 0.1261 0.1882 0.2523 0.3656 0.4539 0.6304 0.761 0.886 0.964 1.1 1 1.166
0.855 0.734 0.690 0.670 0.593 0.565 0.552 0.521 0.47 1 0.466 0.446 0.426 0.395 0.390 0.380 0.382
2 3 3 3 1
2 2 1
a D(0) computed from eq 3.1 using A: = 53.6 S cm2 equiv-I and hq = 80.0 S cm2 equiv-l from ref 18.
and CoS04-7H20. Water, once distilled from a glass system and deaerated by aspiration to a residual conductivity of 1.5 pS/cm, or less, was used to make up all solutions. 2.2. Equipment and Procedures. Three standard Stokes diaphragm cells constructed from 10-16 pm porosity sintered glass disks were operated with VI = V2 and with stirring at 1 Hz in water baths thermostated to 25 f 0.01 OC. Prior to each diaphragm cell run, a concentration gradient was established within the frit following the standard “prediffusion” procedure.‘ The cell was calibrated with aqueous KCl. Values of the relevant parameters were q(0) = 0.5 M and c2(0) = 0 M and D = 1.840 X 10” cm2/s.13 The concentrations, cl(t) and c2(t), of KCl were determined by using a calibrated Radiometer (Copenhagen) Model CDM 83 conductivity meter fitted with a CDC 104 probe. Table I lists the value of the constant, 0,and the lower compartment volume, VI, for each of the three cells. Since all runs involved VI = V2,the volume-averaged mean concentration in the cell was from eq 1.1 simply? = (1/2)(q(O) ~~(0)). When values of E near the solubility limit were required, it was no longer possible to operate the cells with c2(0) = 0. To obtain these high values of E, cl(0)was chosen near saturation, and c2(0) was set somewhat below it. The required ooncentrations were prepared by dilution from concentrated stock solutions, which in turn had been checked both by titration and by conductivity measurement using the Radiometer meter. The titrations and conductivity measurements agreed with f 1%. All diffusion coefficients, D(E), which we report were calculated from cl(t), c2(t), cl(0), and c2(0) by using eq 1.6. 2.3. Analyficol Methods. Analysis of CuSO., solutions was performed by using KI to precipitate copper as CUI followed by titration of the released I2 with Na2S203using starch as an indicator.“ The KI was Malinckrodt AR grade Lot 1123 KCHY, whereas the Na#,03.5H20 was Malinckrodt AR grade Lot 8100 KCHK. KSCN, which was added to release adsorbed I,, was Malinckrodt Lot 7 160 KCEB. The solutions of CoS04 were titrated complexometrically using ethylenediaminetetraacetic acid (EDTA) with murexide as the indicator and with the dropwise addition of aqueous NH3 in order to maintain the indicator co10r.I~ The EDTA was obtained from Fisher as certified ACS grade Na2EDTA-2H20,Lot 752,854. The Ni(S03NH2)2solutions were titrated potentiometrically with EDTA using a calomel reference electrode and a mercury indicating electrode to detect the equivalence point.16 The complex
+
(13) Woolf, L. A.; Tilley, J. F.J. Phys. Chem. 1967, 71, 1962. (14) Skoog, D. A.; We% D. M.:Holler, E J. Fundamentals of Analyrical Chemistry, 5th. ed;Saunders College Publishing: New York, 1988. (1 5) Schwarzcnbach, G.; Flaschka, H.Complexometric Tirrariom; Me-
thuen d Co.: London, 1969; pp 244-245. Lamson. D. W .Anal. Chem. 1958.30, (16) Reilly, C. N.;Schmid, R. W.; 953.
Burns et al. TABLE 111: Diffusion Coefficient of A q w u s Cos04at 25
cell no.
c,(O), M
c2(0). M
P, M
2 1 2
0.02488 0.0622 0.1244 0.2488 0.4977 0.5924 0.1623 0.9148 1.089 1.104 1.104 1.111 1.111 1.111 1.544 1.544 1.544
0 0 0 0 0 0 0 0 0 0.123 0.308 0.528 0.776 0.921 0.888 1.108 1.385
0 0.01244 0.03 1 1 0.06220 0.1244 0.2489 0.2962 0.3812 0.4574 0.5445 0.614 0.706 0.819 0.943 1.02 1.22 1.326 1.465
1 3 3 3 3 3 1 1 1 3 3 2 1 3
* 0.01
D(E), lV5 cm2 s-I 0.87 0.895 0.881 0.764 0.673 0.635 0.595
0.517 0.488 0.463 0.441 0.428 0.422 0.406 0.394 0.377 0.353 0.342
aD(0)computed from eq 3.1 using A! = 55 S cm2 equiv-l and A i 79.9 S cm2 equiv-l from ref 18.
=
TABLE I V Diffusion Coefficient of Aqueous Ni(S0JVH2)2at 25 0.01 O C O D(E), 10-’ cell no. c,(O), M c2(0), M P, M cm2 s-I 0 0.956 2 0.0502 0 0.0251 0.922 1 0.1513 0 0.07565 0.890 1 0.3040 0 0.1520 0.865 2 0.5009 0 0.2504 0.820 3 0.7088 0 0.3544 0.807 1 0.9130 0 0.4565 0.774 3 1.1403 0 0.5702 0.769 1 1.3169 0 0.6584 0.746 3 1.5131 0 0.7566 0.741 1 1.5199 0.3009 0.9104 0.7 15 2 1.5199 0.7042 1.112 0.705 3 1.5083 1.0249 1.2666 0.679 1 1.5691 1.3057 1.4374 0.665 1 2.0624 1.0249 1.5437 0.645 2 2.0624 1.5083 1.7854 0.616
‘ D ( 0 ) obtained from a least-squares fit of eq 3.3 to the data.
of Hg2+ with EDTA, which was required for the titration, was formed by the addition of J. T. Baker purified Lot 37,365 Hg(NO,), to the EDTA.
3. Results and Discussion Tables 11-IV list our results for D(E)for CuS04, CoSO,, and Ni(S03NH2)2,respectively. Included are the values of cl(0)and q(0) for each run and f computed from eq 1.1. For both CuS04 and CoSO,, the value of the interdiffusion coefficient at infinite dilution, D(O), shown in the tables was computed from the Nernst-Hartley formula,”
where ZI, A! and Zz, A(: are the valences and equivalent conductances at infinite dilution of the cation and the anion, respectively; F is the Faraday; R is the gas law constant; and T i s the absolute temperature. For Cu2+, Co2+, and the equivalent conductances are A! = 53.6 S cm2 equiv-I, A? = 55 S cm2 equiv-I, and A; = 80.0 S cmz equiv-I, respectively.l* In the case of CoSO,, D(0) is a few percent less than the values of D(E) that we obtained experimentally at mean concentrations, f I (17) Robinson, R. A.; Stokes, R. H.ElecrrolyteSolurions; Butterworths: London, 1959; p 288, eqs 11.4 and 11.5. ( 18) Reference 17, p 463, Appendix 6.1.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3803
Interdiffusion Coefficients
8.5i A EMANUEL a OLANOER I963 (OIAPHRAOY)
8.0
a WOOLF a HOVELINO 1970 (DIAPHRAOM)
1
I
1
-
I
I
I
I
A CuSO4 (RAYLEIOH) 0 MgSO4 (RAYLEIOH) 0 MgSO4 (HARNEO)
NOULTY (L LEAIST I987 (HARNED)
0 Z n S O 4 (RAYLEIOH) ZnSO4 (HARNED) X N i SO4 (DIAPHRAGM) + C o s 0 4 (OIAPHRAQM)
3.5
4'0
-0
3.0 .20
.40
.60
.80
1.00
1.20
2.5
i I
0
.h? Figure 1. Differential diffusion coefficient of aqueous copper sulfate at 25 f 0.01 O C : (0)this work (diaphragm cell; see Table I1 for values of ~~(0); data analyzed by using eq 1.6); (A)Emanuel and Olander (ref 10; diaphragm cell with c2(0) not stated; data analysis by the graphical method of ref 3); ( 0 )Woolf and Hoveling (ref 11; diaphragm cell with c2(0) = 0; data analysis by the graphical method of ref 3); (El) Awakura et al. (ref 12; diaphragm cell with cz(0) = 0; data analysis by a modification of the method in ref 3); (A) Miller et al. (ref 8; Rayleigh interferometry);).( Noulty and Leaist (ref 9; Harned method). 0.031 1 M. Inasmuch as D(r) < D(0) at low concentration for most electrolyte^,'^ the difference can be due either to errors in the diaphragm cell method or to errors in the values of A! and A!. Figure 1 compares our results with various other determinations of the differential diffusion coefficient of aqueous CuS04. Even though scattered, and taken by different investigators, and analyzed variously by the Stokes graphical method3 and the series expansion method (eq 1.6), the diaphragm cell D(E) values are, nevertheless, in fair agreement with one another. Indeed, regardless of experimental method, all of the o(?)values differ by less than 10% at most concentrations, although the diaphragm cell measurements tend in general to be higher than those obtained by either the Harriedg or Rayleigh methods.8 Below we suggest possible reasons for this: First, Robinson and Stokes have suggested that, due to adsorption of ions on the sintered glass beads, surface-aided diffusion occurs within the frit of the diaphragm cell. This they believe accelerates transport through the frit and accounts for the extent by which diaphragm cell results exceed the interferometric results a t concentrations below 0.05 Mills and Lobo speculate further that, for polyvalent electrolytes, the effect may persist at concentrations as high as 0.5 M.2' Second, in analyzing our data, we have chosen to ignore in eq 1.3 all of the nonzero correction terms beginning with B , ( A C ) ~ . This is always permitted if Ac(t) is sufficiently sma!l for all t . In the 15 runs reported in Table 11, the initial value of Ac(t), namely Ac(O), which was necessarily also the maximum value of Ac(t), ranged from 0.0376 to 1.261 M. These initial values were selected so that, during a run of convenient length, we could observe a large contrast between Ac(0) and Ac(t). By optimizing our analytical techniques, however, we could easijy work with smaller values. Although our Ac's were in general a factor of 10 or more larger than those employed in the interferometric experiments,8 the difference between our D(E) results at the higher concentrations (19)
Horvath, A. L. Handbook ofhlectmlyte Solutions;John Wiley: New
York, 1985; Chapter 2.12.
(20) Reference 17, p 256. (21) Mills, R.; Lobo, V. M. M. Self-difjusion in Electrolyte Solutions; Elsevier: New York, 1989; p 7.
I
I
I
.50
-75
1.00
I
25
I
1.25
I
1.50
I
1.75
2.00
JF(Ml'2)
Figure 2. Differential diffusion coefficients of some 2-2 sulfates in aqueous solution at 25 0.01 OC: (A)CuSO,, ref 8; (0)MgSO,, ref 28; ( 0 ) MgSO.,, ref 26; (0)ZnS04, ref 29; (W) ZnS04, ref 27; (X) NiS04, ref 12; (+) CoSO.,, this work.
*
a t least and the optical results is a few percent. Alternatively, neglect of the term B2(Ac)2implies that B2 is negligible. This will be true if D(2)(E)is sufficiently small that within a neighborhood of E, the differential diffusion coefficient, D(c), can be represented by
D(c) = D(E) + D(')(E)(c- E )
(3.2)
Of course, the local linearity implied by eq 3.2 cannot be guaranteed a priori. It is worth noting, however, that in the interferometric method similar issues arise; namely, correction terms of second order in both D(c) and in the refractive index, n(c), are required in order to cope with the "skew" character of the interference pattern.22 Third, as c 0, eq 3.2 cannot represent D(c) for any c, since terms in c1j2are required.6 Such terms have been introduced, for example, into the interferometric method in order to cope with the special skewness that develops as infinite dilution is app r o a ~ h e d . ~Even ~ . ~ ~though the values of E chosen in our experiment would seem to be mostly outside the c1I2 region, the solution in the frit samples the dilute region for a time during any experiment that begins with c2(0) = 0. Since both c,(t) and c2(t) approach each other most rapidly at the start of the experiment, however, the frit soon gains solute and departs the c1I2region. Nevertheless, the effect of starting with c2(0) values other than zero can be checked by carrying out experiments having the same E but different cl(0)and c2(0). For the purpose of comparing the diffusion coefficients of various 2-2 electrolytes, we have plotted in Figure 2 data for MgS04, CoSO,, NiSO,, CuSO,, and ZnS04. The D(0) values are 0.849 X lW5 cm2 s-I for MgSO, and NiSO,, and 0.847 X cm2 s-' for ZnSO computed by using eq 3.1 and A! = 53.0 S cm2 equiv-' for Mg2+, A: = 53.05 S cm2 equiv-I for Ni2+, and A! = 52.8 S cm2 mol-' for Zn2+.18*25For both MgS0, and ZnSO,, the lowest concentration data were obtained with the Harned m e t h ~ d ? ~ .while ~ ' the data for CuS04and the high concentration
-
(22) Gosting, L. J.; Fujita, H. J. Am. Chem. Sm.1957, 79, 1359. (23) Albright, J. G.; Miller, D. G. J. Phys. Chem. 1975, 79, 2061. (24) Albright, J. G.; Miller, D. G. J . Phys. Chem. 1980. 84, 1400. (25) Reference 19, Table 20.10.1, p 240. (26) Harned, H. S.; Hudson, R. M. J . Am. Chem. Soc. 1951, 73, 5880. See also ref 17, p 513, Appendix 11.1. (27) Harned, H. S.; Hudson, R. M. J . Am. Chem. Soc. 1951, 73, 3781. See also ref 17, p 513, Appendix 11.1.
3804
J . Phys. Chem. 1991,95, 3804-381 1 the values to be so alike at high concentration is indeed remarkable. There appear to be no interferometric results for comparison with our diaphragm cell results for aqueous CoSOe On the other hand, Han and Tang employed a diaphragm cell with a thin Gelman VERSAPORE membrane to determine the interdiffusion coefficient of aqueous C&04 at 25 0C.30 Their results exceed ours by about a factor of 2 at all concentrations; however, an exact comparison is difficult, since they did not specify the technique whereby they unfolded their diaphragm cell integral diffusion coefficient data to obtain values for D(E). Figure 3 shows a plot of our results for aqueous Ni(S03NH2)> throughout the conNote that D(P) is a linear function of centration range considered, which extends from dilute to near saturation. We fitted the data in Figure 3 to the empirical equation, 2
4
6
n
IO
I2
14
Js" (Y"')
Figure 3. Differential diffusion coefficient of aqueous Ni(S03NHJ2 at 25 & 0.01 O C . The straight line is a plot of eq 3.3.
data for MgS04 and ZnSO, were obtained by interferometry.sapB The remaining results are diaphragm cell determinations.I2 Since the infinite dilution equivalent conductance of all the cations are quite close, one might expect on the basis of eq 3.1 that all five salts might have similar diffusion coefficients as c 0; but for
-
(28)
(29)
Rard, J. A.; Miller, D. G. J. Solution Chem. 1979, 8, 755. Albright, J. G.; Miller, D. G. J . Solufion Chem. 1975, 9, 809.
+
D(E) = D(O)[l a(r)'/2]
(3.3)
allowing D(0) and a to be least-squares adjustable constants. We found D(0) = 0.956 X cm2 s-' and a = -0.261 M-'i2. This value of D(0) appears at the head of Table IV.
Acknowledgment. This research was sponsored by the National Aeronautics and Space Administration through Grant NAGW-8 1 with the Consortium for Materials Development in Space at the University of Alabama in Huntsville. Partial support from the donors of the Petroleum Research Fund, administered by the American Chemical Society, is also acknowledged. (30)Han, K. N.; Kang, T. K. Mefull. Trans. B 1986, 17B. 425.
''0 NMR Relaxation Tlmes of the Protein Amino Acids in Aqueous Solution. Estimation of the Relative Hydration Numbers in the Cationic, Anionic, and Zwltterionic Forms Jiirgen hutenvein,* Ioannis P. Gerothansssis,+Roger N. Hunston,t and Martin Schumacherg Institut de Chimie Organique, UniversitZ de Lausanne. CH- I005 Lausanne, Switzerland (Received: August 22, 1989; In Final Form: September 17, 1990)
The I70NMR line widths of the a-carboxyl groups of the protein amino acids includin 4-hydroxyproline, sarcosine, N,N-dimethylglycine, and Omethyltyrosine were measured in aqueous solution at 40 O C ( I ! 0 enrichment 10 atom W). A linear correlation was found between the line widths and the molecular weights of the amino acids at the pH values 0.5, 6.0, and 12.5, which are characteristic of the three ionization states of the neutral amino acids. The slopes of the straight lines were independent of pH; however, the line widths at acidic pH were increased by 98 f 13 Hz relative to those at neutral or basic pH. Since the I7O quadrupole coupling constant is only weakly influenced by the protonation state of the amino acids, it can be concluded that the a-carboxylic group is hydrated by an excess of two molecules of water relative to the a-carboxylate group. The lifetime of the water association is far below the NMR chemical shift time scale. Of the oxygen-containing functional groups of the amino acid side chains, only the phenolate ion of tyrosine was found to form water complexes that are stable within the range of the correlation times. It is shown that the I7Oline widths of the a-carboxyl groups reflect the overall rotational correlation time of the amino acids. In contrast, the a-carbons are characterized by shorter effective correlation times presumably due to internal rotation of the C,-H vector.
Introduction The hydration of amino acids and peptides is a problem of utmost importance and is a prerequisite to the understanding of protein-water interactions.1.2 Hydration phenomena are also essential in understanding, a t a molecular level, such factors as *Address correspondence to this author at the Organisch-Chemisches Institut, UniveniUt Monster, Orltans-Ring 23, D-4400 Monster, F.R.G. Present address: University of Ioannina, 451 10 Ioannina, Greece. *Present address: Ciba-Geigy S.A.. 1870 Monthey, Switzerland. 1 Present address: Lonza AG, 3930 Visp, Switzerland.
0022-3654/91/2095-3804$02.50/0
transport mechanisms, chemical kinetics, and thermodynamic properties Of the amino acids. It iS therefore not unreasonable that the hydration of amino acids has been extensively studied by a variety of physicochemical techniques including multinuclear (1) (a) Rupley, J. A.; Yang, P. H.; Tollin, G. In Wafer in Polymers; Rowland, S.P., Ed.; ACS Symposium Series No. 127: American Chemical Society: Washington, DC, 1089; (b) Pain, R. H. In Biophysics of Water; Franks, F., Mathias, S. F., Eds.; Wiley: New York, 1982; Section 1. (2) Halle, B.;Anderson, T.; Forstn, S.;Lindman, B.J. Am.Chem. Soc. 1981, 103, 500.
0 1991 American Chemical Society
