NATIVE DEXTRAN
Nov., 1954
size is probably the primary factor in the nitrile series in blocking the electrode surface. I n summary it can be said that: (1) The effect of the nitriles on the potential of the hydrogen electrode seems to be due to a displacement of the hydrogen adsorbed on the surface. The potential of the hydrogen electrode is governed by the concentration of adsorbed hydrogen not by the pressure
953
of hydrogen above the solution. (2) The displacement ability of the nitrile seems to be primarily a function of its size. We wish to take this opportunity to express our thanks to the Research Corporation for the financial assistance which they are furnishing for this project and to Mr. Samuel L. Cooke, Jr., for his aid in preparing this article for publication.
IMOLECULAR WEIGHT, MOLECULAR WEIGHT DISTRIBUTION AND MOLECULAR SIZE OF A NATIVE DEXTRAN BY LESTERH. AROND AND H. PETER FRANK Institute of Polymer Research, Polytechnic Institute of Brooklyn, Brooklyn, N. Y. Received December 18, 1063
Native dextran, as produced by a subculture of Leuconostoc mesenteroides NRRL B-512, was separated into a number of fractions. The fractions were characterized as to their molecular weight and size by means of light scattering and intrinsic viscosity in aqueous solutions, and their degree of branching, in terms of l-6/non 1-6 linkages, by periodate oxidations. The niolecular weights ranged from 12 to 600 million. The intrinsic viscosities were fairly low due to the high degree of branching. Flory's viscosity theory did not satisfactorily explain the experimental data. This discrepancy is robably due to the highly branched nature of the dextran molecules and the molecular inhomogeneity of the fractions. &in, a recent theoretical development by Benoit, the molecular inhomogeneity of the fractions and the deviation of their radii of gyration from the radius of a hypothetical linear molecule of the same molecular weight were estimated from the angular dependence of scattered light.
The polyglucose dextran can be produced by Leuconostoc mesenteroides using sucrose as starting material. We felt that it would be of interest to investigate the molecular weight and molecular weight distribution of this polymer more intensively than has been done in the past.' The structures, however, of several types of dextran have been the subject of previous study.2 Therefore, it also seemed worthwhile to attempt a correlation of the structure (degree of branching) of native dextrans and its fractions with their molecular weight and size.
Experimental Fractionation.-A sample of native dextran produced by the so-called whole culture method with Leuconostoc mesenteroides (NRRL B-512) was obtained from the Dextran Corporation. The dextran is produced by massive inoculation of a medium containing approximately 10% sucrose plus cornsteep liquor and mineral salts as nutrients. The population of Leuconostoc reaches a maximum of about 1 billion per milliliter. The culture is kept as sterile as possible in order to keep out other organisms a8 for instance molds. An approximately 1% solution (pH 7.6), which proved to be quite hazy, was used in the fractionation. The solution was centrifuged (approximately 20,000 X gravity) for 50, 90 and 145 minutes. A pellet-like sediment of 2.47, (based on total solids) was obtained, independent of the time of centrifugation. This sediment, apparently an insoluble carbohydrate polymer, was not further investigated (the very low Kjeldahl, N I0.12%' ruled out the possibility of a proteinic composition). The centrifuged solution was used for fractionation. It proved to be extremely difficult to fractionate dong conventional lines. Evidently the molecular weights are so large that there are only. very small differences in the solubility of the various species. However, it was possible to prepare five main fractions by carefully adding methanol and varying the temperature. These fractions were further divided into 10
-~
(1) F. R. Senti and N. N. Hellman, Report of Working Conference on Dextran, July, 1951. (2) I. Levi, W. L. Hawkins and H. Hibbert, J . A m . Chem. SOC.,64, 1969 (1942).
(3) Performed in the laboratory of the Dextran Corporation.
subfractions. I n Table I the precipitation conditions for the 5 main fractions are given.
TABLE I PRECIPITATION CONDITIONS OF THE FIVEMAIN FRACTIONS Fraction
A B C D E
Methanol (vol. %)
42.5 42.5 42.5 42.6 43.3
Temp., O C .
Yield, %
36.6 35.5 34.6 32.3 5.0
20.0 15.6 13.4 24.3 20.8
In addition to fractions A-E, fraction 11 was separated by concentrating the supernatant of fraction E and adding a very large excess of methanol. Fraction 12 was obtained by evaporation of the final supernatant. The latter two fractions seem to be of an irregular character: 11 is very small and shows an extremely large intrinsic viscosity (Table II)4; 12 seems to contain essentially low molecular weight contaminants. The original native dextran contained 0.028% N, 0.14% of reducing sugars in terms of glucose, and lost approximately 10% on dialysis through Visking cellulose casing. Some of the low molecular weight comtaminants were probably occluded in fractions 1-10. The actual yields of the fractions are given in Table I1 (second column). In the third column the weight fractions are adjusted for losses and for the neglect of the centrifuged sediment and of fractions 11 and 12. (B) Viscosity.-Viscosities of aqueous solutions we;e measured in an Ubbelohde dilution viscosimeter at 32.7 In all cases 4 or 5 dilutions were made and qBp/c was extrapolated to c + 0. The intrinsic viscosities are given in Table IT. (C) Light Scattering.-Optical clarification of the polymer solutions proved to be difficult. The customary methods of filtrat,ion and centrifugation both failed. (Filtration using Selas 04 and ultrafine lassinter resulted in clogging of the filters; centrifugation Sed to partial molecular sedimentation of the very large molecules in the comparatively high centrifugal field.) The following procedure was found to be satisfactory: clear water was prepared by distillation and consecutive double filtration (Selas 04 filter). Comparatively concentrated dextran solutions were used as master solutions and were filtered (medium glassinter) in small increments directly into the clear water. The dilu-
.
(4) The reason for thia irregularity ia unknown.
LICRTER H. ARONDAND H. PETER FRANK
954
Vol. 58
TABLE I1 RESULTSOF FRACTIONATION, INTRINSIC VISCOSITY, LIGHTSCATTERING AND PERIODATE TITRATION Yield,
%
Fraction
1 2 3 4 5 6 7 8 9
Adjusted yield, '70
[VI, cm.3 g.-1
(Kc/Ro)-a X 100
9.0 9.6 198 1.7 11.8 12.7 180 3.35 10.5 11.2 170 4.0 4.4 4.7 140 10.0 7.9 8.5 143 10.5 6.8 7.3 130 16.3 3.3 3.5 115 18.8 4.7 5.1 118 22.8 17.5 18.7 105 32.5 17.5 18.7 86 79.0 0.4 .. 318 ... 3.0 96.8 100 + 2 , 4 (sediment, removed. by centrifugation) 151 7.0
10
11 12 Total
-
60 30 25 10 9.5 6.1 5.3 4.4 3.05 1.26
B X
10s
1.0 2.7 1.8 2.0 1.8 4.2 3.0 3.5 4.2
..
A. 2930 2520 2445 1835 1770 1360 1255 1080 850 570
n o n 6
2720
15
6
..
.. .. 18 .. ..
.. .. 35
t
Parent polymer
14.3 1.5 15.5' Calculated by combination of the molecular weight of the fractions, neglecting 11 and 12. tions were ordinarily 50-100-fold; hence, the dust concentration was negligible. Concentrations were followed gravimetrically as well as interferometrically (refractive index increment dn/dc = 0.151 a t 546 mp). A Phoenix B.S. photometer6 equipped with a cylindrical cell having 2 flat facesa was used. The incident light was vertically polarized; in all cases parallel readings a t 436 and 546 mp were
0.4I
1-6
(*/a,
Mw X 10-9
I
I
taken. Depolarization was determined at 90". The angular dependence of scattered light was measured bet,ween 20 and 135" with particular emphasis on the low angles. Reciprocal intensity plots (kc/Re. vs. sin2 e / 2 kc) were drawn.' Recently a correction factor for the angular dependence has been proposed which is caused by the reflection of the incident beam.* This correction is immaterial for our solutions because the angular dependence has essentially been measured in the forward scattering range (2090'). Only in the case of fractions 9 and 10 which are of a comparativelyo small size has the angular range been extended to 135 As a typical example, the plot for fraction I is given in Fig. 1. The final results are tabulated in Table
+
.
11.
(D,) Periodate 0xidations.Q-Oxidations were made on fractions 1 , 5 and 10, and on the original sample. Fraction 1 was sufficiently pure due to repeated precipitations in the course of fractionation. Fractions 5 and 10 and the parent, polymer were purified by dialysis. The results are given in terms of 1-6/non 1-6 linkages in Table 11. (E) Cumulative Methanol Precipitation.-The precipitation was conducted at 32.7' in conically shaped tubes. Increments of water-diluted methanol were added to a known volume of solution by means of a microburet. Some of the results are given in Table 111.
0.3
2
2 a:
TABLE I11 METHANOL PRECIPITATION
0.2 Vol. % MeOH Wt. % precip.
2
0.1
0.2 0.4 0.6 Sin* 8/2 1OOOc. intensity plot for fraction 1: 0, 436 mp; e, 546 mp.
+
Fig. 1.-Reciprocal
(5) B. A. Briae, M. Halver and R. Speiaer, J . O p l . SOC.Am., 40, 768 (1950) (6) L. P. Witnauer and H. J. Scherr. Rev. Sci. Insk., 23, 99 (1952).
40.20 Haze point
40.31 40.40 40.60 40.84 41.10 30.2 46.0 62.4 72.5 76.0
Results All experimental results are summarized in Table 11. A cumulative molecular weight distribution function has been establisAed in the usual manner based on the yields and molecular weights of the different fractions (Fig. 2).'0 Because of the lack of sharpness of the fractions (resulting from the experimental difficulty of the fractionation), the distribution function must be considered rather crude. Qualitatively, however, it can be seen that native dextran is very inhomogeneous and, hence, that the distribution is extremely (7) B . H. Zimm, J . Chem. Phvs., 16, 1099 (1948). (8) H. Sheffer and J. C. Hyde. Can. J . Chem., 30, 817 (1952). (9) A. Jeanes and C. 0. Wilham, J . Am. Chem. Soc., 72, 2655 (1950). (10) As mentioned above, the sediment and fractions 11 and 12 were
not taken into account.
Nov., 1954
NATIVEDEXTRAN
100
$
75
.z
50
955
viously on branched dextran14 and slightly crosslinked p01ystyrene.l~ I n the first case the degree of branching in terms of 1-6/non 1-6 linkages was independent of molecular weight, which is equivalent t o stating that the number of branch points increases proportionally with the molecular weight. M. Wales14 has used the viscosity theory of P. Flory's in a modified form for branched dextran molecules. According to the equation
i
Y 0)
25
0 7
7.5
Fig, 2.-Cumulative
8
[?7l*h/M'/a= gK%
8.5
log M . molecular weight distribution of native dextran.
widespread. Also included in Table I1 is the hypothetical molecular weight of the original polymer as it results from the combination of the molecular weights of fractions 1-10. Agreement between the calculated and the experimental molecular weight is fairly good. The steepness of the cumulative precipitation (Table 111) illustrates again the difficulty of separating different species, ie., the extremely small dependence of solubility on molecular weight in the extremely high molecular weight range. The molecular weights are obtained using the customary double extrapolation of c+ 0 and sin20/z + 0 (Fig. 1). Those values, particularly those of the top fractions, are somewhat uncertain ( f15%). Results at the two wave lengths are in good agreement (&5%) and are therefore averaged. (This was also done with the virial coefficientB and the root mean square radius of gyration To our knowledge, the molecular weight of fraction 1 (600 million) is the highest that has been observed for any polymeric material. However, similarly high molecular weights have been reported lately for other carbohydrate polymers. 11,12 The virial coefficients B are calculated for sin20/z + 0 according t o the equation Kc/Ro = 1 / M w
+ 2Bc
(1)
+ 2C',#.1 [I -
(~/T)I(M/IvI)K oS/2 ~ / ~(3)
one can plot [qI2/3/M1/sversus M / [ q ] . As the molecular weight approaches zero the number of branch units per molecule approaches zero and the factor g approaches unity. Hence Wales obtained K2/8equal 1 X using (100 ~ mg.-l) . ~ as units of intrinsic viscosity. I n order to make our results comparable we employ the same units. I n our case (Fig. 3) the extrapolation is rather uncertain. However, the possible range of Ka/8appears to be 5-7 x 10-3. It is important to note that Wales used viscosity average molecular weights, whereas in this study the molecular weights are weight averages. If the molecular weight distribution is relatively wide, which is undoubtedly the case with our fractions, there will be a considerable difference between the two averages. Using the lower viscosity average would increase the intercept and would give a better numerical agreement with Wales' results.
sr
I
I
I
I
'-3 22 P
Y
The radii are obtained (for c + 0) according to the equation 16$R2/3XZM = (initial slope)
(2)
As pointed out by Zimm13 the thus calculated radii represent a so-called 2-average. I n view of the relative inhomogeneity of the fractions, the latter is appreciably higher than the corresponding weight average. The virial coefficients are all relatively small (of the order of 1-5 X 10-5) in comparison, for instance, with the values for polystyrene in butanone (ca. 1-2 x 10-4). The periodate oxidations show an increasing degree of branching with increasing molecular weight. The lowest fraction (10) is considerably more linear than the higher fractions. Discussion Similar investigations have been carried out pre(11) B. H. Zimm and C. D. Thurmond, J . A m . Chem. Soc., 1 4 , 1 1 1 1 (1952). (12) L. P. Witnauer and F. R. Senti, J . Chem. Phya., 20, 1978 (1952). (13) P.Outer, C.I. Carr and B. H. Zimm, ibid., 18, 830 (1950).
Fig. 3.-Flory-Schaefgen
plot: 0 , fractions; 0, parent polymer.
Plotting intrinsic viscosity vs. molecular weight on the customary double logarithmic plot (Fig. 4) gives a curved line with an initial slope of 0.29 and a final one of 0.13. I n order to compare our results with previous work, l 4 it should be kept in mind that if the curve could be extended to a lower molecular weight range, a considerably steeper slope would most probably be obtained. The decreasing slope (at higher molecular weights) is evidently caused by the increase in the degree of branching which, in turn, decreases the effective volume of the molecules. From the basic assumption [q] a (R")"z/M Flory16 = [VI
x
M/(G)Jh
(5)
(14) M. Wales, P. A. Marshall and 9. G. Weissberg, J . Polymer Sci., 10, 229 (1953). (15) C . D. Thurmond and B. H. Zirnm, {bid., 8, 477 (1952). (18) P. J. Flory and T. G. Fox, Jr., J . A m . Chem. SOC.,73, 1904 (1951).
LESTERH. ARONDAND H. PETERFRANK
956 2.4
VOl. 58
be in Table IV. However, this assumption is certainly not true quantitatively. (The actual differences in the molecular weight distributions of the fractions would be extremely difficult to determine experimentally.) A second approach would be to assume a greater numerical value for Flory’s 9’ for this particular system and to ascribe all variations of @’ for this particular system and t o ascribe all variations of 9’ t o differences of molecular inhomogeneity. This explanation alone does not seem to be sufficient in view of the fact that whereas 7 7.5 8 8.5 the molecular weights of the parent polymer and log fractions 3 or 4 are comparable, the inhomogeneity Fig. 4.-Intrinsic viscosity versus moIecular weight: 0 , obviously differs appreciably; however, CP’ is not fractions; 0, parent polymer. affected very greatly. This fact suggests that any has derived a universal constant where L is the difference in the degree of homogeneity between end-to-end distance for linear molecules. The ra- the fractions (which is certainly less than that bedius of gyration R can be substituted for L in this tween the parent polymer and any given fraction) is not likely to cause variations of 9’such as have case been observed. 9‘ = [?7] x M / ( @ ) % (6) Very probably the variation of 9’ is caused by where 9’ = 6’12 X = 14.7 9. In this form the both effects, ie., by differences of molecular inhoequation can also be tested for branched dextran mogeneity together with a real dependence of 9’ By substituting numerical values for on the molecular weight of those highly branched molecules. R2 as determined by light scattering, the following and extremely large molecules. results for 9‘ are obtained (Table IV). Turning t o E as a function of ATw,we find (Fig. 5 ) that initially appe_ars to increase slightly TABLE! IV more than linearly with M,,, but tends t o level off VALUES FOR FRACTIONS AND PARENT POLYMER with increasing degree of branching. This effect in Fraotion Q’ X 10-21 Fraotion * x 10-2‘ a %on-ideal” solvent is in contrast with previous 0 21.5 6 31.5 results of Zimm16 on branched polystyrene in buta1 47 7 31 none which were explained in terms of the depend2 33.5 8 41 ence of R on the virial coefficient. It seems that 3 29 9 52 in our case water is a more nearly ideal solvent for 4 22 10 65 dextran than butanone for polystyrene. Another 5 24.5 important fact seems to be the very much stronger The numerical value of 9 is given by Flory as increase of the degree of branching with increasing 2.1 X 1021which corresponds t o 9’ = 31 X 1021. molecular weight in our system. From Table IV it can be seen that 9’varies and dif12 fers from the value given by Flory, especially in the case of the extreme fractions. All numerical values of Table IV are affected by the fact that the experimentally determined radii are z-averages. This 11 means that for inhomogeneous fractions the Rvalues will be too large. Hence, 9‘ will be smaller ”. than it would be if ideally sharp fractions were 1% 0 used. This is illustrated by the low 9’for the unfractionated (most inhomogeneous) sample 0. 10 In a later section of this paper it will be shown that a rough estimate of the inhomogeneity of the fractions, as expressed by the ratio of the z-average t o the weight average molecular weight, is of the 91 order of 1.8. If this is taken into account, theX2#7 7.5 8 8.5 values, as obtained from light scattering, can be log M,. reduced to a weight average @ Fig. 5.-Mean square radius versus molecular weight; 0 , fractions; 0 , parent polymer; Q, hypothetical linear E = 1.8 X @ fractions. Under these conditions, all 9’ values given in Table IV would have t o be multiplied by a factor of It has to be emphasized again that the R-values 1.8”2 = 2.4. in Fig. 5 are x-averages. The importance of this is It seems to us that the results of Table IV can be illustrated by the single point representing the parinterpreted in two different ways. ent polymer; since the latter is less homogeneous First, one could assume all the fractions t o be than are the fractions. this Doint falls off the curve. comDarable with resnect to their molecular inhomoFrom the preceding discksion it is quite evident geniity. In this case CP’ will not be a constant but that it would be very desirable to be able to estia function of the molecular weight as it appears to mate the inhomogeneity of the fractions. Very re-
1
a,.
zi
4
NATIVE DEXTRAN
Nov., 1954
cently Benoit" developed a theory based on previous considerations of Zimm which allows one t o draw conclusions on polydispersity and branching from the angular dependence of the reciprocal intensity of scattered light (for zero concentration). The important magnitude is the ratio of the initial slope (SO) a t low angles t o the final asymptotic slope (sa) a t large angles. It was shown that equation 7 holds for monodisperse linear molecules SO/S,,
(7)
= 2/3
For polydisperse linear molecules
- -
SO/S~
(8)
2/3(Ma/Mw)
For monodisperse branched molecules SO/S,
= 2/3(&/&2)
(9)
R is the radius of gyration of the branched molecule
and ROof a linear molecule with the same molecular weight. R2/Eo2= g in the notation of Stockmayer and Zimm.18 For polydisperse branched molecules, we have SO/S,
= 2/3(a2/@,)(22/E~2) = 2/3C
(10)
We have calculated S O / S ~ for all our samples wherever this was possible (0, 1-8). The results a t the two wave lengths agreed fairly well and were averaged (see second column of Table V). From
957
2.0 1.5
d 1.0 0.5
10 15 20 I/& x 109. Fig. 6.-C uersus reciprocal molecular weight.
0
5
25
value of A is also averagecfor the two wave lengths. If C is plotted versus l/Mw (Fig. 6) it can be seen that for decreasing molecular weights a limit of approximately 1.8 is approached. In this low molecular weight range the fractions of native dextran become increasingly linear (see Table 11) so that for the limit 1/M -t 00 with a certain approximation any deviations from SO/Sm =-2/a-can be attributed to the polydispersity factor fiIz/Mw Iim C = 1.8 = Zs/iVw l/M+
m
As a rough approximation and being aware of its quantitative invalidity we shall now make the simplifying assumption that this figure represents the polydispersity of all our fractions. get TABLE V - - =Weg thus R2/Ro2 as given maximal numerical values for Sample &/a A C 0 zoz x 10-0 in column 5 of Table V. Knowing g, we can calcu0 0.93 5.5 1.39 .. ... 1 .20 8.5 0.30 0.17 50.5 late for hypothetical linear dextran molecules 2 .32 .26 24.5 8.5 .47 (column 6). These values are also plotted in Fig. 9 .50 3 .33 .28 21.5 5 and on this double logarithmic plot the relation 7 1.10 .61 5.6 4 .73 seems to be fairly linear with a between @ and 5 .75 7 1.12 .62 5.1 slope of 1.4. 6 1.00 3.5 1.50 .83 2.2 Acknowledgments.-We wish to thank the Dex7 1.10 3 1.65 .92 1.7 tran Corporation for sponsoring this work and for 8 1.15 .94 1.25 2.5 1.69 permission to publish it. We also wish to thank these figures C was calculated (column 4). Also Drs. H. S. Paine and H. Mark for many helpful given in Table V (column 3) is A = (kc/Re)/ discussions and Dr. H. Benoit for making an un(kc/Ro) at which s m was taken. The numerical published paper accessible to us and for discussing it with us. We also wish to acknowledge the help (17) H. Benoit, J . Polymer Scd., 11, 507 (1953). of Dr. L. Philip, who carried out the periodate (18) B. H. Zimm and W.H.Stockmayer, J . Chem. Phys., 17, 1301 oxidations. ' (1949).
a
aW
I
