Aqueous radiation chemistry of cysteine. I. Deaerated acidic solutions

---

STUDIES IN

THE

AQUEOUS RADIATION CHEMISTRY OF CYSTEINE

2395

Studies in the Aqueous Radiation Chemistry of Cysteine. I. Deaerated Acidic by Adnan Al-Thannon, Richard M. Peter~on,~ and Conrad N. Trumbore4 Department of Chemistry, University of Delaware, Newark, Delaware Accepted and Transmitted by The Faraday Society

(November 8, 1967)

Results of studies on the cobalt-60 y radiolysis of acidic cysteine (RSH) solutions, pH 1.0 and 0.5, are reported. Irradiation products which have been identified are Hz, HzS, RSH, and HzOz with radiation yields a t 10+ M cysteine of 3.2, 0.95, 3.0, and 0.68 molecules/100 eV absorbed. Alanine was also observed qualitatively as a radiation product. Yields for the disappearance of the thiol group were measured polarographically during the irradiation and G(-RSH) was found to be 7.0 at M cysteine. A mechanism is postulated for strongly acid cysteine solutions on the basis of competition kinetics, material balances, and comparison with theoretical yields. Analysis of results of competition studies provides evidence for a rate constant of approximately 3 x 1010 1. mol-1 sec-l for the reaction of the hydrated electron with the protonated-amine form of cysteine. Results of scavenger studies a t concentrations higher than lo-* M cysteine require that additional processes be postulated in order to account for high Hi3 yields.

Introduction I n a previous article,6 evidence for the rapid reaction of the hydrated electron and the hydroxyl radical with cysteine (RSH) in neutral solutions was presented. Armstrong and coworkers6 have recently proposed a mechanism for the cobalt-60 y radiolysis of 1 N perchloric acid solutions of cysteine. We have independently studied this system a t higher pH and we provide evidence here on yields and competition studies which are in agreement with their yields and which support, quantitatively, certain steps in their proposed mechanism. I n addition, studies are reported which provide evidence that at higher cysteine concentrations there is very efficient scavenging of the hydrated electron by cysteine in competition with the hydronium ion. A diffusion-limited rate constant for this scavenging by cysteine is in contrast with the earlier reported rate constant for the neutral species, thus demonstrating the enhancing effect of the nearly complete protonation of the amine group in strong acid. Solutions were studied a t pH 1 and 0.5 in order to limit the number of cysteine species to essentially only the amine-protonated one with the structure HSCH2CH(NH3+)COOH.’ Air-free solutions were studied in order to prevent possible chain reaction^.^^^ Experimental Section All irradiations were carried out a t 25” in a Gammacell 220 (Atomic Energy of Canada, Ltd.) cobalt-60 irradiation unit. Absorbed dose rates in solutions in this study were approximately lo3 rads/min. All aqueous solutions were swept with Ar, labeled 99.995% pure, supplied by Linde Air Products Co. and were irradiated in preirradiated Pyrex vessels supplied with standard tapers so that solutions could be transferred

from the Ar bubbler in a manner similar to that described by Swinnerton and Cheek.lo Dose rates were obtained using ferrous sulfate solutions irradiated in the same vessels. All water was triply distilled. I n all cases solutions were prepared immediately before use to minimize air oxidation of cysteine. pH measurements were carried out with a Beckman expandedscale pH meter and spectrophotometric measurements were made with a Zeiss PMQ I1 spectrophotometer. Cysteine (RSH), cystine (RSSR), and alanine (RH) were of the highest purity available from Nutritional Biochemicals Co. and Calbiochemical Co. Only the free-base forms of the amino acids were used in this work. Perchloric acid was either Merck or Baker reagent grade and KN03 was Baker and Adamson reagent grade. p-Chloromercuribenzoic acid was from Aldrich Chemical Co. The rate of disappearance of the cysteine thiol (1) This research was supported by the U. S. Atomic Energy Commission and is AEC Document NYO-3383-9. (2) Based in part upon the Ph.D. dissertations of A. Al-Thannon and R. M. Peterson, University of Delaware, Newark, Del., 1967 and 1968, respectively. (3) Deceased July 17, 1967. (4) To whom correspondence should be addressed. (5) A. El Samahy, H. L. White, and C. N. Trumbore, J . Amer. Chem. SOC.,86, 3177 (1964). (6) V. G . Wilkening, M. Lal, M . Arends, and D. A. Armstrong, Can. J . Chem., 45, 1209 (1967). (7) J. T . Edsall and J. Wymann, “Biophysical Chemistry,” Vol. I, Academic Press Inc., New York, N. Y . , 1958; J. N . Butler, “Ionic Equilibrium,” Addison-Wesley, Ino., Reading, Mass., 1964. (8) A. J. Swallow, J . Chem. Soc., 1334 (1952); J. E. Packer, ibid., 2320 (1963). (9) A. AI-Thannon, R. NI. Peterson, and C. N . Trumbore, unpublished results. (10) J. W. Swinnerton, V. J. Linnebom, and C. H. Cheek, Radiat. Res., 19, 636 (1963).

Volume 72, Number 7 J u l y 1968

2396 group, as well as the rate of buildup of the radiolytic products, HzS and RSSR, was followed polarographically using a Sargent Model XV recording polarograph. The polarographic cell employed a dropping-mercury electrode and a saturated calomel reference electrode. An agar plug, prepared according to Rleites,ll was used between the reference electrode and the salt bridge (KC1) which contacted cysteine solutions (thermostated to 25 f 0.1’) through, a porous glass frit. I n all cases the supporting electrolyte was perchloric acid. Sulfuric acid was found to give poorer polarographic waves for cysteine and cystine. The main technique for gathering polarographic data was that of direct polarography of solutions during irradiation. A special thermostated cell containing the solution to be irradiated and analyzed, the dropping-mercury electrode, the salt bridge, and the standard cell was designed to fit inside the Gammacell irradiation chamber. With this cell it was possible to monitor during the irradiation the changes in concentration of cysteine, HzS, and cystine a t 0.15, -0.15, and -0.56 V; all voltages refer to the saturated calomel electrode. Solutions to be simultaneously irradiated and polarographed were first bubbled with Ar until all traces of polarographically detectable oxygen were removed. The solution was then polarographed a t a given constant voltage while outside the irradiation zone to establish a horizontal “base line” for the desired compound. Polarography continued as the lead drawer containing the sample and the polarographic cell were lowered into the irradiated zone. Polarographic calibration curves for cystine were found to be dependent upon the amount of cysteine present with the known amounts of cystine. The half-wave potentials of RSH, RSSR, and HzS are separated widely enough to monitor independently during the irradiation concentration changes of a single compound. However, since HzS and RSH waves are both anodic-oxidation waves,12 any decrease in RSH during radiolysis was in competition with an increase in HzS concentration. Thus the HzS buildup was monitored in a separate experiment when it was desired to obtain G(-RSH) and appropriate corrections were made on cysteine polarographic data. Independent measurements of the yield of destruction of cysteine were carried out using a modification of the technique described by B o y e P using measurements a t pH 1 rather than with an acetate buffer. These experiments were not as reliable as polarographic methods but, within the larger experimental error, gave qualitatively the same results as the polarographic measurements. Yields of cystine obtained from polarographic studies were not as precise as those available from directly following the optical density of the cystine at The Journal of Physical Chemistry

A. AL-THANNON, R. M. PETERSON, AND C. N. TRUMBORE 248 nm, where there is negligible absorbance from the cysteine and irradiation products other than cystine. I n addition to polarographic determination of H2S at lower cysteine concentrations, the yields of this irradiation product were determined colorimetrically based upon the formation of methylene blue from the careful oxidation of freshly prepared p-aminodimethylaniline in acidic s01ution.l~ Hydrogen peroxide yields were determined using titanous sulfate. l6 Hydrogen was analyzed gas chromatographically using a 13 X molecular-sieve column maintained a t 0” and using Ar as the carrier gas. Samples were injected into the chromatograph according to the technique of Swinnerton, et al.,1° except for the addition of a Drierite column to remove water from the stripped gases from the 3-ml irradiation sample and to allow continuous sweeping of the liquid with Ar. Attempts were made to develop a thin-layer chromatographic procedure employing radioisotope tracers which would separate cysteine from its radiation products. Even using glove-bag procedures and plate predevelopment to exclude oxygen, there was still oxidation of the cysteine to cystine during the chromatographic development period causing tailing. However, cystine and alanine could be qualitatively determined using l-butanol-acetic acid-water (3 : 1: 1 v/v/v) on MN-Polygram (Brinkmann) Si1 S-HR, 110-p layer on a plastic backing. I n experiments with added p-nitrosodimethylaniline, separate experiments were performed to ensure that the radiolysis product HzS did not react with p-nitrosodimethylaniline.

Results The primary kinetic products of the y radiolysis of air-free aqueous cysteine solutions found and measured in this study were Hz, HzS, HzOz,and RSSR, and from chromatography, RH. I n addition, yields for the disappearance of the cysteine thiol group, G( -RSH), were measured polarographically. These yields are reported in Table I along with those from other workers for comparison. I n all cases the yields reported from this work are based upon linear yield os. dose plots or, in a very few cases, upon initial-slope data where noticeable curvature in these plots developed at low doses and low cysteine concentration. The Hz and HzS yields are especially sensitive to RSH concentration at concentrations above 3 X M RSH. Yields from other workers are in most cases (11) L. Meites, “Polarographic Techniques,” 2nd ed, John Wiley and Sons, Inc., New York, N. Y.,1965,p 63. (12) I. M. Kolthoff and C. Barnum, J . Amer. Chem. SOC.,6 3 , 520 (1941); N. Matsuura, K.Muroshima, and M. Takizawa, Jap. Analyst, 13, 324 (1964). (13) P. D.Boyer, J. Amer. Chem. Soc., 7 6 , 4331 (1954). (14) M. 8. Budd and H. A. Bewick, Anal. Chem., 2 4 , 1536 (1952); L. Gustafsson, Talenla, 4 , 227 (1960). (15) A. C.Egerton, et al., Anal. Chim. Acta, 10, 422 (1954).

STUDIESIN

THE

AQUEOUS RADIATION CHEMISTRY OF CYSTEINE

2397 ~

~~~

Table I: Radiolytic Product Yields" in Air-Free Aqueous Cysteine Solutions, pH 1 (HC104)b

1 x 10-4 4 x 10-4 5 x 10-4

5.4

3.05 3.12

6.8

6X

1 x 10-8

7.0 f 0.5 (7.6 f 0.3) (6.7)' 7.0

2 x 10-8 2.5 X 10-8 4 x 10-8 5 x 10-8 1 x 10-2

2.9

0.8 0.9 0.95

3.15 3.22=t00.1 (3.1 f 0.1)

3.0

0.95 f 0 . 1 (0.75 =k 0.05)

3 . 0 f0 . 3 (3.1 f 0.2) 2.8 f 0.5'

0.68 (0.77 f 0.05)

0.95 3.0 3.27

(7.8 f 0.3) (7.0)'

2 x 10-2 3.5 x 10-2 4 x 10-2 5 x 10-2 6X 1 x 10-1 2 x 10-1 4 x 10-1

3.05 (3.35 i 0.1) 2.75

1.0 1.0 1.2 (0.78

0.05)

3.8, 3.0' (3.3, 4.2)

0.68

(0.87 f 0.05)

1.5 1.8

2.0 2.40 2.4 3.3

1.82 1.70 1.40

" All yields are calculated from initial slopes of dose us. yield plots which were normally linear. Values in parentheses are taken from ref 6 unless otherwise noted. Obtained polarographically; averages of several points except a t 10-8 M where the average of eight determinations is given. Average values of polarographic and colorimetric determinations given between 10-4 and 10-8 M RSH. Polarographic data. Obtained from N. Matsuura and K. Muroshima, Sci. Papers Coll. Gen. Educ., Univ. Tokyo, 14, 183 (1964); 0.8 N Hasod. ' Colorimetric data.

'

in agreement, within the combined experimental error, with those reported in the present work. In Table I1 are presented data from a more limited study of the hydrogen yields in air-free perchloric acid (pH 0.5) solutions of cysteine a t varying RSH concentrations. It may be noted that these yields are slightly higher than similar ones a t pH 1 but that the same basic trend in RSH concentration dependence is followed. Table I1 : Hydrogen Yields from Irradiated Air-Free Aqueous Cysteine Solutions at pH 0.5 (HClO4) Initial ooncn of RSH, M

1.0 x 10-4

5.0 x 1.0 x 5.0 x 1.0 x 5.0 x 1.0 x

10-4 10-8 lo-* 10-* 10-8 10-1

Q(H2)

3.10 3.30 3.40 3.57 3.40 3.10 2.60

In an experiment in which a 5 X M RSH solution was made 5 X M in p-nitrosodimethylaniline, the hydrogen yield was only slightly reduced from a normal yield of 3.1-3.0, whereas the hydrogen

sulfide yield dropped from a value of 0.95 to below the detectable limit of the analytical method employed. However, this sensitivity of G(HzS) to additives was and not found when solutions which were 5 X M in RSH, respectively, were each made M in glycine. No change in G(HzS) from that obtained in the absence of glycine was observed. In the thin layer chromatographic experiments, alanine was identified through its Rt value. No other chromatographically detectable products were observed either through ninhydrin tests or through radioisotopic-labeling techniques. Solutions of M RSH and M HzOzshowed no detectable reaction after standing for 3 hr, whether they were air saturated or Ar degassed.

Discussion The yields of products found in our work and those of Armstrong and coworkerss agree, within the combined errors of the experimental measurements. A satisfactory sulfur and material balance between G(-RSH) and the measured products is obtained and agrees well with the following mechanism, which is slightly different from those presented by earlier workers.ls (16) A. El Samahy, H. L. White, and C. N. Trumbore, J . Amer. Chem. Soc., 86, 3177 (1964); V. G . Wilkening, M. Lal, M. Arends, and D. A. Armstrong, Can. J . Chem., 45, 1209 (1967), and references therein. Volume 78, Number 7 July 1968

A. AL-THANNON, R. M. PETERSON, AND C. N. TRUMBORE

2398 HzO

--+

H . , .OH, eaq-, Hz, Hz02

eaq-

+ H+

---f

Ha

(1) (2)

+ RSH +Hz + RS. H . + RSH R . + HzS Re + RSH RH + RS. H . + RSH RH + HS. HS. + RSH HzS + RS. .OH + RSH HzO + RS. RS. + RS. +RSSR H.

---ic

4

4

(4) (5)

(6)

(7) (8)

(9) (10)

It will be noted that there are presented in this mechanism three different pathways for reaction of the hydrogen atom, He, with cysteine, RSH. Reaction 4 leads directly to the production of Hz. Both pathway a [reactions 5 and 61 and pathway b [reactions 7 and 81 lead to the same net over-all reaction products, namely, one molecule of H2S and one molecule of RH. I n this reaction mechanism the precursors to formation of Hz and HzSare both H atoms. I n the experiment with added p-nitrosodimethylaniline, known for its scavenging of OH radicals,” the H2 and H2S yields are affected in markedly different manners. If the p-nitrosodimethylaniline does not react with a precursor of the He and yet cuts down the HzS yield to very low values, it would tend to eliminate pathway a, since HzS is formed directly in step 5 . If pathway b is considered, the HS intermediate could react with p-nitrosodimethylaniline completely to eliminate the HzS yield and yet not affect the Hz yield. If this is so, it may also be concluded that the reaction rate of the H atom with RSH is competitive with that for reaction with the p-nitrosodimethylaniline molecule, which could easily add the H atom to the aromatic ring. From the above mechanism, the following sulfur balance may be derived: G(-RSH) = 2G(RSSR) G(H2S). An over-all theoretical mass balance may also be derived: G(-RSH) = GOH Ge,,CH G(H2S). I n addition G(HzS) must equal G(RH). Within the limits of the combined experimental errors involved in Table I, the data presented are consistent with these relationships a t RSH concentrations greater than 4 X M , if commonly accepted values for acid solutions are taken for GOH and Ge,,-.18 It is, therefore, probable that all of the major primary radiolysis products in the y radiolysis of acid solutions of cysteine have been accounted for. Since the pK for the ionization of the carboxyl group of the cysteine equals 1.8,7it was necessary to maintain a pH of 1 or lower in order to have essentially only one form of the cysteine present to react with

-

+

+

The Journal of Physical Chemistry

+

+

radiolytic intermediates. Since abundant evidence has been presented that the hydrated electron reacts with the neutral (zwitterion) form of c y ~ t e i n e , ~it ~ ~ J ~ was of interest to acquire evidence for the same reaction rate constant for the acid form present at pH 1 and below. The pulse-radiolysis method is presented with formidable problems in this region because of the very short lifetime of the hydrated electron in these strongly acid solutions. If the rate constant for reaction of RSH with eaq- is diffusion limited, there should be a competition for the hydrated electron represented by reactions 2 and 3, which should become important M RSH. Since the reaction product of eq above 3 is the same as one of the products from the series of reactions arising from eq 2, a more complex re1at)ionship than simple competition was anticipated as reflected in eq 11, which is derived on the basis of reactions 2-4, 7, and 8

GeEq-

[

1 &(RSH)][ kz(H+)

“1

+ 0.45

(11)

l+kP

GH represents the “residual” hydrogen atom yield, commonly reported to equal O.6.ls Ge,,- may be taken equal to 3.3, which is higher than commonly reported for neutral solutions18but gives a value which is sufficiently high enough to give the experimental hydrogen yields at lower cysteine concentrations. It is seen from Table I that the sum of G(H2) and G(HzS)is essentially a constant between and 2 X 10-2 M RSH and is equal to 4.3 a t pH 1. This is approximately equal to the sum of the reducing-radical yield (at higher solute concentration) for acid solutions plus the molecular hydrogen yield of 0.45.18 If at relatively low RSH concentration, the predominant reaction of the hydrated electron is with the hydrogen ion to form the hydrogen atom as in eq 2, the ratio ~ ~ ~ equal ~ ~ I ~ ~ ~ G(HzS)/[G(H2)measa- G ( H z ) ~ should k7/k4, the ratio of rate constants for reactions 7 and 4, assuming pathway b is operative rather than pathway a. If a value of 2.2 X 1Olo 1. mol-l sec-I is taken for iiz,20 the only unknown quantity in eq 11 is the value of kB,the electron-scavenging rate constant for the acid form of cysteine. Figure 1 shows the agreement (17) I. Kraljik and C. N. Trumbore, J . Amer. Chem. Soc., 87, 2547 (1965). (18) Proceedings of the Fifth International Conference on the Radiation Chemistry of Water, Notre Dame University, Notre Dame, Ind., Oct 1967,p 27. (19) R. Braams, Radiat. Res., 27, 319 (1966). (20) M. Anbar and P. Neta, J. Appl. Radwact. Ieotopes, 16, 227 (1966).

STUDIES IN

THE

2399

AQUEOUS RADIATION CHEMISTRY OF CYSTE~NE 4

3

GlHpS) 2

I 0 10-1

10-2

10-1

IO"

10-2

[ RSH1MOLAR

Figure 1. Comparison of experimental vs. theoretical (eq 11) radiolysis yields of hydrogen for acid solutions of cysteine as a function of cysteine concentration: 0,pH 1 (experimental results); --, pH 1 (predicted G(Ht), assuming G,,,- = 3.3, GH = 0.6, k7/k4 = 0.33,ks/kz = 1.36, GH? = 0.45); A, pH 0.5 (experimental results); - - -, pH 0.5 (predicted G(Ht), assuming same rate constants and yields as above, except that G,,,- = 3.4).

between the experimental and the calculated results based upon eq 11 when the value of k3 is assumed to be 3 X 10'0 1. mol-' sec-l. Only at higher RSH concentrations of lo-' M RSH and above are there deviations which are slightly outside the limit of experimental error. I n the same figure is shown the agreement between predicted and experimental values of G(Hz) for the data in Table I1 at pH Oa5. I n this calculation all values for yields and rate constants were the same as above, except that Geag- was taken to be 3.4 in order to account for the higher yields of hydrogen at low (RSH). Again good agreement is found over the more limited region of RSH concentration covered. I t would, therefore, appear that, if the assumptions made are correct, the rate constant for the scavenging of the hydrated electron by the acid form is higher by about a factor of 4 than that for the zwitterion. The positive charge of the amino group may be responsible for this increased effectiveness of trapping the negatively charged entity.21 However, it is interesting to note that the eventual product of this reaction is not ammonia, as is the case with amino acids which do not contain the -SH group,z2but instead is HzS. It would, therefore, appear that if the positive ion is neutralized a t the amine site, the neutralization product must live long enough to allow delocalization of the electron in the molecule. It is also possible that the positive charge only serves to accelerate the reaction rate but that the attack of the electron is still directly on the sulfur orbit a l ~ . ~ ~ Again in contrast with the nonsulfhydryl-containing amines, there appears to be no net abstraction of the hydrogen attached to the amino carbon, although this may be the result of secondary reactions. I n the mechanism proposed above, the sum of G(HzS) and G(H2) should equal a constant, namely, about 4.3. Therefore, it should be possible to calculate very simply from the predicted values of G(H2)those anticipated for G(H2S) and to compare them with the experimental ones. Such a comparison is shown in Figure 2. It is

fRSH1MOLAR Figure 2. Comparison of experimental G( Has) yields at pH 1 from irradiated cysteine solutions with those predicted from the proposed mechanism and eq 11: 0,experimental yields ; - - -, predicted from eq 11 using the same yields and rate constant ratios as in Figure 1 (pH 1).

seen that there is an obvious deviation from predicted values above 2 X lodz M RSH and that the deviation becomes greater the greater the RSH concentration. I n this concentration region a "scavenging of the spur" would be expected to play an increasingly important role, especially if the electron-scavenging rate constant is as high as 3 X 1010 1. mol-' sec-'. However, this would be internally inconsistent, since the hydrogen yields should be much lower than predicted in the same concentration region, and if anything they are slightly higher, as seen in Figure 1. At lo-' M RSH the deviation from the expected G(HzS)yield is a relatively high value of about G = 1. I t is entirely possible that a direct effect producing molecular hydrogen from RSH is becoming important, but the concentrations would appear to be rather low for such a phenomenon to occur except through a long-range energy-transfer mechanism. Another possibility is that the chain reaction producing HzS observed in studiese of oxygen-containing cysteine solutions may be important even though the oxygen M. concentration is estimated to be less than Unfortunately other HzS analysis methods tried during this study were not found to be as reliable as that one used in the low-concentration range where initial yields are measured. Thus no analytical cross-checks were possible on the HzS yields, but since blanks were used containing the same RSH concentrations, the only possible interference would come from irradiation products. I t is, therefore, thought that the large excess hydrogen sulfide yields reported are valid. Hydrogen peroxide yields found in this study are those normally anticipated for molecular H20zyields and again indicate the high eficiency of the cysteine in scavenging reactive intermediates. Acknowledgments. The authors wish to acknowledge stimulating discussions with Dr. D. A. Armstrong and to thank him for supplying prepublication data, A. A. T. wishes to acknowledge a fellowship from (21) R.Braams, Radiat. Rea., 31, 8 (1967). (22) B. M.Weeks, S. A. Cole, and W. M. Garrison, J . Phps. Chem., 69, 4131 (1965). (23) D.C.Wallace, J. E. Hesse, and F. K. Truby, J . Chem. Phys., 42, 3845 (1965).

Volume 72,Number 7 July 1968

P. L. LUISI AND P. PINO

2400 the Government of Iraq held during the tenure of this research. The authors also wish to acknowledge

helpful advice from and discussions with Drs. W. McCurdy, H. Bell, and I. Kraljid.

Conformational Properties of Optically Active Poly-a-olefins in Solution

by P. L. Luisi and P. Pino Istituto d i Chimica Organica Industriale dell' Universita d i Pisa, Centro Nazionale d i Chimica delle Macromolecole del C . N . R., Sezione I V , Italy Accepted and Transmitted by The Faraday Society

(November 3,1967)

The molar ratio of monomeric units spiraled in the right-handed (wJ and left-handed (us)screw sense has been related at each temperature to the molar rotatory power of isotactic poly( (S)-4-methyl-l-hexene) in solution. The parameters AE and AL', in terms of which and me are expressed by a statistical treatment previously reported, are hence evaluated by a best-fitting procedure. All the other conformational properties defined by AE and A U , such as the end-to-end distance, the number of inversions between the two screw senses, and the length of the regularly spiraled sequences in each screw sense, are calculated and compared with those of isotactic nonoptically active poly-a-olefins having an analogous structure.

Introduction The molar rotatory power of optically active vinyl polymers in solution has been interpreted by assuming that the main chain of the macromolecule consists of alternated left-handed and right-handed sequences, one of the two screw senses, on the average, being prevalent, depending upon the absolute configuration of the asymmetric carbon atom of the side groups and its distance from the main Birshtein and Luisi4 and, independently, Corradini, Allegra, and Ganis5 have expressed the conformational properties of these macromolecules in solution by a statistical treatment in which the conformation of the monomeric units and their mutual interactions are taken into account. The statistics developed by Birshtein and Luisi is in terms of the two parameters g = e

= e-AU/RT

-AE/RT

(1)

where 2AE = E,,, -

Es,a

2AU

=

Er,s

+

Ee,r

- (Ea,, + E,,,)

(2)

where E,,, and E,,, are the free energies of a pair of monomeric units when included in a left-handed and a right-handed sequence, respectively; E,,, and E,,, are free energies of a pair of monomeric units of which the former is, respectively, right-handed and left-handed spiraled and the latter is, respectively, left-handed and right-handed spiraled. The Journal of Physical Chemistry

Birshtein and Ptitsyn have given a rough estimation of AE on the basis on the relati~nship~~'

AE = RT In (n,/n,)

(3)

where ns and nr are the number of conformations allowed to the monomeric unit when included in a left-handed and in a right-handed sequence, respectively; the number of conformations can be determined on the basis of conformational analysis.' As far as AU is concerned, a value ranging between 600 and 1500 cal/mol can be estimated for some nonoptically active poly-a-olefins on the basis of the data obtained*for the energy a t the conformational reversals (inversions from one sense of spiralization t o the other one). In this paper, an independent evaluation of AE and AU is given, starting from the experimental molar rotatory power and its temperature coefficient and (1) P. Pino, F. Ciardelli, G. P. Lorenzi, and G. Montagnoli, Makromol. Chem., 61, 207 (1963). (2) P. Pino, Advan. Polym. SOC.,4,393 (1965); P. Pino, P. Salvadori, E. Chiellini, and P. L. Luisi, J . Pure A p p l . Chem., in press. (3) P. Pino and P. L. Luisi, J . Chim. Phys., 65, 130 (1968). (4) T. M. Birshtein and P. L. Luisi, Vysokomol. Soedin., 6, 1238 (1964). (5) G. Allegra, P. Corradini, and P. Ganis, Makromol. Chem., 90, 60 (1966). (6) T. M. Birshtein and 0. B. Ptitsyn, Conformations of Macromolecules," Interscience Publishers, New York, N. Y., 1966. (7) Such a procedure, which assumes that all the allowed conformations have the same energy and neglects the higher energy ones, although sufficient to give the order of magnitude of A E , is not sufficient for an approach to the problem in more quantitative terms, particularly when use should be made of relationships involving the dependence of AE on temperature.