On cellulose degradation in heterogeneous reactions

EuropeaJaPolymerJournal, 1971,Vol.7, OP.543-547. PergamonPress. Priatedia England.

ON CELLULOSE DEGRADATION IN HETEROGENEOUS REACTIONS* Iu. V. BRESTKINand S. YA. FRENKEL Institute of Macromolecular Compounds of the Academy of Sciences U.S.S.R, Leningrad, V-4, Bolshoy Prospect 31, U.S.S.R.

(Received 18 February 1970) Abstract--It has been shown theoretically that the quasiperiodical distribution of unordered regions along cellulose microfibrils does not significantlyaffect the molecular weight distribution which arises from heterogeneous reactions of cellulose involving a limited number of acts of chain rupture. IN A SERIES of investigations of the heterogeneous acid hydrolysis of cellulose, (1"-'~ its acetylation, (3) and its alkaline oxidation, (4) it was found that a random chain-scission (with a comparatively small number of scissions) takes place. According to Sharpies (t) the unordered rupture of the cellulose molecules reflects the random distribution of amorphous regions along a particular polymer chain. However, there is some evidence against the concept of the statistical distribution of amorphous regions. The data were obtained by Hess (s) in electron microscope studies of cellulose microfibrils, and also Kiessig (6) who used small-angle X-ray scattering techniques. These authors found a quasiperiodical distribution of amorphous regions along the large microfibril axis which, in accordance with the same authors' proposed model of cellulose structure, corresponds to a quasiperiodical distribution of these regions along a molecular chain. The average distance between the adjacent amorphous regions for different cellulose structures varied between 100 and 200 A. Following Hearl, (7) the data of Hess and Kiessig provide evidence of some periodicity in the distribution of local distortions of the crystalline order along microfibrils. The fringed fibril structure proposed by Head seems particularly probable for cellulose. This model allows a quasiperiodical distribution of unordered regions along polymer chains. In the present paper, an attempt is made to correlate two apparently contradictory experimental facts, viz. random scission of cellulose molecules following the heterogeneous reactions, and the quasiperiodical distribution of amorphous regions. First, it should be mentioned that there exist different types of distortions inherent to the periodical distribution of amorphous regions along polymer fibres, the so-called second kind of distortions (a) being of particular interest. It is known that, in a system o f units with these distortions, only the nearest-neighbours distribution is clearly developed, that of the distantly located units varying over a wide range. Photomicrographs of cellulose given by Hess (s) show that second kind of distortions are inherent to the periodical distribution of amorphous regions along the large microfibril axis. In accordance with Hearl's fringed fibriUar model, these data may be interpreted as absence of a long range order in the distribution of the amorphous regions along a molecular chain. * Paper presented at the International Symposium on Macromolecular Chemistry, Budapest, 25-30 August, 1969. 543

544

IU. V. BRESTKIN and S. YA. FRENKEL

Obviously, in the absence of a long range order, the probability of finding an amorphous region at some large distance along a macromolecule from an arbitrarily chosen point is equal to the weight fraction of amorphous regions (w). Accordingly, the probability of finding a crystalline region at the same point is equal to the weight fraction of crystalline regions (I -- w). It follows that a certain specific value a exists, such that a condition i > a

or I --ff~

1 --

fi~t ---

1--w

I

(1)

w~ being the probability of the occurrence in the amorphous region (or regions) of two bonds belonging to the same chain situated at a distance of i units from each other, and ~, being the probability of occurrence of a bond in an amorphous region at a distance i from a bond situated in a crystalline region and also belonging to the same chain. Now let us consider the degradation of a large number N of chains, each of them containing P units connected with chemically equivalent linkages.* If the reaction proceeds in the presence of excess degrading agent and at a sufficiently low rate (the reverse diffusion processes will influence the degradation kinetics), the "amorphous" link scission probability at a given moment ~-may be defined as ¢tI = I -- e - x l ' . Likewise, the probability of a link scission in a crystalline region will be a., = 1 -- e -K2', K~ and/(2 being the degradation rate constants for amorphous and crystalline links, respectively; since K1 ~ K2 the inequality al >>a2 always holds. The value ct = alw + az(1 -- w)

(2)

fixes the fraction of degraded bonds or the degree of degradation. The a-value is assumed to be so small that the average length of the chains produced exceeds a and at the same time equals several times the average distances between adjacent amorphous regions. Since X-ray long period for cellulose fibres lies between 100 and 200 A, the last condition is equivalent to a requirement that most molecules in a degraded sample have a polymerization degree more than 100 (500 A). During degradation, a molecule with a degree of polymerization p can be formed either as result of scission of two links in the initial chain situated at p units from each other or as result of scission from the end of the initial chain of a fragment consisting o f p units. In the first case, the following independent events take place: (1) scission of some link/, (2) scission of the link (l -+- p), l and (I -+- p) being the respective link number in an arbitrarily chosen chain), (3) conservation of (p -- 1) undamaged links between the links I and (l ,'-- p). Assuming that, in the system under consideration, there is no correlation between the probability of occurrence of an amorphous region at a particular site in a molecule and the distance of the site from the end of this molecule, one comes to the immediate * Sharpies found a low content of weak bonds in high molecular weight cellulosesamples. We neglect these links because, being unordered along a chain, ct~ they do not cause any deviations from random degradation.

On Cellulose Degradation in Heterogeneous Reactions

545

conclusion that the links l of w N chains are situated in amorphous regions and equally numbered links of (1 -- w) N polymer molecules are situated in crystalline regions. Since l may have a value ranging from 1 to ( P - - p -- 1), the probability of formation of a chain with degree of polymerization p as result of two ruptures of links may be expressed as: L~ (p, eL) = w N ( P

- - p - - 1) ct~ ~ (p -- 1) [ct~ ~p + a 2 (1 -- vi,p)]

+ (1-- w) N ( P - - p - -

1) a 2 q ( p - - 1)[=~ fb, + ct,(1 -- ~,)1.

(3)

There is p--1

~--

1)=

/7 1--cqW,--cL z ( 1 -

w,)

1=1 p--1

and

~(p--1)=

/7 1 - - ~ : / ~ , - - ~ ( 1 - - ~ , ) . l=l

The probability of formation of a fragment with a degree of polymerization p as result of rupture of one link is determined in the same way: L2(p,a)=

2[wNcqq(p--

1)+(1--

w) Nct 2 ~ ( p -

1)]

(4)

the factor 2 taking into account the probability of the separation of the fragment from both chain ends. Now let us evaluate ~ (p -- 1) characterizing the probability of conservation of (p -- 1) links in a part of the molecule, the origin of this part coinciding with an "amorphous" link; and then evaluate the value ~ (p -- 1) characterizing the probability of conservation of (p -- 1) links in a part of the molecule, this latter part originating from a "crystalline" bond. It is obvious that, with an ideal periodical distribution of the "amorphous" links, the quantity in a chain part containing zn links equals z n w independent of the type of link from which it originates; z being the distance between amorphous region centers, n being 1, 2, 3, etc., and w z being the number of links in an amorphous region. If z and w z distortions occur with an equal probability in any direction, w n z is the average quantity of "amorphous" links in part of a chain containing n z units. Accordingly, the average number of "crystalline" finks in a given part equals (1 -- w)nz. Therefore q~ (nz) = c~ (nz) = (I -- al) "'w. (1 -- ~2)"-'(I-w),

(5)

o r , a s ct2 < a t < O,l

(o (nz) = c# (nz) ~_ [1 -- =t w -- ct2 (l -- w)]n= = (1 -- ct)".

(6)

If nz > p - - 1 qo(nz)=fo(p--

I) /~ 1 - - ~

~,--ct2(l--

~,)=(1--~)"-"

(7)

and (nz)=q(p--

1) /~ 1 - - a i / ~ , - - ~ 2 ( 1 - - ¢ 0 ) = ( 1 - - c 0 " - ' .

(8)

However when i > a, in accordance with the expressions (1) and (2)

~1~,+a2(1-E.P.J. 7/5--K

~,) ~_ c q / 0 , + ~ 2 ( 1 - - i 0 3 _

~lw+a2(1--w)=a.

(9)

546

IU. V. BRESTKIN and S. YA. FRENKEL

Substituting the expression (9) into expressions (7) and (8), we obtain that for p > a (/9 -- 1) = (1 -- a)v-1,

(I0)

(p -

(11)

1) - - (1 -

~)~-~.

Combining the equations (9), (10) and (I 1) with the equations (3) and (4) and summing the two latter, we obtain the probability of formation of a a chain with p units: L (39, ~) = N~ (I -- ~)'-~ [(e -- p -- 1) ~ + 2].

(12)

Since following the equation (I0) and (11), the probability of conservation of ( p - 1) links equals (1 -- c0v- t, the probability of conservation of the original chain may be put as L (P, c0 = N(1 -- =)P-1.

(13)

Multiplying (12) and (13) by pu, the weight of one molecule (u being the repeating unit weight), and dividing the product by NPu, the total weight of the molecules, we obtain the weight concentrations of product and undegraded molecules:

q. (p) = ~ (l _ ¢Ov-~ [(P - p - 1 ) c' + 2] P

q,~ ( P ) = (1 -- e)~,-x.

, p < P,

(14) (15)

When a is rather large, so that P >>if, ff being the average degree of polymerization, equation (14) reduces to qw(P) = e 2 p ( 1 - a )

"-t = e2pe-~,

since

(P--p--

1) ct + 2 P

~'

O..

In this case the concentration of undegraded molecules becomes neghgible. Equations (14) and (15) were obtained by Montroll and Simhag for the case of chain degradation with an initial degree of polymerization P and an equal probability of bond scissions. The problem solved by these authors corresponds to the case of homogeneous hydrolysis of cellulose esters which is well known to be accompanied by a chain scission31°) The identity of our equations and those of Montroll and Simha shows that, in the absence of long range order in the distribution of amorphous regions at at small degrees of degradation, the macromolecular scission in heterogeneous reactions can also be considered as random. In other words, the periodicity in the distribution of amorphous regions in the mentioned conditions does not affect the resulting distribution. In conclusion, let us consider a molecular size distribution arising as a result of many acts of scission assuming that these acts take place mainly in the amorphous regions. In accordance with the expression (3), a rather sharp distribution must occur in this case, the average size of the molecules produced corresponding to the average length of the crystalline regions. However such a conclusion is in disagreement with the fractionation data for extensively hydrolysed cellulose samples, which reveal a rather wide size distribution311) The electronmicroscopic evaluation of sizes of the

On Cellulose Degradation in Heterogeneous Reactions

547

microfibrillar fragments disconnected b y extensive hydrolysis also gives evidence for the absence o f periodicity in the d i s t r i b u t i o n o f r u p t u r e points31~ These d a t a m a y be interpreted as a s u p e r p o s i t i o n o f a recrystaUization process on the h y d r o l y t i c d e g r a d a tion o f the cellulose. It is well k n o w n t h a t such a process is a usual consequence o f cellulose hydrolysis consisting in a t r a n s f o r m a t i o n o f a m o r p h o u s regions into a crystalline phase. (I) P r o b a b l y as a result o f such recrystallization, the periodicity in the d i s t r i b u t i o n o f a m o r p h o u s regions is lost; thus it is n o t surprising that this periodicity is not f o u n d in p r o d u c t s o f extensive d e g r a d a t i o n . REFERENCES (1) A. Sharpies, J. Polym. Sci. 13, 393 (1954); 14, 95 (1954). (2) H. Vink and R. WikstrOm, Steak. Pappers Tidn. 3, 55 (1963). (3) V. M. Golubev and S. Ya. Frenkel, Vysokomolek. Soedin. A10, 750 (1968). (4) Yu. V. Brestkin and M. M. Chochieva, Zh. Prinkl. KAim. 40, 2049 (1967). (5) H. Hess, H. Mahl and E. Gutter, KolloidZ. 151, 1 (1957). (6) H. Kiessig, Das Papier 12, 117 (1958). (7) J. Hearl, J. appL Polym. Sci. 7, 1175 (1963). (8) R. Hosemann and S. N. Bagchi, Direct Analysis of Diffraction by Matter. North-Holland, Amsterdam (1962). (9) E. W. Montroll and R. Simha, ar. chem. Phys. 8, 721 (1940). (10) N. Grassie, Chemistry of High Polymer Degradation Processes. Butterworths, London (1956). (I 1) V. I. Sharkov, In: Trudy Instituta lesohosyaystvennihproblem, Acad. Sci. LaW. SSR (1955). Resume----On a montr6 throriquement que la distribution quasiprriodique des rrgions drsordonn~es le long de microfifres de cellulose n'affecte pas de fa~on significative la distribution des masses mol~culaires que l'on obtient h partir des r~actions h~t~rogrnes de la cellulose inerrant en jeu un nombre [imit~ de ruptures de chaine. Sommario--E' stato dimostrato teoricamente chela distribuzione quasi periodica delle zone ordinate lungo le microfibrille cellulosiche non influenza in modo significativo la distribuzione del peso molecolare che si ha dalle reazioni eterogenee della cellulosa che implicano un numero limitato di azioni di rottura della catena. Zusammenfassung--Es ist theoretisch gezeigt worden, dass die quasi periodische Verzweigung ungeordneter Regionen entlang Zellstoff~erchen die Molekulargewichtsvcrteilung unwesentlich beeinflusst, welche aus heterogenen Zellstoffreaktionen entsteht, die eine begrenzte Anz~hl yon Kettenbruch vorg~ingen mit sich bringen.