3990
CHARLES L. CRONAN AND FRIEDEMANN W. SCHNEIDER
However, a number of measurements in more concentrated solutions including partial molar vo1umes,6t1z heats of mixing,Z0 and volumes of mixing10 provide strong evidence for some kind of higher aggregation, Furthermore, the similarities in behavior in water and the alcohols do not extend to higher concentrations; in water P2for BueNBr decreases with concentration while in methanol” and ethanolz8 it increases. We believe that an explanation that is applicable to the more concentrated solutions and which is compatible with the results for dilute solutions is one that involves a reaction of the ion pairs (either the solvent separated or contact ion pairs of eq IX) with another cation to give a triple ion.
R8X
+ RIN+
[RINXRIN]+
Unlike the triplicates found in media of low dielectric constant where stabilization is entirely coulombic in nature,z9 part of the stabilization of this entity in aqueous solution must be attributed to a hydrophobic effect.
Acknowledgment. This work was supported by Contract No. 14-01-001-1281 with the Office of Saline Water, U. S.Department of the Interior. (28) W.Y. Wen, in “1966 Saline Water Conversion Report,” U. 9. Department of the Interior, Washington, D. C., 1966, p 13. (29) H. S. Young and C. A. Kraus, J . A m e r . Chem. Soc., 73, 4752 (1951).
Cooperativity and Composition of the Linear Amylose-Iodine-Iodide Complex l*$b by Charles L. Cronan and Friedemann W. Schneiderlo Department of Chemistry, University of Southern California, Los Angeles, California 90007 (Received August 19,1968)
Adsorption isotherms of iodine-iodide in the helical cavity of amylose (D.P. = 800) have been determined by spectrophotometric measurements of titration curves at various iodide concentrations (10-5 to 2.5 x 10-2 M KI) and temperatures. A new description of the stoichiometry of the bound species is given in terms of two limiting models: A t very low iodide concentrations the predominantly bound species is considered to be Iz whereas at high iodide the bound species is 1 3 - (the theoretical Ising lattice treatment predicts Id2-). Both models apply in the intermediate transition region where competition for binding sites occurs between Iz and Is-. The over-all composition of the bound species can be expressed approximately as Ia.Ib- where b varies between zero and unity. Statistical analysis of the isotherms using the exact one-dimensional Ising model (n = 15) with first nearest neighbor interactions (between 1.6 and 3.0 kcal/mol) shows that the degree of cooperativity is moderate. The main source of the stability of the complex originates from the intrinsic binding of a species by one turn of the amylose helix. The enthalpy and entropy of binding have been determined at i W KI. Factors affecting the position of A, of the blue band are attributed to the aggregation of partially or completely filled amylose helices.
-
Introduction Although the blue amylose-iodine-iodide (AI) complex has been known for over 150 years, its detailed structure and composition are not yet completely understood. Basic to the understanding of its over-all stability is an insight i n t o the role played by cooperative interactions between bound species which for many years have been suspected to be importanta2 I n previous work a quantitative model treatment of cooperaM KI and 20.0” tivity in the linear AI complex a t has been given for the first time.3 Complex formation was treated as a one-dimensional adsorption process of iodine species into the helical cavity of amylose, and it was shown that cooperativity in the linear complex is surprisingly moderate, the over-all stability being due T h e Journal of Physical Chemistry
-
mainly to the intrinsic binding of an iodine species to a helical turn of ca. eight anhydroglucose units. This work complements the previous equilibrium dialysis measurements and presents spectrophotometric titration studies which cast new light on the stoichiometry and thermodynamics of the complex. The degree of (1) (a) Presented a t the Pacific Conference on Chemistry and Spectroscopy, Anaheim, Calif., Oct 1967. (b) Abstracted in part from the h1.S. Thesis of C. L. Cronan, University of Southern California, 1968. (c) T o whom correspondence should be addressed. (2) (a) For a general review of the complex, see H. Morawetz, “Macromolecules in Solution,” Interscience, New York, N. Y., 1965; (b) R. L. Whistler and E. F. Paschall, Ed., “Starch: Chemistry and Technology,’’ Vol. 1, Academic Press, New York, N. Y., 1965, Chapter 1; (c) J. Szejtli and S. Augustat, Staerke, 18, 38 (1966). (3) F. W. Schneider, C. L. Cronan, and S. K. Podder, b. P h y s . Chem., 72,4563 (1968).
AMYLOSE-IODINE-IODIDE COMPLEX cooperativity is determined over the widest possible range of KI concentrations. It is known from X-ray studies4 that the complex is helical in the solid state with the iodine species trapped inside the helical cavity of amylose. Flow dichroism5 studies lead to the conclusion that the helical configuration also prevails in solution. Evidence from osmotic pressure, optical o ~ i d a t i o nand , ~ mechanochemical1° degradation studies indicate that the helices are deformed resulting in short helical segments of 15 helical turns each for an amylose D.P. (degree of polymerization) N 900 as used in this work. This model of a kinked helical structure in aqueous solution is further supported by Paulson's electric dichroism" studies which indicate that the hydrodynamic length of the complex is less than that expected for a rigid, rodlike helix. No clear picture exists with regard to the stoichiometry of the complex. While potentiometric titration studies by Gilbert, and ?rIarriott12lead to a 2:3 ratio13 of bound I- to I, at low percentage adsorption at and 11/1 KI. spectrophotometric studies by Kontos14 are used as evidence that the above ratio is 1: 1 due to the fact that the intensity of the blue color is highest when the ratio of 12tot.l/I-tota, is unity. Kuge and Onoi5 give a titration curve at Jf K I at 15.0" and report an enthalpy of formation of -15.5 kcal/mol at 15.0" independent of chain length, a value which is comparable in magnitude with previously reported values between -11 and -20 kcal/moL2 Richter and Szejtli16 compare continuous photometric titration with amperometric titration and give an adsorption isotherm for which the amylose and presumably the KI concentration are not held constant. Bersohn and Isenberg17 have considered the iodine chain as a one-dimensional metal in which iodine atoms and ions are equivalent. On the other hand, Peticolas18 and Paulson found the conductivity of solid AI samples to be dependent on adsorbed water, a fact which mas ascribed by Paulson'l to an ionic conduction mechanism in the wet solid. A theoretical model to explain the optical spectrum of the complex in the solid state has been postulated by Robin.lg I t is based on the linear polytriiodide model which successfully describes the related triiodidebenzamide complex. In the latter complex the chromophoric group has been shown to be an infinite triiodide chain in which the individual triiodide ions are strongly coupled with each other, the excitation energy resonating between them. An optical spectrum is obtained which is quite similar to that of the AI complex. I n earlier theoretical work, ^11urakami20assumed 1 4 , - ions to be the basic units in the linear chain. The foregoing discussion is not considered to be a review, but it is intended to show that the linear description of the blue complex and the assumption of ionic species occupying the voids of the segmented helix seem to be justified.
3991
Experimental Section Unbranched potato amylose was obtained from K & K Laboratories, Lot No. 59690X:. Its approximate molecular weight is 150,000, corresponding to a D.P. between 800 and 1000. Potassium iodide and iodine mere of commercially available reagent grade. Spectrophotometric measurements were made on a Beckman DK-2A recording spectrophotometer with constanttemperature attachment. Temperatures mere held constant within 0.05" with a Forma-Temp Jr. constanttemperature bath. Amylose Solutions. Solutions of slightly soluble amylose can be made according to various procedures: (a) solution in concentrated NaOH or KOK and subsequent neutralization with acid; (b) solution in DAISO; (c) solution in boiling water. Nethods a and b produce solutions including unwanted ions and solvents, while method c was considered as possibly too drastic. I n the present work saturated amylose solutions were prepared by constant stirring (24 hr) of a mixture of excess amylose in water at room temperature. Each mixture was allowed to settle, and the semiclear liquid mas filtered through a 5-p millipore filter. The resulting stock solutions (ca. 0.50 mg/ml of amylose) mere of extreme clarity, indispensible for spectrophotometric measurements. Aliquots of these solutions were analyzed for amylose by a standard enzymatic degradation method2' and used for titrations within 1 to 2 days. TitTations. A 100-ml solulion of amylose-KI (4.5 mg of amylose/100 ml) was thermostated and titrated under constant stirring with a 0.0005 M 1 2 solution containing identical concentrations of amylose and KI. Aliquots were withdrawn after each addition of titrant. (4) R . E. Rundle and F. C. Edwards, J . A m e r . Chem. Sac., 65, 2200 (1943), and references therein. (5) R. E. Rundle and R. R. Baldwin, ibid.,65, 554 (1943). (6) J. Ho116 and J. Szejtli, Staerke, 10,49 (1958). (7) T. Kuge, Bull. Univ. OsakaPrefect., Ser. B , 11, 121 (1961). (8) (a) T . Kuge and S. Ono, Bull. Chem. SOC.Jup., 34, 1264 (1961) ; (b) ibid.,33, 1269 (1960). (9) S. R. Erlander, H. L. Griffin, and F. R. Senti, Staerke, 17, 151 (1965). (10) J. Szejtli, 11.Richter, and S.Augustat, Biopolymers, 5 , 5 (1967), and references therein. (11) C. M. Paulson, Ph.D. Thesis, University of California a t Berkeley, 1965. (12) G. A. Gilbert and J. V. R. llarriott, Trans. Faraday Sac., 44, 84 (1948). (13) See also D. L. Mould, Biochem. J., 5 8 , 593 (1954). (14) E. Kontos, Ph.D. Thesis, Columbia Cniversity, New York, N. Y., 1959. (15) T. Kuge and S.Ono, Bull. Chem. Soc. J u p . , 33, 1273 (1960), (16) 31.Richter and J. Szejtli, Staerke, 18, 95 (1966). (17) R. Bersohn and I. Isenberg, J . Chem. Phys., 35, 1640 (1961). (18) W. L. Peticolas, S a t u r e , 197, 898 (1963). (19) M. B. Robin, J . Chem. P h y s . , 40, 3369 (1964). (20) H. Murakami, ibid.,22, 367 (1954). (21) S. -Meites and N. Bohman, A m e r . J . M e d . Technol., 29, 327 (1963). V o l u m e 73, N u m b e r 11
Nol;ember 1569
CHARLES L. CRONAN AND FRIEDEMANN W. SCHNEIDER
3992 Table I : Titration Data and Calculated Isotherm a t 2.5 X ODapo mF
0,008 0.022 0.049 0 076 0 I109 0.138 0.167 0.193 0.233 0.272 0.331 0.389 0.448 0.517 0.578 0.639 0.699 0.758 0.836 I
O h 6 3 mp
0,008 0.017 0.027 0.036 0.046 0.055 0.065 0.075 0.086 0,098 0.116 0.134 0.154 0.175 0.193 0.213 0.229 0.248 0.276
IIzlT
x
lo6
0.0497 0.0993 0.1938 0.2839 0.3715 0.4580 0.5374 0.6159 0.7300 0.8359 1.003 1.116 1.327 1.508 1.672 1.842 1.994 2.150 2.348
ODass mp
[IeIT x los
0.067 0.140 0.221 0.313 0.401 0.535 0,655 0.811 0.974 1.081 1.155 1.215 1.233 1.285 1.303
0.037 0.062 0,085 0.114 0.140 0,180 0.215 0.289 0.314 0.347 0.390 0.449 0,519 0.614 0.713 0.812 0.922 1.032 1.162 1.290 1.505 1.904
0.2752 0.4981 0.7337 0.9913 1.232 1.607 1.940 2.368 2.816 3.137 3.423 3.735 4.091 4.532 4.986 5.395 5.871 6.375 6.939 7.490 8.368 10.09 50.03
... 1.334
...
1.360 1.373 1.386 1.410 1.621
...
... 602 602 602 602 602 602 602 602 602 602 602 602 602 602 602 602 602
0.006 0.016 0.037 0.057 0.081 0.103 0.125 0,144 0.174 0.203 0.247 0.290 0.334 0.386 0.431 0.477 0.522 0.566 0.624
e
...
0.080 0.105 0.166 0.236 0.302 0.402 0,492 0.610 0.733 0 813 0.869 0.914 0.943 0.966 0.980 1.oo
...
607 607 607 607 607 607 607 607 608 610 612 615 617
...
[I3-]F x 10'
0.0276 0.0403 0 0636 0.0827 0.0845 0.0952 0.0991 0.109 0.119 0.127 0.137 0,101 0.156 0.158 0.163 0.174 0.171 0.173 0.169 I
[IPIF
x
lo6
0.00128 0.00186 0.00294 0.00382 0.00390 0.00440 0.00458 0.00506 0.00550 0.00572 0.00633 0.00465 0.00722 0 00730 0.00756 0.00803 0.00790 0.00800 0.00780 I
am1
x
10-1
3.39 11.1 8.02 7.18 8.37 8.33 8.96 9.19 9.01 9.25 9.28 10.6 9.69 9.93 9.98 10.1 10.1 10.3 10.7
M KI, 20.0"
Xmax, m p
I
[ISIF
x
los
0.0886 0.116 0.136 0.150 0.158 0.179 0.194 0.210 0.227 0.262 0.343 0.482 0.711 1.03 1.39 2.11
[IZIF
x
10s
0.0102 0.0134 0.0157 0.0174 0.0183 0.0207 0.0224 0.0243 0.0263 0.0304 0.0398 0.0559 0.0824 0.120 0.162 0.246
e3531
x
lo-'
7.71 8.50 8.42 9.02 9.31 9.43 9.51 9.54 9.91 9.77 9.85 10.1 10.0 10.1 10.0 10.4
619
... 619 620 62 1 622 648
Spectrophotometric measurements were done in a 1-cm cell with water as the reference solution. The aliquot was then returned to the mixture to avoid any loss of material. Throughout the titration the amylose and K I concentrations were kept constant; no other ions were present. The pH was approximately 6 for all titrations. To ensure equilibration of the stirred solutions we allowed at least 15 min between each spectrophotometric measurement. There was no sign of any slow reaction in the stirred solutions. Further evidence of equilibration was shown by the fact that their The Journal of Physical Chemistry
0
Amax, mp
Table 11: Titration Data and Calculated Isotherm a t 1.0 X ODera mp
M KI, 20.0'
absorption spectra were identical before and after a All of our data refer to forheating cycle to -50". ward titrations, ie., to forward equilibrium paths at a constant over-all K I concentration. For this reason no hysteresis behavior was observed. Titrations were performed at 20.0" at the following III concentrations: 2.5 X 5X and 1.07 X M K I (Tables I-V, VII). Isotherms were measured at 13.0, 20.0, and 30.0" for loe4 M K I (Tables VI-VIII). Tables I through VI11 give the observed optical densities at 640 and 353 mp, the total concentration of IZ
AMYLOSE-IODINE-IODIDE COMPLEX
3993
Table 111: Titration Data and Calculated Isotherm a t 5.0 X l o d 8M KI, 20.0' ODMO #,,,
OD333 m s
0.055 0.129 0.218 0.347 0.486 0.631 0.777 0.909 1.078 1.198 1.248 1,294 1.319 1.346 1.364 1.377 1.396 1.410 1.428 1,628
0.033 0.057 0.084 0.120 0.159 0.202 0.242 0.284 0.335 0.394 0.431 0.508 0.586 0.711 0.833 0.958 1.149 1.382 1,772
...
IhIT
x lob
0.2396 0,4720 0.7168 1.075 1.451 1.836 2.219 2.592 3.052 3.490 3.715 4.141 4.551 5.173 5.762 6.344 7.280 8.456 10.01 50.02
Amax, mp
600 605 606 607 608 608 609 609 609 610 610 612 614 616 618 618 618 618 618 633
Table IV: Titration Data and Calculated Isotherm a t 1.0 X
0.059 0.098 0.177 0.262 0.343 0.426 0.510 0.672 0.836 0.908 0.985 1.040 1.157 1.205 1.236 1.264 1.302 1.326 1.343 1.356 1.376 1.386 1.398 1.410 1.413 1.616
0.032 0.043 0.065 0.088 0.112 0.135 0.158 0.203 0.250 0.272 0.293 0.314 0.364 0.384 0.404 0.423 0.470 0.510 0.550 0.609 0.692 0.770 0.849 0.962 1.002
...
0.357 0.494 0.728 0.979 1.223 1.455 1.689 2.138 2.605 2,828 3.058 3.268 3.709 2.918 4.134 4.339 7.747 5.153 5.551 6.135 6.898 7.621 8.327 9.342 9.992 49.96
610 610 610 610 613 616 616 616 618 618 618 619 619 619 619 619 619 619 619 619 619 619 619 619 619 630
added, and A,, the wavelength of maximum absorption for each addition of titrant. Selected titration curves are shown at three wavelengths (Figures 1-6): 640 mp, representing the blue amylose-iodine-iodide complex; 353 mp, due to the absorption of free 13- plus the complex; and 288 mp, the free IS- absorption band. In all titrations except atj M KI the amylose con-
e 0.041 0.096 0.162 0.257 0.360 0.467 0.575 0.674 0.799 0.887 0.924 0.960 0.976 0.996
[IS-IF
x
10'
x
II8lF
106
c3aaI
x
10-8
0.0786 0.111 0,122 0.141 0.153 0.160 0.163 0.187 0.205 0.307 0.384 0.633 0.913 1.36
0.0182 0.0257 0.0283 0.0326 0.0355 0.0371 0.0379 0.0435 0.0476 0.0715 0.0894 0.147 0.213 0.317
8.58 8.25 9.13 9.19 9.39 9.75 9.85 9.93 10.0 10.1 10.2 10.1 10.1 10.1
0.0936 0.110 0.122 0.134 0.148 0.154 0.160 0.170 0.186 0.201 0.214 0.244 0.304 0.342 0.403 0.463 0.603 0.758 0.919 1.17
0.108 0.127 0.141 0.156 0.172 0.180 0.187 0 199 0.219 0.237 0.252 0.288 0.360 0.405 0.478 0.550 0.718 0.905 1.10 1.40
4.69 5.43 7.05 7.62 8.07 8.41 8.62 8.94 9.13 9.16 9.12 9.12 9.32 9.26 9.15 9.04 9.07 8.87 8.69 8.42
M KI, 20.0'
0.043 0.072 0.130 0.193 0.252 0.314 0.375 0.492 0.615 0.668 0.725 0.765 0.850 0.886 0.908 0.930 0.957 0.974 0.989 0.996
I
centration was held constant a t 2.75 X N anhydroglucose residues, where N = equivalents/liter. Test of Lineayity of Amylose Sample. The following observations support the linearity of our dissolved amylose. Addition of butanol gives a fine white precipitate of amylose, whereas branched amylopectin solutions will remain clear.2b Our amylose adsorbs 200 Volume 78, Number 11 November 1969
CHARLES L. CRONAN AND FRIEDEMANN W. SCHNEIDER
3994
Table V: Titration Data and Calculated Isotherm a t 1.07 X 10-8 M KI, 20.0'
x los
OD640 r n ~
ODs63 mC
[IalT
0.000 0.010 0.038 0.071 0.126 0.231 0.353 0.465 0.568 0.660 0.790 0 879 0.968 1.028 1.087 1.135 1.177 1.326
0.002 0.008 0 017 0.028 0.043 0.079 0.113 0.148 0.180 0.209 0.250 0.278 0.303 0.328 0.349 0.364 0 382 0.461
0.484 0.989 1.484 1.945 2.402 3.050 3.701 4.335 4.952 5.753 6.706 7.623 8.842 9.994 11.52 12.95 15.27 49.97
I
I
I
... ... 615 620 620 620 620 620 620 620 620 620 620 620 620 620 621 621
Table VI: Titration Data and Calculated Isotherm a t 1.0 X OD640 MF
ODs63 mr
0.073 0.237 0.409 0.550 0.721 0.881 1.022 1.169 1.347 1.428 1.462 1.501 1.529 1.621
0.026 0.069 0.117 0.157 0.200 0.244 0.281 0.323 0.380 0.416 0.438 0.478 0 528 1.148 I
[IZIT
x
10'
0.495 0.980 1.466 1.923 2,381 2.830 3.271 3.734 4.546 5.357 6.140 7.627 10.00 50.00
OD363 mil
[IalT X 106
0.038 0.142 0.280 0.431 0.560 0.716 0.859 0.962 1.161 1.278 1.334 1.382 1.420 1.560
0.018 0.051 0.090 0.132 0.170 0 212 0.253 0.284 0.347 0.389 0.414 0.450 0.497 1.069
0.4950 0.9948 1.456 1.923 2.376 2,830 3.271 3.699 4.545 5.357 6.140 7.616 9.994 50.00
I
I
I
[Ia-]F
x
[Iz$
0.00443 0.00875 0.0124 0.0155 0.0178 0.0202 0.0219 0.0236 0.0252 0.0283 0.0311 0.0345 0.0394 0.0444 0.0513 0.0575 0.0682
x
106
x
cad
10-3
... *..
0.480 0 954 1.36 1.73 2.02 2.37 2.67 2.98 3.30 3.84 4.42 5.08 6.04 7.01 8.36 9.65 11.8 I
12.4 11.6 10.5 11.o 10.6 10.6 10.6 10.6 10.6 10.6 10.5 10.7 10.7 10.7 10.7
M KI, 13.0" e
620 62 1 621 622 622 622 622 622 622 622 622 622 622 622
0.047 0.153 0.264 0.357 0.468 0.573 0.664 0,752 0.875 0.926 0,951 0.974 0,992
M
x
[IS-IF
los
0.0281 0.0325 0.0349 0.0420 0.0419 0.0436 0.0488 0,0542 0.0807 0.127 0.181 0.285 0.452
x
[h]F
lo6
0.275 0.324 0.354 0.433 0.442 0.468 0.533 0 603 0.920 1.47 2.11 3.39 5.52
dx
10-3
9.65 9.68 10.0 10.1 9.95 10.0 9.97 10.0 10.1 10.2 10.1 10.2 10.1
I
KI, 20.0'
Amax, my
8
620 620 620 620 620 620 620 620 620 620 620 620 620 622
0.026 0.098 0.193 0.297 0.386 0.494 0.592 0.664
mg of Iz/g in very good agreement with literature data.2b There is no spectrophotometric evidence of any branched contaminant, since none of our blue soThe Journal of Physical Chemistry
0.000 0 008 0.031 0.057 0.102 0.186 0.285 0.375 0.458 0.532 0.637 0.709 0.781 0.828 0.875 0 915 0.948
hmx, m y
Table VII: Titration Data and Adsorption Isotherm at 1.0 X ODwa mil
e
XMSX~my
0.808
0.881 0.920 0.954 0.980
IF X IOa
0.0313 0.0486 0 0555 0.0599 0.0676 0.0696 0.0732 0.0836 0.104 0.137 0.179 0.266 0.410 I
[h]F
x
10s
0.364 0.573 0.664 0.729 0.835 0.876 0.937 1.08 1.39 1.86 2.45 3.71 5.85
€363'
x
10-3
9.68 10.2 10.2 10.2 10.3 10.3 10.3 10.3 10.4 10.5 10.4 10.4 10.4
lutions have a A,, lower than 600 mF. We observe the same shift in A,, with KI as reported in the literature.sb A comparison at 15.0" shows that our titration curve
AMYLOSE-IODINE-IODIDE COMPLEX
3995
Table VIII: Titration Data and Adsorption Isotherm at 1.0 X IO-* M KI, 30.0" ODMOmp
ODasa m p
0.003 0.028 0.080 0.141 ' 0.224 0.317 0.423 0.529 0.638 0 845 0.994 1.111 1.162 1.215 1,252 I . 508
0.007 0 * 020 0.039 0.057 0.085 0.116 0.150 0.183 0.216 0.278 0.327 0.373 0.398 0.423 0.449 0.951
I
b1T
x
10s
X m x , mp
...
0.4950 0.9852 1.461 1.918 2.376 2.830 3.275 3.704 4.128 4.955 5.762 6.893 7.627 8.678 10.00 50.00
...
612 612 612 612 612 612 613 613 613 613 613 613 613 620
e
[ISIF x 106
[h]F x los
0.002 0.020 0.058 0.103 0.163 0.232 0.308 0.386 0.466 0.616 0.725 0.812 0.849 0.887 0.914
0.0315 0.0587 0.0799 0,0981 0.112 0.124 0.133 0.140 0.147 0.160 0,180 0.224 0.285 0.302 0.366
0.456 0.853 1.17 1.45 1.67 1.87 2.03 2.17 2.30 2.57 2.96 3.74 4.31 5.18 6.34
rat2
x
10-1
... 5.92 8.41 8.31 9.34 9.94 10.3 10.5 10.5 10.6 10.7 10.7 10.8 10.7 10.7
1.50
1.50
1.00
1.00
d
d
0
0
0.50 0.50 1
1
2.0
2.0
4.0
6.0
[IZlT x
8.0
4.0
10.0
io5.
Figure 1. Titration curve a t 1.0 X M KI, 20.0'; optical density as a function of IzT concentration.
0.0
6.0
[I,],
x
1
10.0
io5,
Figure 3. Titration curve at 1.07 X M KI, 20.0'; optical density as a function of ZzT concentration.
1.50
1.50
1.00
1.00
d
0
ti
0
0.50
0.50
2.0
2.0
4.0 [IZlT x
6.0
0.0
10.0
io5.
Figure 2. Titration curve a t 1.0 X 10-8 M KI, 20.0'; optical density as a function of Z2= concentration.
for M KI is virtually identical with that of Kuge and Ono15 who dissolved their potato amylose in concentrated KOH. Our (unpublished) dichroism studies in electric fields are in agreement with Paulson'sll work
4.0
6.0
8.0
10.0
[I2 IT x 10'.
Figure 4. Titration curve a t 1.0 X 10-4 M KI, 13.0'; optical density as a function of 12*concentration.
on the amylose complex. Branched amylose would not orient in the same manner in an electric field. Degree of Polymerization of the Amylose Sample. Our mild extraction procedure is expected to preferentially dissolve lower molecular weight amylose2b whose D.P. Volume 75,Number 11 November 1069
3996
CHARLES L. CRONAN AND FRIEDERMANN W. SCHNEIDER tributions of bound as well as of the free species I,, and
IsFOD353
+
~a~~[Iz*Io-] ~asa”[Iz]F
+ ~ a s a ~ ~ ~ [ I a(2) -]~
0.50k
f
2.0
353 rnp
4.0
6.0
0.0
a
where €640, E ~ eas31r, ~ ~ and ~ E~~~~~~ , are the molar extinction coefficients of bound species at 640 mp, bound species at 353 mp, free Iz,and free 13-at 353 mp, respectively; (c) the triiodide equilibrium relating the free species to each other
10.0
(3)
C I ~ xIio5. ~
and finally, two mass conservation relations
Figure 5 . Titration curve at 1.0 X loT4M KI, 20.0’; optical density as a function of ZtT concentration.
1.50
(4)
1
and [IZIT
=
[IZIF
+
+
[IZIB
(5)
The latter five equations contain 14 parameters of which the following seven are known: E~~~~~ (18)22 (26,400)22KF = 866 at 20.0°,23[I-IT, [12]~, and ODa53. Unknown parameters are €640, b, E ~ S BItF, I , 1aF-, IF-,and Iz,. The degree of saturation 8 is defined as
1.00
d
0
0.50
2.0
4.0
6.0
0.0
10.0
C I ~ xIio5. ~ Figure 6. Titration curve at 1.0 X M KI, 30.0’; optical density as a function of ItT concentration.
we estimate to be approximately 800. Attempts at molecular weight determinations by viscosity measurements were not successful due to the low amylose concentrations in the saturated solutions. Even if our amylose chains would have a D.P. of only 120 in the extreme case, our conclusions in the present binding study are not affected, since we are using indeed an effective length of 15 helical turns in our theoretical calculations (see Introduction, etc.). Treatment of Data The method used for calculating the concentrations of free and bound species is similar to that of Kuge and Ono.I5 In addition, we have introduced the possibility that a variable amount of I- may be bound together with 1 2 resulting in the bound species I2and 1 3 - whose over-all average contribution to the bound state can be expressed as Iz.Ib-,where b varies between zero and 1 (or 2 for the one-dimensional model). The following five equations comprise the model. (a) absorption at 640 mp due to bound species only OD640 =
[I2 10-1
(1) (b) absorption at 353 mp representing the sum of con€640
The Journal of Physical Chemistry
is the calculated value of bound Iz at where [Iz.I,-],,~ saturation. Since €640 is constant, the relationship
holds, where 0D640,sat refers to the saturated polymer. Experimentally at high I-, an increase of 0D6robeyond ODsa$is observed which indicates, along with a shift in A, that a second process takes place after or near saturation of the helix, which makes it somewhat difficult to determine ODsat,exactly. A possible way to obtain ODs,$ is to determine the point of intersection of two tangents, one being the tangent to the titration curve at high total Iz concentration and the second representing the tangent to the steep rise of the isotherm as seen in Figure 1. This method cannot be applied to the M KI where an extrapolated isotherm at 1.07 x value for ODsatis used. It is fairly certain that the “second process” at the latter iodide concentration is negligible. The present model measures “chromophoric” iodine adsorption, and it neglects any I- which might be bound to amylose itself but not t o 1 2 . Viscosity and other measurements*” have not been able to show I- binding to amylose alone. (22) A. D. Awtrey and R. E. Conniok, J. Amer. Chem. SOC.,73, 1842 (1951). (23) M. Davies and E. Gwynne, ibid., 74,2748 (1952).
3997
AMYLOSE-IODINE-IODIDE COMPLEX Table IX : Isotherm Parameters
2.50 X 1.00 x 10-2 5.00
x
1.00 x 1.07 x 1.00 x 1.00 x 1.00 x
10-3
10-8
10-5 10-4 10-4 10-4
20.0 20.0 20.0 20.0 20.0 13 .O 20.0 30.0
38,500 38,000 38,500 38,000 35 ,000 38,000 38,000 38,000
-1.0 -1.0 -1.0 -0. 7b 0.1-0.3 -0.6 -0.5 -0.4
a Assigned value on the basis of other results a t high I-. * See ref 12. in this case, whereas for all other titrations it is 2.75 X lo-' N .
' Extrapolated.
(1.34)o 1.33 1.35 1.36 1.24' 1.54d 1 .45d 1.37d
(3.48)" 3.50 3.50 3.58 3.54 4.Obd 3.82d 3.61d
N
Amylose concentration is 2.96 X
Results In applying the mathematical model the values of two parameters b and €640 are chosen. From equilibrium dialysis measurements3 a value of €640 has been obtained (38,500) at M KI. Nevertheless, €640 was allowed to vary between 35,000 and 44,500 in intervals of 500. For the known parameters above and at each value of €640 sets of isotherms were calculated on a Honeywell 800 computer for b increasing from zero to beyond unity in intervals of 0.1. The criterion for selecting the "correct" isotherm is the requirement that E~~~~ be constant over the titration range. Conversely, b and could have been chosen and €640 calculated. The latter method turned out to be less accuratelb than the former. Values of the parameters b, €640, and ODsatdetermined for use in the calculated isotherms are listed in Table IX. The amount of bound Iz at ODsat(approximately 3.5 X M , or 20 mg of 12/100 mg of amylose) compares well with previously reported values determined by potentiometric titrationsJ2bie., between 18 and 20 mg of 12/100 mg of amylose. The latter quantity of bound 1 2 corresponds to one I2 molecule per eight anhydroglucose units. The calculated isotherms including values for eab31 are also given in Tables I-VIII, some of which appear in Figures 7-12. 8.6 x 10- M K I . Higher K I concentrations than M could not be attained owing to precipita2.5 X M KI tion of the blue complex. Even at 2.5 X onset of a slow precipitation prevented measurement beyond 8 N 0.6 when stirring was terminated. OD,,$ could not be measured, and it was assumed that it is similar to that at, M KI, This follows from the general result that ODsatwas similar for all isotherms at high KI. A value of €640 38,500 was found to fit the (602 mp) data well. There was no obvious shift in A,, (Table I) indicating that similar species are adsorbed over the low 0 range studied. The calculated isotherms were insensitive to b since the maximum amount of bound iodide is only a negligible fraction of IT-. The best values of E~~~~ show moderate constancy and tend to increase mildly with 0.
0.01
0.02 0.03 0.05
0.1
0.2 0.3
0.5
1
m x105.
M KI, 20.0';
Figure 7 . Calculated isotherm a t 1.0 X
e as a function of m, where m is IzFand Iss-, respectively: full lines, theoretical calculation; points, experimental.
1.00
0.80
0.60
6 0.40
0.20
0.01
0.02 0.03 0.05
0.1
0.2 0.3
0.5
1
rn x105.
Figure 8. Calculated isotherm a t 1.0 X 10-8 M KI,20.0°; 8 as a function of m,where m is IzFand l a p - ) respectively: full lines theoretical calculations; points, experimental.
M K I . The value of €640 (38,500) obtained from equilibrium dialysis3 as well as Kuge and OnoJs16estiM K I compare well with the mated €640 (36,300) at present one of 38,000. At this concentration of I- any b values chosen had no effect on the calculated Izrand Volume 78, Number 11
November 1969
3998
CHARLES L. CRONAN AND FRIEDEMANN W. SCHNEIDER
1.00
r
0.60
1
0.60
B
4 0.40
: I J/I
/
t r’
0.01
0.401
J’
0.02 0.03 0.05
A , V
Q,
0
1 rn x
2
x
0.20
,
0.05
I
3
d d
d
5
0.1
0.2 0.3
0.5
1
2
3
5
m x IO5.
10
io5.
iM KI, 30.0’;
Figure 12. Calculated isotherm a t 1.0 X
e as a function of m, where m is I z F and IBF-, respectively:
Figure 9. Calculated isotherm a t 1.07 X 10-6 M KI, 20.0’; respectively: full lines, theoretical calculation; points, experimental.
full lines, theoretical calculation; points, experimental.
e as a function of m, where m is IzF and ISF-,
r
lo/[
0.80
0.60 -
6 0.40
.
i
0.20,
/ L
L
O
0.03 0.05
0.1
I
’
0.2 0.3
0.5
1
2
4 t
5
3
m x105.
Figure 10. Calculated isotherm a t 1.0 x loF4M KI, 13.0’; e as a function of m, where m is I t p and Zap-, respectively:
-5
full lines, theoretical calculation; points, experimental.
-4
-3
-2
Log [I-I,. Figure 13. Apparent binding constant l/m us. free [I-IB.at = 0.5, where m refers to [lJF and [I3-IF, respectively.
e
0.05
0.10
0.200.30 0.50 1.0 m XI@.
Figure 11. Calculated isotherm at 1.0 X
2.0 3.0
5.0
M KI, 20.0’;
e as a function of m, where m is I t F and I,,-, respectively: full lines, theoretical calculation; points, experimental.
13-F. While, , ,X is quite constant up to e N 0.8 (Figure 16c), a strong increase occurs beyond 0 = 0.8 due to a “second process” to be discussed later. The The Journal of Physical Chemistry
gradual sigmoid shape of the isotherm (Figure 7) indicates only a “moderate” degree of cooperativity. Over-all binding with respect to Is- is quite high: [1/ &-IF N 6.3 X l o 5 at e = 0.5 (Figure 13). 6 X M K I . Values for the individual parameters are found to be similar to the ones at M KI, as seen in Tables I11 and IX. M K I . Similarities with all previously discussed isotherms exist (Table IV, Figure 8). At 0 = 0.5 values for 13-p are almost identical for all isotherms discussed so far, indicating that a similar species may be responsible for binding. The maximum amount of I- which can be bound as 13- is less than -4% of the total iodide concentration. Thus b cannot be determined spectrophotometrically at low3M KI. Potentiometric titration studies indicate,12 however, that b g 0.7 at low e, a value adopted in the present study. lov4 M K I . A change in the composition of the
AMYLOSE-IODINE-IODIDE COMPLEX bound species is indicated due to a lower value of b = 0.5 0.1. The latter value was determined on the basis of those calculated values of e 3 d per isotherm which showed the least variation over the titration range (Table VII). A slight difference in isotherm shape is found when the free species is taken to be in one case and 12, in the other (Figure 11). 1.07 X M KI. The nature of the bound species at this lowest I- of our study is found to be markedly different from that a t high I-. Values of b cannot be larger than 0.2 for 1.07 X 10-6 M K I owing to the fact that for b 2 0.2 negative 13-F are calculated (TableV, Figures 3 and 9). Contributions of I- from the hydrolysis of 1 2 (Khyd = 4.3 x at 2O.OoZ4) may be as high as 20% for the highest Iz concentrations used in the titration. The possible production of I- by processes other than hydrolysis such as reduction of IZin the presence of amylose would tend to increase b somewhat. A visual comparison with the titration curve at M K I (Figure 5 ) shows immediately that [I-]T for the present curve must be substantially lower than M . Therefore the b value for this curve must be M KI). Assmaller than the previous b = 0.5 (at suming, in the extreme case, that [ I - ] T were twice as large, ie., 2 X 10-5 fW,our calculations have shown that b might be as high as 0.3 but certainly not higher for the present titration curve. Thus it has been unequivocal1.y shown that the bound species cannot be Is- a t this low iodide concentration, since there is not enough I- available for their formation. This result invalidates the assumption14 that Is- is the binding species a t any concentration of KI. The value of b has but does have a large no effect on the calculated IzF effect on the calculated 1 3 F - which is higher for lower b values. The value of €640 is found to be lower than 38,000, probably due to the drastically different cornposition of the bound species. The extrapolated value of OD,,, appesrs to be somewhat lower than the one at the higher I- concentrations (Table IX).
Nature of the Bound Species The reciprocal free species concentration at constant can be used as a measure of binding strength at various total I- concentrations. This I- dependence25 of l/m, is shown in the following to lead to the postulate of two limiting binding models for either of the two binding species, Izand I3-. At very low iodide concentrations the bound species is postulated to be Iz; Le., b = 0 for Iz Ib-, according to the equilibrium
3999
At high iodide concentrations the bound species is postulated to be 13-; i.e., b = 1. For Izas free species
Alternately, for Is- as free species
For the limiting model of ISbinding to hold (equilibria 6 and 7), the apparent binding constant K1 as well as Kz/(I-)F should be independent of I-. It is seen from Figure 13 that the [Iz]F-' curve could gradually apM KI. This beproach a constant value below havior is also reflected in the [13-]~-1 curve whose slope M KI. could approach a limiting value of - 1below Thus it can be inferred that the limiting model of IZ binding is likely to be realized at somewhat lower I- concentrations than that attained in this study. Further experimental lowering of the K I concentration is complicated by interference of I2hydrolysis and reduction. At high iodide concentrations the formal predictions of equilibria 8 and 9 are borne out. For I2 and 1 8 - as the free species, K3[I-]F and K4 are found to be constant, respectively, above M KI, indicating that the bound species is likely to be I3-. However, further uptake of I- to form 142cannot be entirely ruled out. Since, at high [I-IT, the equivalent concentration of the complex is negligible with respect to [I-]T, a distinction between 1 3 - and as the bound species is not possible by use of the l/me relationship alone. A later one-dimensional model calculation shows that 14'- binding cannot be entirely excluded. At intermediate iodide concentrations both limiting models contribute according to 12.1b-where b varies from zero to 1 (or -2 on the basis of the one-dimensional model) with increasing iodide concentration. To express the average composition of 1%. Ib-in terms of bound Izand bound 13-,one could define a quasi onedimensional equilibrium constant K Bsuch as
e (l/me)
which approximately describes the composition of the bound species as a function of the free iodide concentration. However, due to the cooperativity and competitive nature of the adsorption process, one would not expect K B to be constant at all iodide concentrations used.
Theoretical Model for Adsorption where A' represents an empty site having one nearest neighbor. For 13- as the free species, at low I-
The theoretical isotherms are calculated from a sta&tical model3 which postulates equilibrium between species in their free and bound state. The bound state (24) M. Eigen and K. Kustin, J . Amer. Chem. Soc., 84, 1355 (1962). (25) J. A. Thoma and D. French, J. Phus. Chem.,65, 1825 (1961).
Volume 73, Number 11
November 1.96'9
CHARLES L. CRONAN AXD FRIEDEMANN W. SCHNEIDER
4000 ~~~~~
~~
Table X : Values of KOand K,t obtained by a Nonlinear Least-Squares Calculation -1
KO
2.50 1.0
x x x x
10-2
10-3 1.0 10-3 1.07 X 1.0 x 10-4 1.0 x 10-4 1.0 x 10-4 5.0
a
2.20 X 1.10 X 4.72 X 8.59 X 1.06 X 3.90 X 2.43 X 1.06 X
20.0 20.0 20.0 20.0 20.0 13.0 20.0 30.0
10+
lo4 10‘ lo3 loa 106 104 lo4 lo4
5.83 5.42 4.93 5.28 6.74 6.01 5.88 5.59
30.9 57.3 166 81.1 38.9 71.4 69.7 75.3
2.00 2.36 2.98 2.56 2.13 2.43 2.47 2.60
4.85 X 9.52 x 2.10 x 8.18 x 2.00 x 5.23 x 2.96 X 1.06 x
lo6
104 104 103 103 103 loa
103
----------
-AK5
Kst
7.63 6.68 5.80 5.25 4.43 4.87 4.66 4.20
30.4 57.2 160 72.2 15.0 49.6 44.8 47.2
Wa
1.99 2.36 2.95 2.49 1.57 2.22 2.21 2.32
AFo and w are in kilocalories per mole.
is represented by the occupied one-dimensional Ising lattice of finite length. The model assumes all binding sites to be equivalent and all bound species t o be “localized.” First nearest neighbor interactions are considered between bound adsorbate molecules which leads to a quantitative description of cooperativity in terms of the stacking coefficient. The degree of saturation, 0, is calculated as a function of the free adsorbate concentration, m, at a given chain length, n, cooperative energy of interaction, w,and intrinsic association constant, KO, according to3
0=D(
1
- R”) + Rn+l - 2R(1 n ( l - R)
Intrinsic Association Constant
where
D
Xo - 1 = -__ A0
- XI
E = -X I XO
XOJ = 0.5(1
n = 15 represents a lower limit, and it is assumed to be independent of K I and temperature. A lowering of n tends to increase Kat for the same experimental isotherm shape. Therefore the reported values of KStrepresent maximum values. This is to say that the “true” degree of cooperativity may be even somewhat less than that reported in this work. A good theoretical fit was obtained at all iodide concentrations as shown in Figures 7-12 for some representative isotherms. Values for K,$ and K Ohave also been determined by a second method: a nonlinear least-squares fit3 calculated on a Honeywell 800 computer. The latter method can be used to refine the less accurate results of the former. Table X summarizes values of K,b and KO determined by the nonlinear least-squares calculation for either IZor 13- as the free species.
+ KstKOm d(1- KaSom)’
+ 4Kom
where Katis the “stacking coefficient” (KSt= exp(-w/
RT). Kat is obtained by curve fitting of the experimental isotherm to a theoretical isotherm curve of 0 vs. log Kom at a given n. The value of KOis calculated from KO
=
(mKO)theor
at any
(m)exptl
A short-chain isotherm model, n = 15, was adopted3 mainly on the basis of the previously mentioned mechanochemical degradation studies of amylose done by Szejtli, et al, Io The nonsymmetric shape of the experimental isotherms immediately suggests that n should be substantially smaller than the highest possible value of 120150. It is believed for the present amylose sample that The Journal of Physical Chemistry
At any given iodide concentration we may define two intrinsic binding constants: one with respect to 1 2 and the other with respect to Is- as the free species. The dependence of KOIzon IT- reflects the behavior of [Iz]~-l(Figure 13) at low values of IT-; KO eventually approaches a constant value as expected for the proposed limiting Iz binding model (Figure 14). At high IT-,however, a somewhat stronger dependence on ITis observed than that of [IZIF-l: a slope of -1.7 is found at 2.5 X 10-2 M KI. Thus the bound species is predicted to approach I d z - (for a slope of 2) at very high IT-,rather than Is- as predicted by the [ I z ] T -curve. ~ A similar conclusion is reached upon inspection of the KoI,- curve: K O declines with I T - in a manner indicating limiting I2 binding at low IT-, then it passes through a horizontal region expected for 1 3 - binding and finally it increases with I T - indicating that further I- is taken up into the complex (Figure 15). The latter behavior again predicts the species I d 2 - for a slope of +1, which is not quite attained yet at 2.5 X M HI. Thus the KO plots predict Id2-as the limiting bound species at high K I whereas the experimental l / m plots (Figure 13) lead to Is- as the bound species.
Stacking Coefficient Two types of stacking coefficients can be defined; one
AMYLOSE-IODINE-IODIDE COMPLEX
4001
8-
6-
$ cn
4-
4 2-
-6
-5
-4 -3 Log [I-I,.
-2
-1
Figure 14. Calculated values of KO,Ksel K o K , as ~ a function of free [I-],. Free species is taken as Itp a t e = 0.5.
L
I
-6
-5
-4
-3
-2
-1
Log cI-lF. Figure 15. Calculated values of KO,Kat, KoK,, as a function of free [I-],. Free species is taken as IS- a t e = 0.5.
with each other. Support for this argument comes from the fact that even for saturated solutions of Izin water no aggregation has been reported. Thus the cooperative energy of interactio,n w, is approximately -1.57 kcal/mol, corresponding to K,t = 15.0 for IZas the free species. As more I- is bound into the complex the cooperative energy of interaction is found to increase; ie., w = -2.47 kcal/mol for Kst = 69.7 at M KI. At Kst(m.x)the bound species can be calculated from K B to be approximately Iz.213- (b = z/3) for the limiting 13-model, whereas for the limiting I d z - model the bound species are approximately 1 8 - at this particular K I concentration. In any case, addition of I- to the polyiodine chain increases the cooperative energy of interaction between bound species to a certain value a t the maximum. The formation of higher 13- aggregates occurs in aqueous solution to a small extent.23 If an analogy to bound Is- is permissible, then a relatively moderate interaction in the bound state as exemplified by Kst(max) is conceivable. As I T - increases M , Kst is observed to decline almost beyond 2 X linearly withIT-. At 2.5 X M KI, w = -2.0 kcal/ mol for Kat = 30.9 (relative to I~-F’).Thus further uptake of I- is seen to increase the electrostatic repulsion between bound species as evidenced by the decreasing value of w. From the behavior of Kst the binding species is again predicted to be 1 4 z - at very high iodide concentration. Extrapolation to very high K I concentrations, which are experimentally not attainable owing to precipitation, predicts that eventually repulsive interactions should take over and w should become positive. Thermodynamic Parameters For a cooperative system the isosteric heat of binding, AHe, is expected to be a function of e as well as of temperature. In this work, due to the moderate degree of cooperativity, variations of AHe with e and T were within experimental uncertainty. Best results were obtained at M K I to which the following calculations apply. Use of the ClausiusClapeyron-type equation log &)e
with respect to Iz,, the other with respect to I3-p as the free species. At sufficiently high IT-,where b does not affect IT-, the two types of Kst should be identical. At low IT-,however, where the concentration of bound Ibecomes comparable with I T - the two types of K,$ should be different as seen from Table X and Figures 14 and 15. Interestingly, a slight maximum in Kat is found as a function of IT- for both Kat. This maximum occurs approximately a t I T - ‘v 2 X lod3 for a Kat(max) = 120. What is the composition of the bound species a t the maximum? First, at 1.07 X 10-5 M KI, where b = 0.1-0.3, the bound species consist mostly of 1 2 which would not be expected to interact very strongly
=
----(‘ Ti - ;-
- AHe
2.303R
leads to an enthalpy of binding, AH0.5, at 8 = 0.5, of -16.6 f 0.5 and -12.8 =k 0.5 kcal/mol for Iz and 13as the free species, respectively. The difference (-3.8 kcal/mol) between the two values is probably due to the enthalpy of formation of free 13-which has been reported to show a mild dependence on temperature.z3 Previously given values for AH of binding in the amylose-iodine-iodide system range from - 11to -20 kcal/ mol of bound 12.1z915,26 Using AFe = -RT In (l/me) for the over-all free-energy change, the over-all entropy (26) J. Ho116 and J. Szejtli, Btaerke, 9,109 (1957).
Volume 78,Number 11
November 1969
4002
of binding a t 0 = 0.5 is calculated as -33.7 and - 15.6 eu for Iz and 1 3 - as the free species, respectively. The difference (A(A8,) = - 18.1eu) between the latter two values is noteworthy, since it cannot be due to the free triiodide whose A S of formation is calculated to be approximately +0.5 eu a t 20.0” from Davies and Gwynne’s dataeZ3 It is likely that this difference is partially due to the particular composition of the bound species which on the average is approximately 12*1-0.6 at M KI, whereas the free species is taken to be IZand I3-, respectively. Furthermore, hydration effects may have to be considered as seen from the fact that the above discrepancy is found in AS, only. Thermodynamic parameters obtained from the one-dimensional model compare satisfactorily with the above: AH, due to intrinsic binding with one helical turn (KO)is - 16.3 and - 13.3 kcal/mol for Izand 13-,respectively. The good constancy of w over the temperature range suggests that it might be regarded as an enthalpy rather than a free energy: for 1 2 , w = -2.25 kcal/mol; for I3-, M KI. The product KoKst is w = -2.50 kcal at an exact measure of over-all binding at the point of inflection of the nonsymmetric isotherm which occurs a t ~ 0 = 0.28. Here KoKBt= l/mexpt~. AH, for K o K ,at 0 = 0.28 is - 18.5 and - 15.7 kcal/mol for 1 2 and Is-, respectively, in satisfactory agreement with the “experimental” AH,. It is evident that practically all of the over-all entropy loss occurs when the species gets “trapped” into one helical turn. The difference in AS, between I2 and 13-binding is similar to the above A(As,) which again suggests that hydration effects may play an important role in binding. Importantly, such hydration effects seem to be associated almost exclusively with intrinsic binding rather than with cooperative interaction. The temperature dependence of the isotherms at M K I has been measured at 13.4, 20.0, and 30.0”.lb Since the results show greater scatter, we do not report them here. However, it appears that values for AHe fWKI. are somewhat less negative than those at Amax
and the “Second Adsorption”
A difficulty in determining values of OD,,$ was mentioned earlier with regard to a “second adsorption process” which was suggested by Higginbothamz7to explain the continuous shift of A, toward longer wavelengths when iodine is added after apparent saturation. Figure 16a shows the relationship between A,, and the total I- concentration at a total 1 2 concentration of 50 X 10-6 & morel than , ten times the concentration needed for saturation. If A,, is characteristic of the degree of the “second adsorption,” then this process is facilitated by a saturated helix at high Iz and I-. Alternative explanations for the “second adsorption phenomenon” have been given? association of helices by intermolecular hydrogen bonding and the displacement of counterions (K+) from nonhelical regions by additional 13The Journal of Physical ChenzistrZp
CHARLES L. CRONANAND FRIEDEMANN W. SCHNEIDER
6
630
2 610 620
-
L-Lu2.2 -4
-2
Log
620
1 L
I
1
L
[I-3.
Log
I
I
, 620
I
0.2 0.40.6 0.0 1.0
e. Figure 16. Am,
i
-2
-4
1.00 x I O - ~ M . K I
t
6i20
0.8
[I-I.
I-
1.00x I O - 4 KI ~
t
0.2
0.6
1.0
e.
relationships.
binding. We believe the aggregation of partially or completely filled helices to be the most likely process to explain the “second adsorption” phenomenon. Thus aggregation seems to be promoted by increasing K I concentration, i.e., increasing ionic strength. Interhelix interaction would be expected to add a third dimension to the largely one-dimensional species-species interaction within one helix thus increasing A, due to a greater delocalization of the resonance energy between bound 12-18- species. At lower degrees of saturation, 0 = 0.8, A,, decreases with I - (Figure 16b), indicating that the adsorbed species do indeed change in nature as a function of KI in support of the findings of this work. At a constant K I concentration of M , A,, is found to be constant (-620 mp) over the isotherm range (Figure 16d) lending support to the assumption that the nature of the bound species does not change appreciably at a constant K I Concentration. At M KI, A, (-607 mp) is constant up to 0 = 0.8 beyond which it increases probably due to increased aggregation of amylose helices (Figure 16c). The tables may be consulted for listings of A, for all points measured.
Discussion This work shows convincingly that the main stability of the complex originates from the intrinsic binding as seen from the high values of KO(Table X). Thus one helical turn which has a pitch of -8 A in the solid is (27) R. 9. Higginbotham, J . Teztilelnst. Trans., 40,783 (1949).
AMYLOSE-IODINE-IODIDE COMPLEX capable of trapping either the Iz or IS- species rather strongly with a substantial loss in entropy. It is cert E in from entropy considerations that internal solvation effects must be important here. The channel diameter (outer diameter inside the helix is ap roximately 6-7 of the helix is -13 which is large enough to accomn-odate species such as other anions or HzO molecules together with the iodine-iodide chain. Strong intrinsic binding as found in this work makes the existence of a chain of bound species possible, and it therefore is indirectly responsible for chain stability. Qualitative evidence for cooperativity has been cited earlier.2*13,2*-30Rundle, et ~ 1 observed . ~ that ~ if~ only half of the iodine needed for saturation is present in an amylose solution and the complex is precipitated with excess KI, the iodine is found entirely in the precipitate with half of the amylose still in solution. It should be kept in mind, however, that a heterogeneous phase change is involved in the latter process. Statistical calculations using the present parameters of KBtand KO showS2that for the moderate degree of cooperativity found in this work the often cited ‘‘all or nothing’’ is not important. Instead, for present magnitudes of K,t there is a gradual increase in the average chain length of bound species from a value of 2-4 to the maximum value of 15 as e increases from 0.1 to 1.0, respectively. This is to say that the probability of finding short chain lengths of bound species is appreciable even at relatively high e. Thus we do not consider the binding reaction for the present amylose sample as highly cooperative, although it might be argued from an energetic standpoint that first nearest neighbor interaction energies of -1.6 to -3.0 kcal/mol represent relatively strong interactions for the case of mutual iodine species interactions. The use of a higher effective chain length in the calculations would lead to an even lower degree of cooperativity in this study in which an effective chain length of 15 helical turns has been employed. An independent determination of w by equilibrium dialysis3at M K I and 20.0” is in general agreement with the spectrophotometric results. The value of f640 -38,500 obtained by equilibrium dialysis at f W K I is used in the spectrophotometric isotherm calculations. Surprisingly, this value is found to be a good measure of 6640 over the KI range from 2.5 X to 1X M despite the finding that the composition of the bound species changes to some extent. At 1.07 X lod5M KI, €640 has decreased by -8% to a value of 35,000, whereas the limiting concentration of bound species expressed in terms of Iz has remained practically constant over the total K I range for a constant amylose concentration of 2.75 X N . Therefore, in the present K I range, 6640 (unlike Amax) is not very sensitive to the amount of I- bound in the complex although it is known that €640 will eventually approach zero a t zero iodide concentration. The expected drastic drop in E640 seems to occur at even lower I- concentrations
1)
A4
4003 than attained in this study. Pure IZbinding as predicted in the limit of zero K I concentration will therefore not show a blue band a t 640 mp; it is likely to have a A,, around 460 mp similar to free 1 2 in aqueous solution. Spectra at low K I show already a pronounced shoulder at 460 mp, which is higher than that expected for free Iz present at equilibrium. The values for range in the neighborhood of 10,000 with good constancy for the isotherms a t low K I concentrations. Inspection of a large number of machine calculations shows that there is a latitude in the choice of b. At the lowest K I concentration (1.07 X M ) , it is required that b = 0.1 t o 0.3. The latter b range has been calculated from the consideration of additional production of I- by hydrolysis and reduction of IZat the very low K I level used. If [I-]T=2 X instead of 1.07 X M , then b is -0.3. Thus there is convincing proof that the composition of the bound species is drastically different from that a t high KI. The value of b is understood to be an average approximate value over the isotherm, and it should reflect conditions well at 0 = 0.5, where most of our conclusions are drawn. A more refined model would use a variable b as a function of 0. The apparent change of b from 0 to 1 with KI leads to the postulate of the quasi-one-dimensional binding constant K B which is the analog to K F of the free triiodide equilibrium. The value of K B will depend on KI, since KRtis found to change as a function of KI. However, K g shows in a qualitative fashion that a competition exists between the IZand 13- species for a binding site. The average over-all composition of the sum of the bound Izand 13- species is expressed formally in terms of 1,.Io,whereas it is the IZand IS-species that are considered to bind. This is to say that at low K I the equilibrium in the bound state is shifted toward in the direction of the limiting model. The extrapolated binding constant for limiting I, binding is predicted to be approximately lo3 M-l or less from Figure 13. At high K I the limiting l / m model leads to 13-,whereas predictions based on the one-dimensional Ising model lead to 14’- as the binding species. Robin’slg polytriiodide as well as Murakami’szO12- model (in the solid state) seem to be formally supported, although data obtained in homogeneous solution should be applied only with care to the solid complex, since the two systems are separated by a heterogeneous phase change. Thus in aqueous solution the polyelectrolyte character of the AI complex is enhanced as KI increases where K + is the counterion. (28) F.L. Bates, D. French, and R. E. Rundle, J . Amer. Chem. SOC., 6 5 , 142 (1943).
(29) R. R. Baldwin, R. S. Bear, and R. E. Rundle, ibid., 66, 111 (1944). (30) R. S.Stein and R. E. Rundle, J. Chem. P h ~ s .16, , 196 (1948). (31) R. E.Rundle, J. F. Foster, and R. R. Baldwin, J. Amer. Chem. SOC.,66, 2116 (1944). (32) P.K.Rawlings and F. W. Sohneider, J. Chem. Phys., 50, 3707 (1969). Volume 73, Number 11
November 1060
4004 Up to the present time the main proof that 1 3 - is the binding species at all K I concentrations has been the work of Kontos.14 However, if the triiodide equilibrium and the amount of bound I2 are taken into account a recalculation of Kontos' data assuming 1 3 - binding predicts his spectrophotometric results with unsatisfactory accuracy. lb We therefore conclude that Kontos' often cited work does not strictly support IS-binding at very low K I in accordance with our work; for a quantitative discussion see ref lb. In the closely related benzamidetriiodide solid complex which is used as a model of the AI complexa3the triiodide ion chains in the crystal are slightly nonlinear with a normal 2.92-8 interval distance per triiodide and a distance of separation between adjacent triiodide ions of only 3.80 A, which is considerably shorter than the van der Waals distance of 4.7 8. The Coulomb repulsion between the similarly charged 13-ions is evidently overcome by attractive forces. According to Robinl9 the latter are largely due to dispersion forces as seen from a calculation of the secondorder mixing term in the exciton coupled triiodide chain. As more I- ions are taken up in the AI complex the attractive interactions are more and more compensated by increasing repulsion as seen from the decrease of K S t beyond themaximum. On the other hand, this decrease might be artifact of the model which does not consider higher order interactions (which might be important, especially at, low ionic strengths) nor parallel aggregation of helices which is likely to occur at higher KI. The latter would tend to decrease the nearest neighbor interactions per nearest neighbor pair, while intrinsic binding to the matrix might then increase. As seen from the existence of the blue benzamide-triiodide complex, it is not necessary that the matrix be of helical configuration in order for the iodine species to bind. For example, a solid water structure provides the rigid matrix in the case of frozen Is- solution^'^ such that the trapped 1 8 - species can interact with each other to give the blue color. Thus the interaction with the "rigid-preformed" lattice seems to be rather unspecific.lg As concluded earlier3 there seems to be no experimental evidence that a helix coil transition occurs in the temperature range employed for the present neutral aqueous solutions. Our early kinetic measurements by the temperature jump method1* show an electric field and @-dependent dichroism in the microsecond region which is caused by the parallel alignment of the AI helices1' while the condenser discharges into the soli-
The Journal of Physical Chemistry
CHARLES L. CRONAN AND FRIEDEMANN W. SCHNEIDER tion (ionic strength of This transient dichroic effect may obscure any relaxation time which could be due to the rapid portion of the binding process. Concentration-dependent relaxation times which were measured in the millisecond region were attributed to the contributions of the slower portion of the cooperative binding equi1ibrium.l" According to Rao and Foster34a partial breakdown of the already deformed helical structure occurs above pH 12. Hence, the temperature dependence of the blue band in this study is due to the temperature dependence of the binding equilibrium in which the helical backbone remains essentially intact. Some additional experiments have shown that the experimental adsorption isotherms are independent of amylose concentration. The proposed model for Iz/I~binding in this study describes the stoichiometry and cooperativity of the AI complex to a good approximation, and it unifies a large body of literature data.2 It is likely that the limitation of the spectrophotometric method and the oversimplification of the one-dimensional model do not warrant better agreement than that actually found. Refinements such as higher order nearest neighbor interactions35z36might be introduced for the long-range electrostatic interactions. A more realistic statistical description of the complex is to treat adsorption and mutual interactions of limiting species as a competitive process for which exact model calculations are presently being made. Recent ruby laser studiesa7have shown an interesting optical property of the AI complex in aqueous solution; it represents a novel class of optically saturable absorbers capable of passive Q switching. This Q switch action has been shown to produce giant laser pulses in a ruby laser. 37
Acknowledgment. We thank Miss Maymie Chenoweth of the Department of Biological Sciences for the enzymatic analysis of amylose solutions, and Mr. P. K. Rawlings for performing the nonlinear least-squares calculations on a Honeywell 800 computer. F. W. S. gratefully acknowledges a Frederick Gardner Cottrell grant administered by the Research Corporation. (33) J. M.Reddy, K. Knox, and M. B. Robin, J . Chem. Phys., 40, 1082 (1964). (34) V.5.Rao and J. E'. Foster, Biopolymers, 1,527 (1963),and refer-
ences therein. (35) M. E. Baur and L. H. Nosanow, J . Chem. Phys., 37, 153 (1962). (36) S.Lifson, ibid., 40, 3705 (1964). (37) L. Huff, L. G. DeShazer, and F. W. Sohneider, Photochem. Photobiol., in press.
