Nov., 1954
`
`NATIVE DEXTRAN
`
`953
`
`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 elec-
`trode seems to be due to a displacement of the
`hydrogen adsorbed on the surface. The potential
`of the hydrogen electrode is governed by the con-
`centration of adsorbed hydrogen not by the pressure
`
`(2) The displace-
`of hydrogen above the solution.
`ment 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 finan-
`cial 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 LESTER H. 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 branch-
`This discrepancy is robably due to the
`Flory's viscosity theory did not satisfactorily explain the experimental data.
`ing.
`highly branched nature of the dextran molecules and the molecular inhomogeneity of the fractions. &in, a recent theo-
`retical 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 inten-
`sively than has been done in the past.' The struc-
`tures, 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 dex-
`trans and its fractions with their molecular weight
`and size.
`
`Experimental
`sample of native dextran produced by
`Fractionation.-A
`the so-called whole culture method with Leuconostoc mesen-
`teroides (NRRL B-512) was obtained from the Dextran
`Corporation. The dextran is produced by massive inocu-
`lation 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 pos-
`sible 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 investi-
`gated (the very low Kjeldahl, N I 0.12%' ruled out the
`possibility of a proteinic composition). The centrifuged
`solution was used for fractionation. It proved to be ex-
`tremely 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 . Am. Chem. SOC., 64,
`1969 (1942).
`(3) Performed in the laboratory of the Dextran Corporation.
`
`In Table I the precipitation conditions for
`subfractions.
`the 5 main fractions are given.
`TABLE I
`CONDITIONS OF THE FIVE MAIN FRACTIONS
`PRECIPITATION
`Yield, %
`Fraction Methanol (vol. %)
`Temp., O C .
`A
`20.0
`42.5
`36.6
`B
`42.5
`35.5
`15.6
`C
`42.5
`34.6
`13.4
`D
`42.6
`32.3
`24.3
`E
`20.8
`43.3
`5 . 0
`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 con-
`tained 0.028% N, 0.14% of reducing sugars in terms of glu-
`cose, and lost approximately 10% on dialysis through Vis-
`king 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
`measured in an Ubbelohde dilution viscosimeter at 32.7 .
`of aqueous solutions we;e
`In all cases 4 or 5 dilutions were made and qBp/c was ex-
`trapolated to c + 0. The intrinsic viscosities are given in
`Table IT.
`clarification of the poly-
`(C) Light Scattering.-Optical
`mer solutions proved to be difficult. The customary meth-
`ods 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 sedi-
`mentation 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). Com-
`paratively 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.
`
`Pharmacosmos, Exh. 1023, p. 1
`
`

`

`954
`
`LICRTER H. AROND AND H. PETER FRANK
`
`Vol. 58
`
`Fraction
`1
`2
`3
`4
`5
`6
`7
`8
`9
`10
`11
`12
`Total
`
`t
`
`A.
`2930
`2520
`2445
`1835
`1770
`1360
`1255
`1080
`850
`570
`
`6 .. ..
`..
`18 ..
`..
`. .
`. .
`35
`
`TABLE I1
`RESULTS OF FRACTIONATION, INTRINSIC VISCOSITY, LIGHT SCATTERING AND PERIODATE TITRATION
`
`(Kc/Ro)-a -
`[VI,
`1-6
`Yield,
`Adjusted
`(*/a,
`Mw X 10-9 B X 10s
`yield, '70
`%
`cm.3 g.-1
`X 100
`n o n 6
`1.7
`60
`9 . 0
`9 . 6
`198
`1.0
`11.8
`12.7
`180
`3.35
`30
`2 . 7
`10.5
`11.2
`170
`4 . 0
`25
`1 . 8
`10.0
`2 . 0
`4 . 4
`4 . 7
`140
`10
`7 . 9
`8 . 5
`143
`10.5
`9 . 5
`1 . 8
`6 . 8
`7.3
`130
`16.3
`6 . 1
`4 . 2
`3 . 3
`3 . 5
`115
`18.8
`5 . 3
`3 . 0
`4 . 7
`5.1
`118
`22.8
`4 . 4
`3 . 5
`17.5
`18.7
`105
`32.5
`3.05
`4 . 2
`..
`17.5
`18.7
`86
`79.0
`1.26
`..
`0 . 4
`318
`...
`3 . 0
`96.8
`100
`+2,4 (sediment, removed. by centrifugation)
`151
`7 . 0
`
`Parent polymer
`
`15
`
`1.5
`
`2720
`
`14.3
`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 concen-
`taken. Depolarization was determined at 90". The an-
`tration was negligible. Concentrations were followed
`gular dependence of scattered light was measured bet,ween
`Reciprocal intensity plots (kc/Re. vs. sin2 e/2 + kc) were
`gravimetrically as well as interferometrically (refractive in-
`20 and 135" with particular emphasis on the low angles.
`dex increment dn/dc = 0.151 a t 546 mp). A Phoenix B.S.
`photometer6 equipped with a cylindrical cell having 2 flat
`drawn.' Recently a correction factor for the angular de-
`facesa was used. The incident light was vertically polar-
`pendence has been proposed which is caused by the reflection
`ized; in all cases parallel readings a t 436 and 546 mp were
`of the incident beam.* This correction is immaterial for
`our solutions because the angular dependence has essen-
`0.4 I
`tially been measured in the forward scattering range (20-
`90'). Only in the case of fractions 9 and 10 which are of a
`tended to 135 . As a typical example, the plot for fraction
`comparativelyo small size has the angular range been ex-
`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
`precipita-
`tion 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.
`TABLE I11
`METHANOL PRECIPITATION
`
`I
`
`I
`
`0.3
`
`2 2 0.2
`2 a:
`
`Vol. %
`MeOH 40.20
`Wt. %
`Haze
`precip.
`point
`
`40.31 40.40 40.60 40.84 41.10
`30.2 46.0
`62.4 72.5 76.0
`
`0.1
`
`Fig. 1.-Reciprocal
`
`0.4
`
`0.6
`
`Sin* 8/2 + 1OOOc.
`0.2
`intensity plot for fraction 1: 0, 436 mp;
`e, 546 mp.
`(5) B. A. Briae, M. Halver and R. Speiaer, J . Opl. SOC. Am., 40, 768
`(1950)
`(6) L. P. Witnauer and H. J. Scherr. Rev. Sci. Insk., 23, 99 (1952).
`
`Results
`All experimental results are summarized in Ta-
`ble 11. A cumulative molecular weight distribu-
`tion function has been establisAed in the usual man-
`ner 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 inhomogene-
`ous 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.
`
`Pharmacosmos, Exh. 1023, p. 2
`
`

`

`Nov., 1954
`
`NATIVE DEXTRAN
`
`955
`
`100
`
`$ 75
`.z 50
`
`i
`
`0) Y
`
`25
`
`0
`7
`
`7.5
`
`8
`
`8.5
`
`log M .
`Fig, 2.-Cumulative molecular weight distribution of native
`dextran.
`widespread. Also included in Table I1 is the hypo-
`thetical 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 dif-
`ficulty of separating different species, ie., the ex-
`tremely small dependence of solubility on molecu-
`lar 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 ( f 15%).
`Results at the two wave lengths are in good agree-
`(This
`ment (&5%) and are therefore averaged.
`was also done with the virial coefficient B and the root
`To our
`mean square radius of gyration
`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 to the equation
`Kc/Ro = 1 / M w + 2Bc
`(1)
`The radii are obtained (for c + 0) according to the
`equation
`
`viously on branched dextran14 and slightly cross-
`linked 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 equiva-
`lent to stating that the number of branch points in-
`creases 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
`[?7l*h/M'/a = gK% + 2C',#.1 [I -
`( ~ / T ) I ( M / I v I ) K ~ / ~
`(3)
`one can plot [qI2/3/M1/s versus M / [ q ] . As the
`molecular weight approaches zero the number of
`branch units per molecule approaches zero and the
`factor g approaches unity. Hence
`
`oS/2
`
`Wales obtained K2/8 equal 1 X
`using (100
`
`~ m . ~ g.-l) as units of intrinsic viscosity.
`In 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/8 appears 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 dis-
`tribution is relatively wide, which is undoubtedly
`the case with our fractions, there will be a consider-
`able difference between the two averages. Using
`the lower viscosity average would increase the inter-
`cept and would give a better numerical agreement
`with Wales' results.
`sr
`I
`
`I
`
`I
`
`I
`
`'-3
`
`22
`
`P
`
`Y
`
`( 2 )
`16$R2/3XZM = (initial slope)
`As pointed out by Zimm13 the thus calculated
`radii represent a so-called 2-average.
`In 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 in-
`stance, with the values for polystyrene in butanone
`(ca. 1-2 x 10-4).
`The periodate oxidations show an increasing de-
`gree of branching with increasing molecular weight.
`The lowest fraction (10) is considerably more lin-
`ear than the higher fractions.
`Discussion
`Similar investigations have been carried out pre-
`(11) B. H. Zimm and C. D. Thurmond, J . Am. Chem. Soc., 14,1111
`(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. In order to compare our results
`with previous work, l4 it should be kept in mind
`that if the curve could be extended to a lower mo-
`lecular 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 ) J h
`(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 . Am. Chem. SOC., 73, 1904
`(1951).
`
`Pharmacosmos, Exh. 1023, p. 3
`
`

`

`956
`
`2.4
`
`7
`
`log a,.
`7.5
`
`Fig. 4.-Intrinsic viscosity versus moIecular weight: 0,
`fractions; 0, parent polymer.
`has derived a universal constant where L is the
`end-to-end distance for linear molecules. The ra-
`dius of gyration R can be substituted for L in this
`case
`
`9‘ = [?7] x M/(@)%
`(6)
`where 9’ = 6’12 X = 14.7 9. In this form the
`equation can also be tested for branched dextran
`-
`By substituting numerical values for
`molecules.
`R2 as determined by light scattering, the following
`results for 9‘ are obtained (Table IV).
`TABLE! IV
`VALUES FOR FRACTIONS AND PARENT POLYMER
`* x 10-2‘
`Fraotion
`Fraotion
`Q’ X 10-21
`21.5
`6
`31.5
`0
`7
`31
`1
`47
`8
`2
`33.5
`41
`29
`9
`52
`3
`4
`22
`10
`65
`5
`24.5
`The numerical value of 9 is given by Flory as
`2.1 X 1021 which corresponds to 9’ = 31 X 1021.
`From Table IV it can be seen that 9’ varies and dif-
`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 experi-
`mentally determined radii are z-averages. This
`means that for inhomogeneous fractions the R-
`values will be too large. Hence, 9‘ will be smaller
`than it would be if ideally sharp fractions were
`used. This is illustrated by the low 9’ for the un-
`fractionated
`(most
`inhomogeneous) sample 0.
`In a later section of this paper it will be shown that
`a rough estimate of the inhomogeneity of the frac-
`tions, as expressed by the ratio of the z-average to
`the weight average molecular weight, is of
`the
`order of 1.8. If this is taken into account, theX2#-
`values, as obtained from light scattering, can be
`reduced to a weight average @
`E = 1.8 X @
`Under these conditions, all 9’ values given in Ta-
`ble IV would have to be multiplied by a factor of
`1.8”2 = 2.4.
`It seems to us that the results of Table IV can be
`interpreted in two different ways.
`First, one could assume all the fractions to be
`comDarable with resnect to their molecular inhomo-
`In this case CP’ will not be a constant but
`geniity.
`a function of the molecular weight as it appears to
`
`VOl. 58
`
`8
`
`8.5
`
`LESTER H. AROND AND H. PETER FRANK
`1
`be in Table IV. However, this assumption is cer-
`tainly not true quantitatively.
`(The actual dif-
`ferences in the molecular weight distributions of
`the fractions would be extremely difficult to deter-
`mine experimentally.) A second approach would
`be to assume a greater numerical value for Flory’s
`9’ for this particular system and to ascribe all vari-
`ations of @’ for this particular system and to as-
`cribe all variations of 9’ to differences of molecular
`inhomogeneity. This explanation alone does not
`seem to be sufficient in view of the fact that whereas
`the molecular weights of the parent polymer and
`fractions 3 or 4 are comparable, the inhomogeneity
`obviously differs appreciably; however, CP’ is not
`affected very greatly. This fact suggests that any
`difference in the degree of homogeneity between
`the fractions (which is certainly less than that be-
`tween the parent polymer and any given fraction)
`is not likely to cause variations of 9’ such as have
`been observed.
`Very probably the variation of 9’ is caused by
`both effects, ie., by differences of molecular inho-
`mogeneity together with a real dependence of 9’
`on the molecular weight of those highly branched
`and extremely large molecules.
`Turning to E as a function of ATw, we find (Fig.
`5 ) that initially zi appe_ars to increase slightly
`more than linearly with M,,, but tends to level off
`with increasing degree of branching. This effect in
`a %on-ideal” solvent is in contrast with previous
`results of Zimm16 on branched polystyrene in buta-
`none which were explained in terms of the depend-
`ence of R on the virial coefficient. It seems that
`in our case water is a more nearly ideal solvent for
`dextran than butanone for polystyrene. Another
`important fact seems to be the very much stronger
`increase of the degree of branching with increasing
`molecular weight in our system.
`
`12
`
`11
`”.
`1%
`0
`4 10
`
`9 1
`7
`
`7.5
`
`8
`
`8.5
`
`log M,.
`square radius versus molecular weight;
`Fig. 5.-Mean
`0, fractions; 0 , parent polymer; Q, hypothetical linear
`fractions.
`It has to be emphasized again that the R-values
`in Fig. 5 are x-averages. The importance of this is
`illustrated by the single point representing the par-
`ent polymer; since the latter is less homogeneous
`than are the fractions. this Doint falls off the curve.
`From the preceding discksion it is quite evident
`that it would be very desirable to be able to esti-
`mate the inhomogeneity of the fractions. Very re-
`
`Pharmacosmos, Exh. 1023, p. 4
`
`

`

`Nov., 1954
`cently Benoit" developed a theory based on previ-
`ous considerations of Zimm which allows one to
`draw conclusions on polydispersity and branching
`from the angular dependence of the reciprocal in-
`tensity of scattered light (for zero concentration).
`The important magnitude is the ratio of the initial
`slope (SO) at low angles to the final asymptotic
`slope (sa) at large angles.
`It was shown that equation 7 holds for monodis-
`perse linear molecules
`SO/S,, = 2/3
`For polydisperse linear molecules
`- -
`S O / S ~ 2/3(Ma/Mw)
`For monodisperse branched molecules
`(9)
`SO/S, = 2/3(&/&2)
`R is the radius of gyration of the branched molecule
`and RO of 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
`(10)
`SO/S, = 2/3(a2/@,)(22/E~2) = 2/3C
`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
`TABLE V
`zoz x 10-0
`C
`...
`A
`Sample
`..
`& / a
`1.39
`5.5
`0.93
`0
`1
`50.5
`0.17
`0.30
`8 . 5
`.20
`.32
`2
`24.5
`.26
`.47
`8 . 5
`.50
`9
`21.5
`.28
`.33
`3
`7
`1.10
`5 . 6
`.73
`4
`.61
`1.12
`7
`.75
`5
`5.1
`.62
`1.00
`6
`1.50
`3 . 5
`I 2 . 2
`.83
`1.10
`1.65
`3
`7
`1 . 7
`.92
`8
`1.15
`1.25
`.94
`1.69
`2 . 5
`these figures C was calculated (column 4). Also
`given in Table V (column 3) is A = (kc/Re)/
`(kc/Ro) at which s m was taken. The numerical
`(17) H. Benoit, J . Polymer Scd., 11, 507 (1953).
`(18) B. H. Zimm and W. H. Stockmayer, J . Chem. Phys., 17, 1301
`' (1949).
`
`( 7 )
`
`( 8 )
`
`0
`
`NATIVE DEXTRAN
`
`957
`
`2.0
`
`1.5
`
`d 1.0
`
`0.5
`
`20
`
`25
`
`0
`
`5
`
`10
`15
`I/& x 109.
`Fig. 6.-C uersus reciprocal molecular weight.
`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 mo-
`lecular 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
`C = 1.8 = Zs/iVw
`Iim
`l / M + m
`As a rough approximation and being aware of its
`quantitative invalidity we shall now make the sim-
`plifying assumption that this figure represents the
`- -
`polydispersity of all our fractions. We thus get
`maximal numerical values for R2/Ro2 = g as given
`late a for hypothetical linear dextran molecules
`in column 5 of Table V. Knowing g, we can calcu-
`(column 6). These values are also plotted in Fig.
`between @ and aW seems to be fairly linear with a
`5 and on this double logarithmic plot the relation
`slope of 1.4.
`Acknowledgments.-We wish to thank the Dex-
`tran Corporation for sponsoring this work and for
`permission to publish it. We also wish to thank
`Drs. H. S. Paine and H. Mark for many helpful
`discussions and Dr. H. Benoit for making an un-
`published paper accessible to us and for discussing
`it with us. We also wish to acknowledge the help
`of Dr. L. Philip, who carried out the periodate
`oxidations.
`
`Pharmacosmos, Exh. 1023, p. 5
`
`