The Molecular Weights of Cellulose and Cellulose Derivates - The

THE MOLECULAR WEIGHTS OF CELLULOSE AND CELLULOSE DERIVATIVES‘ ELMER 0. KRAEMER

AND

WILLIAM D. LANSING

The Experiinental Station of E . I . duPont de Nemours & Co., Inc., Wilmington, Delaware Received June 1.4, 1934 INTRODUCTION

The nature of the solutions of the lyophilic colloids has long been a favorite subject for investigation by colloid chemists. Evidence has gradually accumulated from many sources to show that the well-known typical lyophilic colloids such as the proteins, rubber, gutta percha, starch, cellulose, and other polysaccharides and their derivatives, are polymeric materials of high molecular weight (45). I n recent years a large number of synthetic high polymers possessing also the properties of lyophilic colloids have been prepared and carefully studied, particularly in the laboratories of Staudinger (55) and of Carothers (9). Many of the high polymers, both synt,hetic and natural, are now recognized to be “linear polymers;” Le., the molecule is a single chain of recurring structural units bound together by primary valences. When, as is sometimes the case, the number of recurring groups in a molecule attains the magnitude of hundreds, it is indeed a giant or “macro” molecule. I n many cases there is good reason to believe that these macromolecular substances are dispersed in solution to the individual molecule, and to a considerable degree the physical and colloidal properties of the solutions appear to be determined by the size and shape of the molecule. A substantial part of our understanding of the lyophilic colloids has come out of the study of the synthetic high polymers, which constitute excellent models for their better-known, naturally occurring prototypes. A problem of fundamental importance in the interpretation of the behavior of macromolecular materials is the determination of their molecular weights. Numerous efforts have been made to employ the various colligative properties of solutions in accordance with classical methods for de1 Presented before the Eleventh Colloid Symposium, held a t Madison, Wisconsin, June 14-16, 1934. Communication No. 144 from the Experimental Station. Second paper in the series on The Molecular Weight of Linear Macromolecules by Ultracentrifugal Analysis. The first paper appeared in J. Am. Chem. SOC.66, 4319 (1933).

153 THE JOURNAL OF PHYSICAL CHEMISTRY, VOL. 39, NO. 2

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ELMER 0. KRAEMER AND WILLIAM D. LANSING

termining molecular weights, but the results have frequently been uncertain or inconclusive. Whenever the molecular weight exceeds a few thousand, the change in freezing point, boiling point, or vapor pressure is too small to be measurable with sufEicient precision a t the low concentrations necessary for satisfactory molecular weight determinations. Many of the values in the literature obtained by these methods for the naturally occurring high polymers and their derivatives are undoubtedly erroneous for one reason or another. A number of investigators have made limited use of osmotic pressure measurements, but the most comprehensive and conclusive work hitherto carried out on the problem is without question that of Svedberg and his associates for the proteins, using the Svedberg ultracentrifuge (58). Although these investigations have demonstrated the superiority of the ultracentrifuge over other methods, relatively little application of the method has yet been made to high polymers other than the proteins, partly because there are only two laboratories possessing the necessary equipment. The sum total of data obtained by other methods for proteins as well as other macromolecular substances is relatively meager, and the individual items are difficult to assess. I n spite of this fact, it has become clear that protein solutions, a t least for the cases that have been carefully studied, differ from most other macromolecular solutions in that the dissolved protein molecule is approximately spherical in form, whereas for other high polymers the solute unit is highly elongated. The difference is particularly strikingly manifested by the marked difference in viscosity characteristics, dilute protein solutions commonly having viscosities relatively independent of the molecular weight and in approximate agreement with Einstein’s equation for spherical particles. On the other hand, the viscosities of most other macromolecular materials are very sensitive to molecular weight differences and are much greater than would be the case for spherical molecules (33). The theory for the influence of highly elongated, perhaps flexible, molecules upon the free energy of a solvent has not yet been worked out, and it is therefore not known how far conventional methods for estimating molecular weights are applicable to polymers of the high-viscosity type. Having recently shown, however, that for one such case the molecular weight can be correctly determined with the ultracentrifuge (34), and taking into account the experimental efficacy of the instrument, we believe that it provides the most reliable and most effective method now known for estimating the molecular weights, in solution, of linear macromolecules of all kinds. We have accordingly selected this method of study for what we hope will eventually be a comprehensive investigation of cellulose and its derivatives. Cellulose and its derivatives represent, next to the proteins, the most thoroughly studied class of high polymers and typify the high-viscosity

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MOLECULAR WEIGHTS OF CELLULOSE AND ITS DERIVATIVES

group. For theoretical investigations concerning the nature of lyophilic colloids and their solutions, cellulose and its derivatives are particularly valuable. As will be seen, in certain cases they permit chemical conversions with little if any change in the length of the molecule. They offer several chemically related series of derivatives of considerable chemical stability for comparative studies. Many of them are soluble in a wide variety of solvents and permit avoidance of the ionic complications so characteristic of protein solutions. The molecular weight may be varied a t will over very wide limits without a detectable change in chemical composition. Finally, x-ray crystal analysis has provided an unusual amount of valuable correlative information concerning the solid forms of cellulose and its derivatives. It is now very generally agreed that the cellulose molecule is a long chain of anhydroglucose residues linked together by 1,4 glucosidic oxygen (reference 45, p. 91), in accordance with the following scheme: H

CH20H

OH

C W H

H

H

OH

CH$H

OH

CH-OH

H

OH

On each glucose residue in the chain there are three hydroxyl groups which react with suitable reagents to give the various cellulose derivatives. Presumably, on one end of the chain the terminal glucose residue possesses four alcoholic hydroxyl groups, and a t the opposite end there is a hemiacetal group. The length of the chain may vary within wide limits, probably being very long in native cellulose and passing through all intermediate lengths, as depolymerization occurs by breaking the oxygen links, until the final product is glucose. Whether the chains of native cellulose are uniform in length is not known, but in all probability, the length (or molecular weight) of degraded celluloses and derivatives is never uniform. This is a general characteristic of high polymers. Usually, therefore, when reference is made to chain length or molecular weight, an average value is meant. When comparing various celluloses and derivatives with respect to their molecular lengths, it is useful to specify the “degree of polymerization” (D.P.), by which is meant the number of glucose residues per niolecule. For many years, industrial chemists interested in products manufactured from cellulose have assumed in a rather vague way that molecular “degradation” (without specification as to its chemical nature) of cellulose and its derivatives leads to reduction of the relative viscosity of their solutions (4,48). As will be discussed in more detail below, it now appears that the viscosity characteristics of dilute solutions in good solvents are primarily determined by the degree of polymerization.

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PREVIOUS INVESTIGATIONS O F THE MOLECULAR WEIGHT OF CELLULOSE AND

CELLULOSE DERIVATIVES

Every method for the estimation of the molecular weight of macromolecules that we are aware of has been applied to cellulose and its derivatives. In a number of investigations, particularly the earlier ones in which freezing point or boiling point methods were usually used, values were obtained ranging from a few hundred to a few thousand (3, 5, 8, 29, 32, 46). I n many cases later work failed to confirm these results, and in the light of present knowledge, it may be assumed either that the experimental technic was faulty (2, 17, 22, 44;55, p. 453), or that the cellulosic materials were far more degraded than was suspected. Calculations of molecular weights by means of Einstein’s equation for the diffusion coefficient of spherical molecules (24, 61) are now realized to be invalid, because the diffusion of cellulose and cellulose derivatives does not obey Fick’s law and the solute particles are non-spherical (27, 38). On the basis of the breadth of the lines in the x-ray diffraction pattern, Mark (reference 42, pp. 163, 197) has inferred that the length of the crystallite in native ramie cellulose is about 600 A.U. Assuming that the length of the cellulose molecule is not longer than the length of the crystallite, and taking into account data from other sources, he has concluded that the molecule probably contains one hundred and fifty to two hundred glucose residues. Although this is a n interesting speculation, it is admittedly not the only possible interpretation of the x-ray observations. The most significant results hitherto made public have been obtained by means of osmotic pressure measurements, ultracentrifugal analysis, endgroup determinations, and viscosity measurements. Even with these methods, there are gross discrepancies in the results, and there is not, as yet, general agreement as to which results are correct. The principal data are summarized in tables 1, 2, and 3. I n addition to molecular weights, the tables summarize the available data concerning the viscosity characteristics, in order to reveal to what extent a quantitative relationship exists between molecular weight and viscosity. Since the viscosity characteristics were not expressed by the various investigators in a uniform manner, the data were reduced to a common basis for comparative purposes by calculating defined by the expression2 C+O

2 For more detailed discussion of the advantages of comparing viscosities in infinitely dilute solutions, see references 36, 45 (p. 175), and 55 (p. 56).


157

where q r is the viscosity of the solution relative to that of the solvent, and c is the concentration in grams per 100 cc. of solution. Extrapolation to zero concentration was made by means of Fikentscher’s equation (14, 37). As Staudinger has shown, [SI is directly proportional to the molecular weight for linear molecules of considerable length.3

Osmotic pressure results Examinationof table 1 shows that with a single exception the molec-

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ular weights of the cellulose ethers and esters as determined by the osmotic pressure method fall in the range 15,000 to 204,000, with most of the values falling between 25,000 and 100,000. I n most cases the materials were commercial products or fractions thereof. The outstanding discrepancy is provided by the results of Hess and Ulmann (31) for Hess’s crystalline cellulose triacetate I1 (“biosan acetate”) by a modification of the method of Frazer and Patrick (15), in which the vapor phase serves as membrane. Inasmuch, however, as the authors report several quite unusual effects, such as a greater vapor pressure for a solution than for the solvent (60) and a remarkable reversible depolymerization of the triacetate, for which there are a t present no generally accepted interpretations, the results cannot for the time being be considered as conclusive. I n addition, Hess’s crystalline triacetate does not display the properties characteristic of high polymers (e.g., large value of [VI, swelling behavior, and film-forming capacity) and is undoubtedly a relatively low molecular weight degradation product corresponding to a cellodextrin acetate (2, 16, 17, 19, 23, 44; 55, p. 460). An important fact brought out by the osmotic pressure investigations is the non-uniformity of the cellulose derivatives with respect to molecular weight. The fractionation studies of Duclaux and Wollman (13) and of Medvedev (43) for cellulose nitrate, of Herzog and Deripasko (25) and of 3 I n view of the increasing recognition of the value of characterizing the viscosity of solutions of macromolecular materials by the quantity [q], there would be considerable advantage if investigators in this field could agree upon a suitable name for t h e quantity. I n analogy t o specific conductivity, specific volume, specific refraction, specific rotation, and the like, “specific viscosity” would serve very well, Unfortunately, the expression is already in use with two different meanings. It has long been used by Duclaux (10, 12) in referring to the constant k in Arrhenius’s logarithmic equation (log q,. = k c ) . Berl (4) refers to IC as the “specific viscosity constant.” If natural logarithms are used, k = [ q ] for infinitely dilute solutions. Staudinger later adopted the term, “specific viscosity,” for the quantity q r - 1, but proposed no name for the more useful quantity, [q]. I n passing, i t may be pointed out that Staudinger’s expression q s p / c is equal t o our quantity [ q ] multiplied by one-tenth the weight of the structural unit of the particular linear polymer to which it refers, e.g., qsp/c = 162[q1/10 for cellulose, the difference being due to the fact t h a t Staudinger’s concentrations are expressed in molarity with respect to the structural unit.

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Herzog and Herz (26) for cellulose acetate, and of Okamura (47) for ethylcellulose (see table 1) all agree in showing that the original materials contained a mixture of molecules of different weight. Numerous investigators have in other ways also demonstrated the heterogeneity of cellulosic products (39, 40, 49, 50). The accuracy of the results, so far as revealed by internal evidence, varies somewhat for the different investigations. In most cases the ratio of pressure to concentration increases with concentration, Le., the molecular weight apparently decreases with increasing concentration, and there is some question concerning the correctness of the extrapolation to zero concentration, particularly when the concentrations used were 1 per cent or more (6, 7, 20, 21). I n other cases, where an effort was made to use low concentrations (25, 26), there was considerable irregularity in the resulting molecular weights. Notwithstanding, the values obtained are perhaps of the right order of magnitude.

Ultracentrifugal analysis The data obtained from osmotic pressure measurements all refer to cellulose derivatives and leave the question of the molecular weight of cellulose itself entirely open. The only effective solvent for cellulose with a limited degrading action is Schweitzer’s reagent, commonly referred to as cuprammonium solvent, but its complexity precludes its usefulness for osmotic pressure measurements. The molecular weight of cellulose dissolved in cuprammonium solvent has however been investigated by means of the ultracentrifuge by Stamm (54) and by ourselves (35). With respect to sedimentation equilibrium, the ultracentrifuge method is in basic theory similar to the osmotic pressure method as mentioned above. An important advantage, however, of the ultracentrifugal method is the fact that it yields information concerning the homogeneity of the sample being studied. By the sedimentation equilibrium method, as recorded in table 2, Stamm found the molecular weight of the cellulose-copper complex formed in cuprammonium ~ o l v e n t ,and ~ calculated cellulose molecular weights therefrom, on the assumption of one atom of copper per glucose residue. For a cotton-linters alpha-cellulose he obtained an average value of 56,000 for the copper complex or 40,000 on a copper-free basis, with no evidence for appreciable non-uniformity. Approximately the same value was obtained by the sedimentation velocity method. Wood celluloses of various sources were, on the other hand, found to be non-uniform, containing more or less relatively low molecular weight material in addition to various 4 Strictly speaking, Stamm’s method of calculating his results does not yield an exact value of the molecular weight of the cellulose-copper complex because of the difference between the specific volumes of the cellulose-copper complex and of cellulose.

160


amounts of the constituent characteristic of cotton cellulose and a second constituent with a molecular weight of about 20,000 on a copper-free basis. As reported last year (35), we were unable to confirm Stamm’s results and obtained a much larger value for the same cotton cellulose: 300,000 for the cellulose-copper complex or about 220,000 on a copper-free basis, as calculated by Stamm’s method. Even degraded and regenerated celluloses gave values of 100,000 and greater. Although it is not certain, we believe that degradation inadvertently occurred during Stamm’s measurements and, perhaps, that sedimentation equilibrium was not attained. On the basis of our investigation of a synthetic high polymer of known molecular weight, the results obtained by the sedimentation velocity method are of doubtful reliability as absolute values (34). End-group determinations

Molecular weights by osmotic pressure and ultracentrifuge methods depend upon the state of dispersion of the solute in a solvent and are affected by association and solvation, with the consequence that the values so obtained may not correspond to the true molecular weight in the ordinary sense of the term. I n contrast, the end-group method is independent of the laws of solutions, but depends upon knowledge concerning the chemical structure of the substance being studied. I n principle, it is simply necessary to determine by suitable analytical means the proportion of glucose residues showing some chemical property characteristic of a terminal residue, from which the average number of glucose residues per molecule may be estimated. Two types of end-group determination may be used for cellulose or derivatives : one depending upon the terminal hemiacetal group, the other depending upon the terminal tetrahydroxyglucose residue. The so-called copper number measures the reducing power of cellulose and presumably is due, a t least in part, to the hemiacetal groups. The determination, unfortunately, is very sensitive to the conditions of experimentation, and the calculated molecular weights can scarcely be considered reliable (42, p. 192; 55, p. 491). Bergmann and Machemer (2) developed an iodometric method for determining the hemiacetal content of cellodextrin acetates and used it in estimating molecular weights (see data of table 3). Unfortunately, the authors give no viscosity or other independent data indicative of the state of degradation of the products. I n the discussion a t the symposium of the Faraday Society, Machemer (41) reported that the iodometric method and the Haworth and Machemer method, involving the nonreducing end group, gave concordant results for cellodextrins with molecular weights in the range of 3000, but admitted that end-group determinations are not satisfactory for high-viscosity cellulosic products. Staudinger (reference 55, pp. 463, 491) was not able to obtain consistent results with this method for celluloses in any case, and only for highly


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degraded triacetates with molecular weights not exceeding about 10,000 were the results apparently satisfactory. Hess also has found this method to give erratic results (30). On the basis of considerable experience with the method, Mark considers his results, given in table 3, to be of questionable reliability as absolute values (reference 42, p. 196). Haworth and Machemer (23) have employed the terminal tetrahydroxyglucose residue for molecular weight determinations. Cellulose acetate was converted to a completely methylated cellulose which was then COMpletely hydrolyzed and the yield of tetramethylglucose determined. From this value the molecular weight of the methylcellulose may be calculated to be about 35,000. Unfortunately, the method does not appear to be applicable to cellulose acetates in general, or to other derivatives. Although, strictly speaking, an end-group determination in the above sense is apparently not involved, Schmidt and coworkers (51) have applied analogous principles to the calculation of molecular weight from their determinations of the acidity (Le., free carboxyl groups) of various celluloses. Schwarzkopf and Weiss (52), however, deny the suitability of the analytical method, which involved conductometric titration of a heterogeneous system. Regardless of the accuracy of the acidity determination, it is highly improbable that the molecular weights of the different types of celluloses studied by Schmidt et a1 are really equal, as they infer. Considering all the end-group determinations, it must be admitted that the results so far obtained are rather meager. The reactions involved are complicated and of limited applicability and the accuracy in the best of cases is not sufficient for the high molecular weights possessed by the technically important materials.

Viscosity method of Staudinger Although, as pointed out above, it had been generally believed for a good many years that the viscosity of solutions of cellulose derivatives depends upon the molecular weight, no general quantitative relations were formulated until Staudinger discovered that [9] for linear polymers of low molecular weight (i.e., having molecular weights within the range of freezing or boiling point methods) is to the first approximation directly proportional to the molecular length and for many cases is relatively independent of the chemical composition. Thus, Staudinger found that [9] for solutions of cellodextrin triacetates in m-cresol was related to the degree of polymerization, as calculated from molecular weights by the freezing point and Bergmann-Machemer end-group methods, in accordance with the equation5 5 This is equivalent, within the limits of experimental error, t o Staudinger’s equation (reference 55, p. 466) -1 Mol. Wt. = Lq CK, where K,,, = 11 X 10-4 and C is expressed as molarity of glucose residues.


D.P.

163

= 90 [g]

The same acetates were carefully saponified with alcoholic potassium hydroxide and the viscosities of the resulting regenerated cellodextrins in cuprammonium were determined. Upon the assumption that no scission of the cellulose chain occurred during regeneration, i.e., that the degree of polymerization of each triacetate and the corresponding cellodextrin was the same, it was found that

D.P. = 100 [g] The regenerated cellodextrins were also nitrated and the viscosities in butyl acetate measured, and again upon the assumption that no degradation occurred, it followed that D.P. = 77 [q] The methylated derivatives, prepared by the method of Haworth and Machemer, gave somewhat discordant results in that the constant of proportionality varied from 50 to 75, depending on the solvent used (57). Although no actual molecular weight determinations by freezing point or other direct methods were reported for the cellodextrins, nitrates, or methyl derivatives, the approximate constancy of the factor of proportionality (the experimental error being probably f 1 0 per cent) is in agreement with Staudinger’s viscosity laws and thus confirms the assumption that the chemical conversions did not affect the molecular lengths. The same close relationship was found between the viscosities of cellulose acetates having [q] up to 4 and of the regenerated celluloses and nitrates made therefrom (reference 55, p. 506). Since molecular weights by the Bergmann-Machemer method (over the range where it appeared satisfactory) and the osmotic pressure results of Herzog and Deripasko and of Buchner and Samwel (56) indicated that the direct proportionality between D.P. and [g] extended for cellulose acetates to 1111 = ca. 2.8, Staudinger concluded that the linear relationship extends to the highest values of [q] and is applicable to all cellulose derivatives. On this basis, he has estimated the degree of polymerization or molecular weight of many cellulosic materials from viscosity measurements. Thus, he has deduced the degree of polymerization of native cellulose carefully purified in absence of oxygen to be 750 (molecular weight of 120,000), of rayons to be 100 to 200, of socalled high-viscosity nitrocelluloses to be 500 to 2600. At the present time, it is impossible to predict on theoretical grounds whether there should be a direct proportionality between degree of polymerization and [v] of cellulose derivatives or not. The justification for the calculation of molecular weights from viscosity data must rest entirely upon an experimental correlation of viscosity characteristics and molecular weights determined by absolute methods. I n so far as cellulose and its

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ELMER 0. KRAEMER AND WILLIAM D; LANSING

derivatives are concerned, the results on this point are promising but not entirely concordant. Although the osmotic pressure results of Herzog and Deripasko and of Buchner and Samwel appear to confirm Staudinger’s conclusions, other apparently equally reliable data, summarized in tables 1 to 3, fail to agree. Even in the cases cited, the confirmation may be apparent rather than real, for the measurements of Buchner and Samwel were all made a t concentrations too high to give accurate results, and, according to Ubbelohde (59), the viscosity measurements of Herzog and Deripasko are vitiated by a kinetic energy error. A definite parallelism between [g] and degree of polymerization is nevertheless evident, and in view of the recognized difficulties in accurately determining high molecular weights, there is reason to suspect that the inconstancy in the values for the viscosity coefficient (D.P./[q]) obtained by various workers is due to experimental errors. ULTRACENTRIFUGAL ANALYSIS O F CELLULOSE DERIVATIVES

I n order to establish the relationship between viscosity and molecular weight more definitely, we have extended our ultracentrifugal investigations of cellulose to a group of technical cellulose acetates and nitrates. The acetates were acetone-soluble “secondary” acetates having values of [g], in acetone solution, ranging from 0.80 to 2.32. Several members of the acetate series were fractionated samples prepared and used by Herzog and I-Ierz (26) in their osmotic pressure investigatiom6 The nitrates contained 12.0 per cent nitrogen and had values of [g] ranging from 1.41 to 2.20, corresponding to viscosities of 5 to 71 seconds in 12.2 per cent concentration by the A.S.T.M. standard method (1). For both acetates and nitrates, ultracentrifugal determinations and viscosity measurements were made a t 25.0”C. on acetone solutions about 0.1 g. per 100 cc. in concentration. I n all cases, the molecular weights found were converted to degrees of polymerization and values of [g] were calculated. Both acetates and nitrates, including the fractionated products, were found to be distinctly non-uniform with respect t o molecular weight. The average values, obtained by an approximate method, nevertheless showed a proportional relation to [g] corresponding within experimental errors (about A10 per cent) to the expressions D.P. = 230 [g] for the acetates and D.P. = 270 [g] for the nitrates. As shown in table 3, our results on celluloses in cuprammonium solvent are given by the expression D.P. = 260 [ q ] . Thus the degrees of polymerization found by means of the ultracentrifuge are from 2$ to 33 times as great as predicted bystaudinger, his factors of proportionality being respectively 90, 77, and 100. I n interpreting the differences between our results and those of other 6 We are much indebted to Professor Herzog for furnishing us with these samples so that their molecular weights might be determined by two independent, methods.


165

investigators, it is necessary to consider the effects of non-uniformity. For heterogeneous materials, different methods for determining molecular weights give different “average” values. Thus, it may be shown that freezing point, osmotic pressure, and end-group methods, when applied properly to an ideal mixture, result in an average value defined by the expression

where f i is the fraction,al weight of the constituent of molecular weight Mi in the mixture, and the summation is to be applied to all constituents present. This average may be designated as a “number-average molecular weight.” On the other hand, the viscosity method, according to Staudinger’s theory, should give an average value defined by the expression

which corresponds to a “weight-average molecular weight.” The ultracentrifugal method gives a weight-average value. As a consequence, the osmotic pressure method should give a lower apparent molecular weight for a mixture than the viscosity method or the ultracentrifuge method. If the non-uniformity is marked, the difference in the two average values is surprisingly large. I n order that the viscosity method for estimating degree of polymerization may give useful results for practical cases where nonuniform products are inevitably involved, it is essential that “weightaverage” molecular weights be used in determining the proportionality factor. Staudinger’s factors were determined with molecular-weight methods giving “number-averages,’’ and are therefore too small. The improved consistency between viscosity and molecular weight by the freezing point method after fractionation of his samples was taken by Staudinger to mean that the fractionated products were substantially uniform. However, they were probably still distinctly non-uniform (53), and the greater consistency of results really was due to a more nearly constant ratio between the number-average and the weight-average molecular weights following fractionation. Without quantitative information concerning the distribution of molecular weights for a given specimen, it is not possible to convert number-average to weight-average or vice versa, so the magnitude of the error in Staudinger’s values due to this factor alone cannot be definitely estimated. Solvation is another factor affecting molecular weight determinations in various ways. I n the case of osmotic pressure measurements in dilute solutions, solvation to the extent of 100 per cent or so has a negligible effect on the calculated molecular weight. The same is true for ultracen-

166


trifuge determinations unless the partial specific volumes of the solvated and unsolvated molecules differ, whereupon there is a corresponding error in the calculated molecular weight. For cellulose esters and ethers in organic solvents, the effectis probably not marked. [q],on the other hand, is decidedly sensitive to solvation, but the moderate variation in [q] with different solvents (10) and the approximate equality of the viscosity coefficients indicate that the solvation of cellulose acetates and nitrates is not large nor greatly different. In fact, if [q] is reduced to a volume basis by division by the partial specific volume of the solute (acetate, 1.46; nitrate, 1.74), as should logically be done when comparing different solutes, the results for cellulose acetates and nitrates in acetone may be expressed by the single equation

D. P. = 156 [qIvO3. Association also may be involved in molecular weight determinations of high polymers, as so often is the case for ordinary small molecules. Osmotic pressure and the ultracentrifuge should give the weight of the associated molecule, other disturbing factors being absent. The effect of association upon the viscosity depends, according to Staudinger’s theory, upon the relative positions of the molecules associating together. If compact bundles of parallel molecules are formed, the viscosity is supposed not to be affected, but if two molecules associate end to end, the effect on viscosity is supposed to be twice as great as in the absence of association. With so many factors influencing molecular weight determinations and viscosities of solutions of celluloses or derivatives, irregularities in the relationship between viscosity and molecular weight probably will persist even with accurate values for molecular weights. Much accurate data for various solvents and at various temperatures must be obtained before the effects of complicating factors can be properly unscrambled. On account of unavoidable non-uniformity, the ultracentrifuge is the only means a t present available for obtaining molecular weight information with the necessary detail. Useful information can be secured by osmotic pressure methods, but the experimental technique needs further refinement so that reasonably accurate results can be obtained at low concentrations (e.g., 0.1 per cent or less). I n the meantime we believe that the equations we have stated above may be used for estimating the degree of polymerization of technical celluloses, cellulose acetates, and cellulose nitrates by the viscosity method over the range of [q] we have studied and with the solvents we have used. REFERENCES (1) A. S.T. M. Standard No. D-301-33. (2) BERQMANN AND MACHEMER: Ber. 63, 316-23 (1930).


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(3) BERKENFELD: Dissertation, Darmstadt, 1928. (4) BERL ET AL.: 2. ges. Schiess-Sprengstoffw. 2, 381-7 (1907); 4, 81-3 (1909); 6, 82-4 (1910). (5) BERL ET AL.: Kolloid-Beihefte 34, 12 (1931). (6) BUCHNER AND SAMWEL: Proc. Acad. Sci. Amsterdam 33, 749-54 (1931); Trans. Faraday SOC.29, 32-40 (1933). (7) BUCHNERAND STEUTEL:Proc. Acad. Sci. Amsterdam 36, 671-7 (1933). (8) BUMCKE AND WOLFFENSTEIN: Ber. 32, 2493-507 (1899). (9) CAROTHERS: Chem. Rev. 8, 354-426 (1931). Also numerous papers in J. Am. Chem. Soc. from 1929 to date. (IO) DOBRY AND DUCLAUX: Compt. rend. 197, 1318 (1933). (11) DUCLAUX AND NODZU:Rev. gBn. colloIdes 7, 385-92 (1929). (12) DUCLAUX AND WOLLMAN: Compt. rend. 162, 1580-3 (1911). (13) DUCLAUX AND WOLLMAN: Bull. soc. chim. 27, 414-20 (1920). (14) FIKENTSCHER: Cellulosechem. 13, 58-64, 71-4 (1932). AND PATRICK: Z. physik. Chem. 130, 691-8 (1927). (15) FRAZER (16) FREUDENBERG: Ber. 62, 383-6 (1929). ET AL. : Rer. 62, gO78-83 (1929); 63, 535-6 (1930). (17) FREUDENBERG (18) FREUDENBERG ET AL. : Ber. 63, 1510-30 (1930). (19) GARTHEAND HESS: Ber. 64. 882-97 (1931). (20) GRARD:J. chim. phys. 29, 287-96 (1932). (21) GRARD:Compt. rend. 196, 773-5 (1933). J. Chem. SOC.1931, 821. (22) HAWORTH, HIRST,AND THOMAS: (23) HAWORTH AND MACHEMER: J. Chem. SOC. 1932, 2270-7, 2372-4. ET AL.: Kolloid-Z. 36, 193-8 (1924); 39, 250-2 (1926); J. Phys. Chem. 30, (24) HERZOG 457-69 (1926); 33, 179-89 (1929). (25) HERZOG AND DERIPASKO : Cellulosechem. 13, 25-31 (1932). (26) HERZOG AND HERZ:Trans. Faraday SOC. 29, 57 (1933). (27) HERZOG AND KUDAR: Z. physik. Chem. 167A. 343-53 (1933). AND SPURLIN:Z. physik. Chem., Bodenstein Festband, pp. 239-46 (28) HERZOG (1931). (29) HESS: Die Chemie der Zellulose und ihrer Begleiter, p. 590. Akademische Verlagsgesellschaft, Leipeig (1928). (30) HESS ET AL.: Ber. 63, 1922-7 (1930); Ann. 491, 52-106 (1931). (31) HESS AND ULMANN:Ann. 604, 81-94 (1933). AND HIEMER:Cellulosechem. 6, 101-22, 125-32, 153-66 (1925). (32) HEUSER (33) KRAEMER:Chapter XX in Taylor’s Treatise on Physical Chemistry, 2nd edition, p. 1616. D. Van Nostrand Co., New York (1931). (34) KRAEMERAND LANSING:J. Am. Chem. SOC.66, 4319-26 (1933). (35) KRAEMER AND LANSING: Paper presented a t the Chicago Meeting of the American Association for the Advancement of Science, June, 1933. See also Nature 133, 870 (1934). (36) KRAEMER AND SEARS:J. Rheol. 1, 231-9 (1930). (37) KRAEMER AND VANNATTA:J. Phys. Chem. 36, 3175-86 (1932). (38) K R ~ G EAND R GRUNSKY:Z. physik. Chem. 3.6OA, 115-34 (1930). (39) KUMICHEL:Kolloidchem. Beihefte 26, 161 (1928). (40) MCNALLY AND GODBOUT: J. Am. Chem. Soc. 61, 3095-101 (1929). . (41) MACHEMER: Trans. Faraday SOC.29, 47 (1933). (42) MARK:Physik und Chemie der Cellulose. J. Springer, Berlin (1932). (43) MEDVEDEV: Kunststoffe 23, 249-51 (1933). (44) MEYERAND HOPFF:Ber. 63, 790-1 (1930).

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The Molecular Weights of Cellulose and Cellulose Derivates - The

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