Faraday Symp. Chem. SOC.,1983 18 131-143 Dynamics of Xanthan Biopolymer in Semi-dilute Aqueous Solution Studied by Photon Correlation Spectroscopy Comparison with Solution Viscosities BY A. M. JAMIESON J. G.SOUTHWICK AND J. BLACKWELL Department of Macromolecular Science Case Western Reserve University Cleveland Ohio 44106 U.S.A. Received 7th September 1983 Recent theoretical treatments of molecular motion in entangled solutions of rod-like polymers lead to results which describe the rheological behaviour in terms of the concentration- dependent rotational diffusion coefficient D,. Thus a comparison between experimental values for D,and rheological data is possible and provides an exacting test of such theory. Here dynamic light scattering (DLS) studies of semi-dilute aqueous solutions of xanthan gum are presented and compared with independent rheological data.Despite extensive precautions unambiguous interpretation of these data is precluded by the known tendency of xanthan for self-association. Such problems appear to be common when dealing with rod-like polymers and indeed many features of the observed DLS and viscometric data for xanthan in water are strikingly similar to published results on other rod-like polymers. In particular strong correspondences are found when comparing numerical estimates of D,determined by DLS and shear-rate-dependent viscosities q(j) with a similar analysis of D,and q(j) for semi-dilute methanesulphonic acid solutions of poly(p-phenylene-2,6-benzobisthiazole),a rod-like polymer with a reportedly weak potential for self-association.For each system the D,and q(j) data are qualitatively consistent with recent modified versions of the Doi-Edwards dynamical theory for entangled solutions of rod-like polymers. However large ( x 100) quantitative discrepan- cies are found when comparing q(0)and D via this theory. A survey of rod-like polymer solvent systems for which D and q(j) are available indicates comparable discrepancies and none produces a completely self-consistent interpretation in terms of the above theory. INTRODUCTION Photon correlation spectr~scopy~-~ (PCS) generates useful information regarding the molecular dynamics of polymer molecules in solution in the form of the dynamic structure factor S(q,t) S(q7 0 = cc (exp [iqR,(t)l exp [iqRj(o)l> (1) ij where R,(t) denotes the time-dependent position of the ith chain segment.PCS provides numerical data in the form of characteristic relaxation times which describe the motion of R,(t)relative to Rj(0).Since these relaxation times are also determinants for the viscoelastic behaviour of the solutions PCS provides a means of testing molecular theories of viscoelasticity. In this paper we are concerned with the application of PCS to determine S(q,t) for entangled solutions of stiff or rod-like polymers and the comparison of these experimental data with appropriate theory. We review in detail results of a PCS study by Southwick et aZ.5-9of xanthan biopolymer in two solvent systems uiz. deionized water containing 0.003 mol dm-3 Na sodium 131 5-2 DYNAMICS OF XANTHAN BIOPOLYMER azide and water containing 4 mol dm-3 urea in the absence of salt after thermal cycling from 25 to 70 OC.These data are compared with similar experimental studies taken from the more recent 1iterature.lo*l1 A further comparisong of our PCS relaxation spectrum for xanthan in water with rheological data12 is presented Striking similarities are found with a recent independent study13 in which rheological experi- ments on solutions of rod-like polymers were subjected to an analysis in terms of molecular-dynamic relaxation times. Xanthan polysaccharide has a repeat pentasaccharide unit consisting of a back- bone of (1 -+ 4)-B-~-glucose linked to a trisaccharide side-chain at the 3 position on al- ternate glucose residues.The side-chain is p-D-mannopyranosyl-( l -+ 4)-a-~-glucuro-pyranosyl-( 1 -+2)-b-~-mannopyranoside 6-0-acetate. The terminal mannose exhibits a variable degree of pyruvate substitution. Each repeat unit therefore has an average of 1.3-1.5 charges. The native structure of xanthan appears to be a fivefold helix14 and the question of whether xanthan is a single- or multi-stranded helix remains ~nsett1ed.l~ A major difficulty in solution of studies of xanthan is that in common with many other rod-like polymers,13 it tends to form aggregate structures by a self-association mechanism.16 The stability of the native xanthan structure17~ and the degree of aggregationl69 l9are in each case enhanced by addition of salt. Since slow self-association of xanthan occurs after ultrafiltration of the sample preparation history must be carefully controlled.EXPERIMENTAL SOLUTION PREPARATION Xanthan polysaccharide ('Kelzan') was obtained from the Kelco Co. and purified by the method described by Ho1zworth.20 A stock solution containing 0.45% xanthan was prepared in deionized water prefiltered through 0.1 pm Millipore filters and dialysed for 4 days against deionized water. Light-scattering experiments were carried out on two solvent systems (a) deionized water containing 0.02% sodium azide (3 mmol dm-3) and (b) deionized water containing 4 mol dmP3 urea. The method of preparing solutions for light scattering was a critical parameter which strongly affected the quality of data obtained from PCS experiment^.^ Solutions of xanthan were obtained by dilution of the stock solution to the approximate desired concentration with pre-filtered (0.1 pm Millipore) deionized water containing 0.02 % sodium azide or 4 mol dm-3 urea.The solutions were adjusted to pH 7 if necessary by adding a small quantity of NaOH and filtered directly into the scattering cell. The filter size used strongly influenced the light-scattering results. Filtration through 0.45 or 0.8 pm filters resulted in solutions with unsatisfactory light-scattering characteristics because of the presence of large xanthan aggregates. Only filtration through 0.22 pm Millipore filters produced solutions with useful i.e. reproducible scattering proper tie^.^ It is important to note that the latter procedure resulted in significant concentration losses e.g.6% loss for a nominal 0.0115% solution and 35% loss for a nominal 0.115% solution. The concentrations of xanthan solutions were therefore determined after light-scattering analysis by evaporating the solutions to dryness and weighing the residual film. Solutions of xanthan in 4 mol dm-3 urea were heated to 90 "C for three hours then cooled to room temperature prior to light-scattering analysis. Filtration of these solutions through 0.22 ,um filters was much easier than for the first system and negligible concentration losses were detected. In 0.02 mol dm-3 sodium azide xanthan retains its native rod-like structure. In 4 mol dm-3 urea after heat treatment we discovered based on polarimetry and intrinsic viscosity measure- ments that the denatured form of xanthan was stabilized at room temperat~re.~.~.~~ Subsequent studies in other laboratoriesle* 21 have shown that the principal effect of thermal cycling in 4 mol dm-3 urea is to aid dissolution of xanthan aggregate structures and that 4 mol dm-3 urea does not in fact stabilize the denatured form.It appears that our isolation of denatured xanthan at room temperature was primarily because of the extreme salt depletion A. M. JAMIESON J. G. SOUTHWICK AND J. BLACKWELL [a1 / 20 40 1 I 1 I I I 20 40 60 80 temperature /"C Fig. 1. Temperature dependence of optical rotation of xanthan in deionized water 0,increasing temperature; 0,decreasing temperature; vertical arrow at T = 22 OC indicates decrease of rotation on addition of salt.of the 4 mol dmP3 urea solutions which did not contain azide and were derived from the deionized stock solution. Thus it is possible,33 as shown in fig. 1 to denature xanthan irreversibly in deionized water in the absence of added salt as shown by the irreversible loss of optical rotation after thermal cycling between 25 and 90 OC. The original optical rotatory characteristics of the xanthan deionized water solution indicative of a renaturation is recovered only after the addition of salt. The observations shown in fig. 1 essentially parallel those reported earlier for thermal cycling of xanthan in 4mol dm-3 urea. For heat-treated xanthan solutions in 4mol dm-3 urea we determined the molecular weight to be M = 2.16 x lo6 daltons.This value is in excellent agreement with independent determinations for samples of comparable history studied in both 4 mol dm-3 urea and in aqueous NaCl. It is finally noted that the PCS data reported below were in each case obtained from solutions subjected to filtration through 0.22 pm Millipore and centrifugation at 4500 g for 30 min immediately prior to light-scattering analysis. PHOTON CORRELATION SPECTROSCOPY OF ROD-LIKE POLYMERS As noted above PCS produces information regarding molecular dynamics of polymer solutions in the form of the dynamic structure factor S(q t) [eqn (l)]. The characteristics of S(q,t) are strongly dependent on the magnitude of the inverse scattering length 1qI-l relative to the radius of gyration of the macromolecules R,.For small gR one can neglect terms in eqn (1) reflecting motion of chain segments relative to others on the same chain and consider only the relative motion of pairs of molecules. The latter process is described by Fick's diffusion equation and one S(q,1) = exp ( -D,s") (2) where D is the rotationally averaged translational diffusion coefficient of the polymer. Thus for monodisperse solutes S(q t)is a single exponential. For polydisperse systems S(q,t)= G(D)exp (-Dq2t)dD (3) jOm DYNAMICS OF XANTHAN BIOPOLYMER where G(D)is the distribution of diffusion coefficients. It is possible to analyse such data by the method of 1 P2 2!r2lnS(q,t) = -i+t+-_( -rt)2+ ... (4) where the first moment is related to the z-average diffusion coefficient I? = D,,,q2 and the second moment gives the variance in r p2 = i=2-(f)2.(6) When qR 2 1.5 i.e. q-L & 6 PCS detects contributions to S(q,t) reflecting internal m~tions,l-~ uiz. rotational motion in the case of rigid rods. These are manifested for monodisperse rods as the appearance of a second exponential decay in addition to eqn (2)of the form Sr,t(q t) = exp -(0,q2+60,)t (7) where D is the rotational diffusion coefficient. The relative amplitude of S,,,(q,t) increases as q is increased beyond q*Lx6. It is also pos~ible~-~~~~ to determine D and D from PCS studies of depolarized light scattering if the rod polymers have sufficient anisotropy in their molecular polarizability. The characteristics of S(q,t) are strongly dependent on the concentration of macromolecules.In dilute solution where the centres of mass of the solute molecules are on average separated by distances which are large compared with R, the numerical values of Dt and D may vary with c~ncentration,~ reflecting the effect of direct and indirect (hydrodynamic) forces between molecules. Furthermore above a characteristic concentration c* where the domains of individual chains overlap it may be anticipated that the physical entanglement of rods will produce changes in S(q t)because of the coupling of rotational motions with anisotropic translational diffusion. At least three theoretical discussions have been given for the case of monodisperse rod-like molecules which imply that the effect of entanglements is to change S(q,t) from a single-exponential decay to a markedly non-exponential form.Lee et aZ.24deduce that S(q t) will be the sum of two exponential decays with time constants and relative amplitudes which depend strongly on the magnitude of D,q2 relative to D,. A generalized form of this theory has been given recently by Zero and Pecora.l0 For the weak coupling limit defined as y 5 10 where y = AD,g2/D,,with ADt = Dll-DI the diffusional anisotropy Zero and Pecora derivelo T2 = Dtq2-&Dry2 where D = $(Dll +2D1) is the average translational diffusion coefficient. Doi and 26 have presented an alternative derivation using a similar initial equation of motion which deduces for the strong coupling case ADtq2/D,% 1 that S(q t) contains a continuous distribution of relaxation times.The initial and long-time decay regions of S(q,t) can be approximated however as single exponentials with time constants rl= to,,, q2 = iDtoq2 (10) r2 = (q2DrDtoY (1 1) A. M. JAMIESON J. G. SOUTHWICK AND J. BLACKWELL where D, is the infinite-dilution value of D,. The discussion of Doi and Edwards includes a prediction2' of the concentration dependence of D where D, is the infinite-dilution value p* = 1/L3 and p** = l/dL2 are the overlap concentration and the liquid-crystal transition concentration respectively p is a constant of order unity and f(c/c**)= (1 -Bc/c**)-2 (13) with B a constant slightly smaller than unity. For c* 4 c 4 c** evidentlyf(c/c**) = 1. Since the dynamical analysis of Doi and Edwards26 also predicts that the rheological properties of the solution will scale with concentration and molecular weight in a manner that is dictated uniquely by the behaviour of D,,a numerical comparison between S(q t) and rheological experiment is in principle possible.More recently certain deficiencies in the original Doi-Edwards theory have been recognized and improved versions 29 The changes lead to significant numerical differences in the predicted rheological results e.g. the onset of entanglement interaction occurs at a much higher polymer concentration i.e. p M 100/L3 and hence in eqn (12) /?M O(lo4). However certain of the qualitative scaling predictions of the original Doi-Edwards theory are still valid for the revised theories.For example r, the zero-shear viscosity for c > c* is given by28 Also q(0)/qsis expected to fall on a master curve independent of concentration when plotted against the reduced shear rate j/D,. The revised dynamical theories do not appear to imply a modification of the predicted shape of S(q,t) but certainly suggest that the onset of non-exponential behaviour will be seen at a much higher concentration. The modified versions of the Doi-Edwards theory have been found to fit available rheological data on semi-dilute solutions of stiff-chain molecules semi-quantita- tively.28* 29 Comparisons of theory with experimental S(q,t) data have also been described for such systems. Bimodal exponential decays which are qualitatively .~~ consistent wth the theory of Lee et ~1have been observed in DNA PCS data qualitatively in agreement with Doi-Edwards theory have now been reported for several rod-like polymer^.^-^^^ 30 RESULTS We begin by re-examining our dynamic light-scattering studies of xanthan solutions.PCS data from xanthan in 0.003 mol dm-3 sodium azide showed a slow decrease in D,, and an accompanying increase in p2/r2when observed over a period of 100 h after filtration through 0.22pm Millipore.' This indicates slow self-association behaviour.' Table 1 summarizes the hydrodynamic parameters deduced from dilute freshly filtered solutions of xanthan in aqueous NaCl and 4moldrnF3 urea. The data in table 1 indicate that [q] and DY,* each decrease with increasing ionic strength.Furthermore the filterability of the solutions decreases with ionic strength and filtration losses increase.16 Thus it appears likely that the screening of intermolecular electrostatic repulsions at higher ionic strength results in enhanced predominantly DYNAMICS OF XANTHAN BIOPOLYMER Table 1. Summary of hydrodynamic data for xanthan in various solvent systems solvent H,O (0.003 mol dmF3 azide) > 7000 -2.42 1005 0.01 mol dm-3 NaCl 5150 0.633 0.3 rnol dm-3 NaCl 1.94 1226 1.0 mol dm-3 NaCl 4700 0.724 1.55 1436 4 mol dm-3 urea (heated) 2000 0.083 2.75 800 ~~ a Huggins constant. 0 0 =I 0.01 0.02 I I I 0.25 0.5 time/s Fig. 2. Effect of concentration on photon correlation function of light scattered by xanthan in 0.003 mol dm-3 sodium azide (a) c = 0.026% w/v (b) c = 0.069%w/v (c) c = 0.092%W/V, 0 = 40° R = 6328 A.side-by-side association. The larger Dt and smaller [q] observed for xanthan in 4 mol dm-3 urea presumably reflect partial flexibility in the denatured state. It should be noted however that the values of [q]and D:,z indicate a hydrodynamic volume considerably larger than calculated for a xanthan random coil.lS Evidently the denatured form in 4 mol dm-3 urea is highly extended presumably because of the A. M. JAMIESON J. G. SOUTHWICK AND J. BLACKWELL xxX xX X X X X X X X I 5 0 10 20 time/ms Fig. 3. Photon correlation function of light scattered by xanthan in 4 mol dm-3 urea at c = 0.15%W/V,e = 400 A = 6328 A.1 0.04 0.08 0.12 0.16 concentration (% w/v) Fig. 4. Concentration dependence of average PCS relaxation frequencies for light scattered from xanthan in 0.003 mol dm-3 sodium azide. For c < 0.046% w/v data plotted are first moments from cumulant fits; for c >/ 0.069% w/v points plotted are rl and Tzfrom bi-exponential fits. bulky side-chains and intramolecular electrostatic repulsions. Note that for freshly filtered dilute xanthan solutions in all solvents p2/T2z0.3-0.4. Thus even in dilute solution PCS observes non-exponential decays and the xanthan molecules are polydisperse. Based on a discussion of Kubota and Chu," we estimate M,/M z 1 +p2/T2z 1.35 k0.05. DYNAMICS OF XANTHAN BIOPOLYMER \ \ \ \ \ 1 \ \ \ \ \ .--I r-.--,--a 0 0.1 0.2 0 -3 concentration (% w/v) Fig.5. Concentration dependence of average PCS relaxation frequencies for light scattered from xanthan in 4 mol dm-3 urea. For c < 0.075%w/v data plotted are first moments r from cumulant fits; for c 2 0.15%w/v points plotted are rl and Tzfrom bi-exponential fits. As the xanthan concentration is increased in both 0.003 mol dm-3 sodium azide (fig. 2) and in 4mol dm-3 urea (fig. 3) a significant increase in the deviation from exponentiality occurs over a narrow concentration range. The latter coincides accurately with the concentration regime where independent measurements of the macroscopic viscosity6 l2and microviscosity9 of the solution show sudden increases associated with the onset of entanglement interactions.At concentrations above 0.069% w/v for 0.003 mol dm-3 sodium azideg and above 0.15% w/v for 4 mol dmP3 urea,5 the experimental S(q,t) can be approximately interpreted as the sum of two exponential decays as indicated in fig. 4 and 5. DISCUSSION As we have discussed elsewhere,s it is not possible to achieve a definitive molecular- dynamic interpretation of the available PCS data on concentrated solutions of xanthan. Similar difficulties have been noted in interpreting rheological data on solutions of rod p01ymers.l~ Because of the intrinsic polydispersity of xanthan and its tendency to form aggregates one possibility is that at higher concentrations association occurs to form slowly diffusing Although such a process would be expected to decrease solution viscosity if side-by-side association is present,13 it may be that at sufficiently high concentration the aggregates act as junction zones in a gel Also if a random association process occurs enhancement of the viscosity and gel formation may res~1t.l~ Even for the case of xanthan in 4 mol dm-3 urea where evidence suggestslg~ that aggregation does not occur at lower concen- 21 trations we cannot definitively exclude the possibility that the appearance of a slow decay process above c = 0.15% w/v is due to a weak residual tendency for self-association.Morris et a1.l9 have observed a slow mode in PCS data of concentrated xanthan solutions which disappeared upon ultracentrifugation and ultrafiltration and therefore was assigned to the presence of aggregates.The aggregate structure is A. M. JAMIESON J. G. SOUTHWICK AND J. BLACKWELL Table 2. Dynamics of xanthan in water 0.069 ~ 832 42.0 3.03 670 14 0.092 560 4.0 2.18 8.2 9 0.14 536 2.8 2.07 4.1 3.6 a Assumes DYlc = DF:lc (c*/c)~,where c* = 3 x w/v. interpreted19 as due to side-by-side association of 47 units. One potential difficulty of this approach for polydisperse solutes however is that such treatment is likely also to fractionate the polymer even if aggregates are not present and thus will also dramatically alter the hydrodynamic properties of the solutions which are very sensitive to rod length [see eqn (12)]. As noted above we have attempted to exclude aggregates by ultrafiltration immediately prior to light-scattering analysis.On the other hand since a small degree of side-by-side association produces aggregates of the same approximate length as a single molecule PCS and rheological data on polydisperse solutions of rod-like chains may be expected to retain the principal dynamical features discussed by Doi and Ed~ards.~~-~~ Thus the rheological studies of Whitcomb and Macosko31 show evidence for the existence of conventional shear-thinning viscometric behaviour in concentrated solutions of xanthan in water. Approximate estimates of q(0) from these data9 scale as c3.0 for concentrations 0.1 5 c(wt%) 5 0.20 consistent with Doi-Edwards the~ry.~~-~~ Similarly the PCS data for c > 0.1% observed in our experiments show features qualitatively consistent with such theory.Thus the initial slope becomes concentration independent while the long-time decay varies as c-l in accord with eqn (10) and (1 1). Table 2 shows a comparison of experimental data for xanthan in water with the modified Doi-Edwards theory uiz. eqn (10) and (1 l) based on the values L x d = 15000 A x 20 A p M lo3 and c* = @/L3N" 3 x This comparison is amplified in fig. 6 which compares experimental values of q(j)/q(O) against j/D with the Doi-Edwards theory and subsequent modifications. Bearing in mind the intrinsic polydispersity of xanthan and that the PCS and rheological data were performed on different xanthan samples it is interesting to note several features of the above results which are remarkably similar to observations made independently on other rod-like polymers (1) our estimates of D for c > 0.1% w/v are numerically very similar to those reported in other PCS experimentslO7 11,30 and indicate #? z 103-104; (2) utilization of our experimental relation for D, viz.D,(s-') = 6.6 x (conc.% w/v)-~ (15) results in reduced shear viscosity curves q(j)/q(O)against j/D (fig. 6) which are very consistent with theoretical expectation28v 29 and experimental analyses;l3? 29 (3) the 28v observed values of Dtl,are much larger than the predicted result Dtll = $Dto and there is no formal basis in theory for the observed maximum in rl(fig. 4); (4) the value of p deduced from D predicts values of q(0)based on eqn (13) which are much larger (ca.x 100) than the experimental q(0).Note that a similar maximum in the short-time decay constant of S(q,t)appears in the PCS study of concentrated solutions of rod-like poly(y-benzyl glutamate) (PBLG) by Kubota and Chu. l1 Also comparable internal numerical discrepancies in the scaling of q(0)against D and ~(j) to against (?/Or) DYNAMICS OF XANTHAN BIOPOLYMER 0.0 -*.O t Fig. 6. Reduced plots of shear viscosity from ref. (12) v(j)/q(O) as functions of j/Dr where D is estimated from eqn (15); solid lines are theoretical predictions; DE ref. (26); JC ref. (28); FD ref. (29); 0,0.1% w/v; x 0.2%w/v; 0, 0.35% w/v. those referred to under (4) above are encountered in much of the literature data on rod-like polymers.1o$ l1 139 28 At least two factors are likely to contribute to the existence of a maximum in rl.First we note that the PCS experiment probes the mutual diffusion coefficient and that this quantity can exhibit significant concentration dependence even in dilute solution because of thermodynamic and hydrodynamic forces. For a system of rods interacting through predominantly repulsive forces one might anticipate a significant increase in D,as one nears the concentration where the equivalent hydrodynamic spheres overlap. Since the effect of entanglement coupling is seen at such comparatively high concentrations these effects cannot be neglected. Conversely rotational self- diffusion is driven by Brownian collisions and is expected to stay essentially constant or slowly decrease as c increases towards c*.A maximum in rl is thus plausible at c* when rotation couples to the enhanced mutual diffusion process. Secondly the onset of entanglement interaction is gradual and there is clearly a range of concentrations which coincide with the observed maxima9?l1 in rl,where a comparatively weak coupling of translational and rotational motions occurs. In this regime as indicated by eqn (8) and (9) theory SuggestslO that rl >Dtq2and Tz<D,q2 are reasonable. As the concentration increases the coupling strength y increases and since in the y +co limit the Doi-Edwards theory [cf. eqn (10) and (I l)] implies rl <D,q2 and T2 6 Dtq2 it appears that a maximum in rl must occur even in the absence of thermodynamic and hydrodynamic contributions to D,.Note comparing fig.4 and 5,that xanthan in 4 mol dm-3 urea shows behaviour similar to that for xanthan in water albeit at a higher concentration. This is consistent with the idea that denaturation of xanthan at low ionic strength produces an extended stiff coil which will however have a smaller axial ratio because of the extended side-chains and a smaller hydrodynamic volume because of the enhanced chain flexibility. The precise origin of the numerical discrepancies in comparing experimental estimates of ~(0) against D via eqn (14) is more difficult to identify. Similar problems were encountered in a rheological study by Chu et aZ.13of several rod-like polymers A. M. JAMIESON J. G. SOUTHWICK AND J. BLACKWELL in which experimental estimates of D were calculated from ~(0)and the limiting recoverable compliance R(0) via the equationI3 z = q(O)R(O)= (6Dr)-'.Chu et aZ.13observed systematic numerical disparities for these polymers in comparing ~(0) against eqn (14) which correlate closely with the experimental variation in observed values for c** the concentration for onset of the ordered anisotropic phase for each polymer. Thus they suggest the deviations may be due to systematic variations in chain flexibility or interchain association which alter ~(0) and c** in the same way.31 For example ~(o),~(1;)and D values for the semi-flexible polymer poly(pphenyleneterephtha1amide) (PPTO) in methanesulphonic acid (MSA) fall in the concentration range c* 6 c 6 c** and are found to give a good self-consistent fit when tested against the Doi-Edwards theory.However the rheological data for the more rigid poly(p-phenylene-2,6-benzobisthiazole)(PBT) in MSA show strong discrepancies which are remarkably similar to those noted above in our observations on the xanthan + water system. Specifically the experimental D produce q(j/Dr) curves which accurately fit the modified 29 of Doi-Edwards and predict ~(0) values from eqn (14) which show the anticipated scaling behaviour against concentration but which are 100 times larger than experiment. The rheological data reported for PBT in MSA fall in a narrow concentration range near c** 0.8 c** 5 c 5 c**. For xanthan preparations similar to those studied in our work a value c** = 2.5 g dm-3 has been reported;32 thus it is evident that our analyses indeed fall in a concentration regime very similar to that referred to for PBT in MSA.Further as we have noted el~ewhere,~~ the viscosity of xanthan in water appears to increase faster than c3-0in this concentration range in agreement with the deduction that the functionf(c/c**) 6 1. Chu et aZ.13 interpret their data for PBT in MSA as suggesting a relatively low degree of (side-by-side) association and a high rigidity for PBT. However PCS studies of dilute solutions of PBT in MSA34 indicate that while most of the polymer is present in a low state of aggregation (1-2 chains per aggregate) a small percentage is in fact associated in very large loosely organized aggregates. Also slow time-dependent increases of viscosity have been observed for PBT in MSA.13 It seems worth noting that in the xanthan+water and PBT+MSA systems the aggregation processes occur even though in each case we are dealing with a highly charged polyion in a solvent of low ionic strength.It is also pertinent that smaller but significant (x 10) differences are found for semi-dilute solutions of helical poly(y-benzyl-L-glutamate) (PBLG) between values of determined28 from ~(0)via eqn (13) and those estimated from D data either uia reduced ~(j) curves28 or from PCS studies,lo the latter again being smaller. These discrepancies may derive from one or more of several factors. For example the polymers studied generally have rather broad molecular-weight distributions and different rheological quantities may represent different molecular-weight averages.Moreover for a given mass/volume concentration side-by-side association may have a relatively minor effect on the average rod length and hence D, but decrease ~(0) significantly by reducing the average number of particles. For the particular examples of the xanthan + water and PBT + MSA systems studied near c** where the discre- pancies are rather large the influence of strong electrostatic repulsions between molecules and/or the possible presence of small numbers of giant aggregates in such highly congested systems may significantly modify the viscometric properties through some as yet unexplained mechanism. Finally near c** as noted by DO^,^' the dynamical model from which eqn (12) and (1 3) are derived is an approximation and may be inadequate.For example the situation near and above c** may be analogous 142 DYNAMICS OF XANTHAN BIOPOLYMER to the onset of a glass-transition 33 As a result the width of the relaxation spectrum may be increased and individual rheological quantities may be influenced by different portions of this spectrum. In summary correlation of experimental data for D,and q(p) represents an exacting test of theories of molecular dynamics in entangled solutions of rod-like molecules. In view of the extreme sensitivity of such data to rod length and particle number density it is difficult however to realize in practice an appropriate experimental test of such theory because of the intrinsic polydispersity partial flexibility and the strong tendency for self-association.In our PCS study of xanthan in water a definitive interpretation of the long-time portion of S(q,t) is precluded because of the possible formation of small concentrations of large aggregate structures. However the short-time decay shows behaviour similar to that reported in comparable studies in other congested solutions of rod-like polymers. These observations are qualitatively consistent with the molecular-dynamic theory. Furthermore estimates of D derived from the long-time decay compare with ~(9) data for xanthan in water in a fashion consistent with theory. A survey of systems for which D,and q(j)data exist indicates reasonable qualitative agreement with theoretically predicted scaling laws for D and ~(0)via eqn (12) and (14).Also experimental estimates of D appear to produce reduced viscosity curves ~(f)/q(O)in reasonable harmony with theory. However systematic numerical dis- crepancies appear to exist when comparing q(0)against D,via eqn (14) which range from values of ca. 100 for highly congested systems (c x c**) such as xanthan in water or PBT in MSA to comparatively minor differences in the system PPTA+MSA. Paradoxically however PPTA appears to be a comparatively flexible molecule with a persistence length approximately four times smaller than the contour length for the polymers studied.13 We thank the National Science Foundation for support through grant CPE 8017821. We also thank Prof. G. C. Berry for discussions which aided our under-standing of the rheological properties of entangled solutions of rod-like polymers.I B. Chu Laser Light Scattering (Academic Press New York 1974). 2 B. J. Berne and R. Pecora Dynamic Light Scattering (Wiley-Interscience New York 1976). J. M. Schurr CRC Crit. Rev. Biochem. 1977 4 371. A. M. Jamieson and M. E. McDonnell Adv. Chem. Ser. 1979 174 163. J. G. Southwick Ph.D. Thesis (Case Western Reserve University Cleveland Ohio). J. G. Southwick M. E. McDonnell A. M. Jamieson and J. Blackwell Macromolecules 1979,12,305. J. G. Southwick H. Lee A. M. Jamieson and J. Blackwell Carbohydr. Res. 1980 84 287. J. G. Southwick A. M. Jamieson and J. Blackwell Macromolecules 1981 14 1728. A. M. Jamieson J. G. Southwick and J. Blackwell J.Polym. Sci. Polym. Phys. Ed. 1982 20 1513. lo K. M. Zero and R. Pecora Macromolecules 1982 15 87. l1 K. Kubota and B. Chu Biopolymers 1983 22 1461. l2 P. J. Whitcomb and C. W. Macosko J. Rheol. 1978 22 493. l3 S. G. Chu S. Venkatraman G. C. Berry and Y. Einaga Macromolecules 1981 14 939. l4 (a) R. Moorhouse M. D. Walkinshaw and S. Amott in Extracellular Microbial Polysaccharides ed. P. A. Sandford and A. Laskin ACS Symp. Ser. 1977,45,90; (b)K. Okuyama S. Arnott R. Moor-house M. D. Walkinshaw E. D. T. Atkins and C. H. Wolf-Ullish in Fiber Dzflraction Methods ed. A. D. French and K. H. Gardner ACS Symp. Ser. 1980 141 41 1. l5 (a)G. Paradossi and D. A. Brant Macromolecules 1982,15,874; (b)E. R. Morns Food Chem. 1980 6 15. l6 J. G. Southwick A. M. Jamieson and J.Blackwell Carbohydr. Res. 1982,99 117. l7 E. R. Morns D. A. Rees G. Young M. C. Walkinshaw and A. Darke J. Mol. Biol. 1970 110 1. E. R. Morris in Extracellular Microbial Polysaccharides ed. P. A. Sandford and A. Laskin ACS Symp. Ser. 1977,45 81. l9 V. J. Morns D. Franklin and K. I'Anson Carbohydr. Res. in press. A. M. JAMIESON J. G. SOUTHWICK AND J. BLACKWELL 143 2o G. Holzworth Biochemistry 1976 15 4333. 21 S. A. Frangou E. R. Morris D. A. Rees P. R. Richardson and S. B. Ross-Murphy J. Polym. Sci. Polym. Lett. Ed. 1982 20 531. 22 J. G. Southwick unpublished data. 23 D. E. Koppel J. Chem. Phys. 1972,57,4814. 24 H. Lee A. M. Jamieson and R. Simha Macromolecules 1979 12 329. 25 M. Doi and S. F. Edwards J. Chem. Soc. Faruduy Trans.2 1978 74 560. 26 M. Doi and S. F. Edwards J. Chem. Soc. Furaday Trans. 2 1978,74 918. 27 M. Doi J. Phys. (Paris) 1975 36 607. 28 S. Jain and C. Cohen Macromolecules 1981 14 759. 29 S. Fesciyan and J. S. Dahler Macromolecules 1982 15 517. 30 J. F. Maguire J. Chem. Soc. Faraday Trans. 2 1981 77 513. 31 (a) P. J. Flory Proc. R. SOC.London Ser. A 1956 234 73; (b) P. J. Flory and R. S. Frost Macromolecules 1978 11 11 26. 32 M. Rinaudo and M. Milas Curbohydr. Res. 1979,76 186. 33 A. M. Jamieson Polym. Prepr. 1982 23 69. 34 (a)C. C. Lee S. G. Chu and J. C. Berry J. Polym. Sci. Phys. in press; (b)Y. Einaga and G.C. Berry manuscript in preparation.