J. Chem. SOC., Faraday Trans. I, 1982, 78, 1209-1221 Diffusion of Dextran at Intermediate Concentrations BY BARRY N. PRESTON* AND WAYNE D. COMPER Department of Biochemistry, Monash University, Clayton, Victoria, Australia AND ANTHONY E. HUGHES, IAN SNOOK AND WILLIAM VAN MEGEN Department of Applied Physics, Royal Melbourne Institute of Technology, Melbourne, Australia Received 27th May, 1981 The diffusion properties of dextran molecules in water have been followed by use of boundary relaxation techniques (refractive index and tracer measurements) and by photon correlation spectroscopy. Measurements have been carried out up to concentrations of ca. 250 kg m-3. The diffusion coefficients and their inter-relationships have been interpreted in terms of the non-ideal behaviour of flexible polymers.The kinetic and equilibrium behaviour of macromolecules in a concentrated phase is of interest for many diverse aspects in biology and chemistry. Our studies1v2 in particular have been aimed at obtaining a better understanding of the dynamic behaviour of the extracellular matrix of connective tissues, which is known to contain high concentrations of polysaccharide chains. In this paper we present an analysis of the diffusional properties of dextran. We consider that the study of dextran polysaccharides serves as a useful, simplistic model by which the fundamental dynamic properties of concentrated polysaccharide regions in tissues may be understood. We have determined both the mutual diffusion coefficient and the intradiffusion coefficient of several dextran preparations of molecular weight varying from lo4 to 1.5 x lo5 by boundary relaxation techniques.These studies have been carried out over an extended concentration range (up to 250 kg m-3). For comparison, we have used photon correlation spectroscopy (P.c.s.), a non-perturbing technique, to investigate the motions of the dextran chains in similar solutions. Our experimental studies have been considered in relation to various theoretical treatments of diffusion and the semi-dilute properties of flexible p01ymers.~-~~ This work continues and expands earlier studies of the diffusion of macromolecules in concentrated aqueous solution^.^^ lo THEORY The transport of material by diffusion in a binary non-electrolyte system is usually described in terms of three coefficients which can be derived directly from experimental measurements.They are the differential mutual diffusion coefficient D, which is a measure of the rate of inter-diffusion of components 1 and 2, and the self-diffusion coefficients 0; and D,*. (We define component 1 as solute and component 2 as solvent.) It has been shown that the intradiffusion coefficient, D:, of labelled molecule 1* is at least approximately equal to the self-diffusion coefficient 0; of component 1,3 i.e. D l = 0;. (1) 12091210 DIFFUSION OF DEXTRAN Furthermore, the different types of diffusion are related by4 where c, is the molar concentration and p1 the chemical potential of component 1. This expression for D has been used by various investigators in polymer diffusion studies.6-10 Note that eqn (2) is used here with reservation, as it is based on the assumption of a regular s~lution,~ which is probably not the case for dextran solutions. An expression of the term (apl/ac,),, in terms of thermodynamic non-ideality coefficients can be derived from algebraic expressions for the chemical potential of component 1 given by Ogston5 as (3) where m, is the molality of component 1 [mol (g solvent)-l] and a,, a3... are the coefficients expressing thermodynamic non-ideality. Differentiation of eqn (3) with respect to m, and conversion of units of concentration into mass/volume units (C,) with eqn (2) gives p,-& = RT(lnm,+a,m,+a,m~+. . .) (1 +2A,M,C1+3A3M,q+. . .) (4) 0;' (1 - c, K) D = where and where is the partial specific volume of 1.This expression for D is different from that described previously by Yamakawa6 and used by various inve~tigators~-~~ in polymer diffusion studies. Yamakawa6 found that the (1 - C, F) term occupied the numerator instead of the denominator as in eqn (4). The difference is derived from the fact that Yamakawas assumed C2 = 1, as is approximated in dilute solutions, for his expression of osmotic pressure [his eqn (30.43)]. Furthermore, Yamakawa6 and others12 have evaluated fluxes relative to a cell-fixed frame of reference with the assumption that the volume change on mixing is negligible. In using the consistent expressions of chemical potential in terms of molal quantities as described by Ogston5 no assumptions are further required in the description of eqn (4) except for 5 being independent of C,.An alternative view of polymer dynamics in concentrated polymer solutions lies with the concept of an entangled statistical network mesh. This approach has been the subject of extensive theoretical work.l1* l3 At concentrations equal to or greater than the overlap concentration C* (noting that C = C* corresponds to a close-packed system of non-overlapping coils) divergence from dilute solution behaviour is anticipated. To calculate C* the polymer molecule is arbitrarily viewed as occupying either a sphere of radius R, or a cube of side R,, which gives rise to upper and lower M < C * < L . 3M1 4nNR; NR& bounds : ( 5 ) Further development by de Gennes13 has shown that the mutual diffusion coefficient (also termed a cooperative diffusion coefficient) in the semi-dilute region will vary with concentration as C0.75.The special case of flexible polymer movement within the statistical network mesh has been described by de Gennes as reptation and gives the intradiffusion coefficient 0: cc C-1.75. It is of interest to investigate to what degree the diffusional behaviour of dextran in water (a good solvent) is in agreement with these predictions.PRESTON, COMPER, HUGHES, SNOOK AND VAN MEGEN 121 1 EXPERIMENTAL MATERIALS The polymer dextran samples were either supplied or kindly donated by AB Pharmacia (Uppsala, Sweden). The physicochemical properties of the fractions used in this study are described in table 1. Note that the dextran fraction FDR7782 (with an HW/mn ratio of 1.32) was a purified subfraction obtained by gel chromatography of dextran T150.TABLE 1 .-PROPERTIES OF DEXTRAN SAMPLES virial coefficientsb moisture dex tran H" M W Mza content second (A,) third (A,) classification / 10" g mol-' / l(r g mol-I Hw/Hn / 10' g mol-' / 10-0 g(H,O) g-I /lo-!!? g-I / 10- mol ma g-* / 10-8 mol ma g-4 T10 0.6 1.04 1.68 1.08 9.89 8.7 0.7 2.4 T20 1.65 2.04 1.24 2.28 4.62 12.0 T70 3.95 6.95 1.76 7.36 7.22 23.0 0.47 2.0 T150 8.60 15.40 1.80 16.20 7.90 35.5 FDR7783 12.03 15.82 1.32 17.86 7.46 37.9 0.33 3.1 Calculated assuming symmetrical distribution Hz = Hn[3 -(2Mn/aw)]. From references in ref. (5) and (14) and unpublished results. PREPARATION OF LABELLED DEXTRANS A sample of dextran (5-50 mg) was dissolved in sodium hydroxide (0.01 mol dm-3, 0.5 cm3), [3H]KBH, solution (10 mCi ~ m - ~ , 10 mm3, Radiochemical Centre, Amersham, Bucks) was added and the mixture was stored at 50 OC overnight.The solution was acidified with glacial acetic acid to destroy untreated borohydride and neutralised with sodium hydroxide (1 mol dm-3). The polymer was separated from tritiated water and salts on a Sephadex G-25 column. All preparations were then dialysed extensively against water except for the dextran T10 preparation, which was purified by repeated ultrafiltration with water as solvent using an Amicon UM0.5 filter (Amicon Corp., Mass.) at 2.8 kg m-2. A comparative analysis of the 7 m 5 5 r5 E 1 K,V FIG. 1.4hromatographic profile of [3H]FDR7783 (0) and unlabelled FDR7783 (0) on Sephadex 6BC1 (column dimensions 90 cm x 1.5 cm) in H,O.The [SH]FDR7783 fractions were monitored for radioactivity; 97.5 % of the initial counts placed on column were recovered. The unlabelled FDR fractions were monitored for hexose;lS 100% recovery was obtained for this sample.1212 DIFFUSION OF DEXTRAN distribution of labelled and unlabelled dextrans by gel chromatography revealed no significant difference (fig. l), suggesting that the labelling procedure does not result in any significant change in the molecular size distribution of the dextran. PREPARATION OF DEXTRAN SOLUTIONS Stock solutions of dextrans of known moisture content were made up by weight in either doubly distilled water or in 0.15 mol dm-3 NaCl. Samples for photon correlation spectroscopy were then centrifuged for 1.5 h at CQ.100000 g before being transferred with sterile syringes into the light-scattering cells. All transfers were performed in a dust-free flow cabinet. DETERMINATION OF DIFFUSION COEFFICIENTS MUTUAL DIFFUSION COEFFICIENTS Mutual diffusion coefficients were measured by free diffusion in a Beckman model E analytical ultracentrifuge using the Schlieren optical system (this technique will be referred to as the refractive index method, abbreviated as rim.). A solution of concentration C, was layered over a solution of concentration C, (with C, > C,) in a synthetic-boundary cell and the speed was reduced to ca. 5000 r.p.m. The concentration step, AC = C,-C,, was close to 5 kg m-3 for routine measurements. Diffusion measurements for solutions of concentration 2 kg m-3 were made with C, = 0.Diffusion was observed at 20 O C in cells with 0.5, 1.2 or 3.0 cm synthetic-boundary centrepieces. The apparent diffusion coefficients, D,,?, were calculated from the broadening of the Schlieren peak by following the change in width at the half-height. If the diffusion is followed by measurement of the broadening of the peak at (dn/t)x),,,,, denoted by T, then 2 Dapp = ( ?Q2/ 16t In 2 where t is the time. Values of Dapp were calculated from the slope of the plot of ( W)z against t. The assignment of Dapp as a parameter describing some average diffusion coekcient for a FIG. 2.-The mutual diffusion coefficient of FDR7783 obtained by r i m . as a function of the difference in concentration across the boundary AC for the mean dextran Concentration maintained at a constant value of 35.5 kg m-3 (V) and 10.1 kg m-3 (A).The values represented by the curve (0) have been obtained by keeping the concentration of dextran C, constant at 35.5 kg m-3.PRESTON, COMPER, HUGHES, SNOOK AND VAN MEGEN 1213 polydisperse system (such as the dextrans used in this study) is regarded as an approximation only. Yet experimental evidence cited below demonstrates that the effect of molecular-weight polydispersity of the sample on its diffusion coefficient suggests that this factor is of minor significance. We shall therefore make the assumption that Dapp is identical to the mutual diffusion coefficient, D, at the mean concentration16 C[ = (C, + cb)/2]. We have performed a limited number of experiments to estimate the error associated with this assumption for a system exhibiting concentration-dependent diffusion coefficients.Fig. 2 shows the variation of DaPp with AC studied at two different constant values of C, namely 10.1 and 35.5 kg m-3 for dextran FDR7783. (Note that this dextran has low-order polydispersity with &fw/Hn = 1.32.) At both mean concentration values, Dapp values decrease linearly with increasing AC. This is in contrast with the predicted variation of Dapp with (AC)2 for monodisperse material, as given by Gosting and Fujita." While the variation of D,,, with AC is found, the value of Dapp at C = 5 kg m-3 is only ca. 3% less than the value obtained by linear extrapolation to AC = 0. In view of this relatively small error, Dapp values measurcd at AC = 5 kg mP3 will be regarded as the mutual diffusion coefficient at the corresponding C value.It is evident from the variation in Dapp with AC (fig. 2) that there is no identity between Dapp and D, the mutual coefficient, for measurements performed at non-zero AC for concentration-dependent systems. In a further attempt to explore an identity of Dapp with the initial concentration on either side of the boundary, experiments were performed with cb constant at a value of 35.5 kg m-3 while AC was varied. In this case, an even more marked, non-linear dependence of Dapp on AC was found, although the extrapolated value of Dapp at AC = 0 for this series gave a similar value of Dapp to those obtained from experiments performed with C constant at 35.5 kg m-3. INTRADIFFUSION COEFFICIENTS These were measured following Park's modification18 of the open-ended capillary method.D* lD All runs were conducted in a water bath at 20f0.01 O C .At the end of the run, the capillary was removed, rinsed in water and the contents centrifuged directly into a vial for radioactive counting. The radioactivity was measured by standard counting techniques in a Packard Tri-Carb model 3003 liquid-scintillation spectrometer. No attempt was made to correct these diffusion coefficients for boundary phenomena, as suggested by Nanis et as the diffusion coefficients obtained by this technique were identical, within experimental error, to those obtained by other techniques.12 DIFFUSION COEFFICIENTS FROM PHOTON CORRELATION SPECTROSCOPY A Spectra Physics argon-ion laser (type 2600, A,, = 488.0 nm) was focused onto a scattering cell in a bath at ambient temperature (20 f 0.50 "C).Light-scattering fluctuations were detected by a Malvern precision device photomultiplier assembly type S/N 101 112 (with a D2608 E.M.I. photomultiplier tube). The output signal was correlated by a Malvern 72 channel digital correlator type K7023 operated in the scaling mode. The field autocorrelation function g(l) (K, z) of the Kth spatial fourier component is related to the diffusion coefficient D by the equation21 g(1) (K, z) = C-flDt. This treatment assumes that the solute is monodisperse, in whch case a plot of In [Ig(l)(K, z)l] against Kzz yields a straight line of slope -D. If the system is polydisperse there is no general theory relating molecular parameters to g(l) (K, t) for concentrated solutions.In this paper the correlation function has mainly been analysed by the method of cumulants. We have found that for the dextran concentrations studied the quadratic cumulant used suitably describes the experimental 23 (fig. 3). No depolarised scattering was observed for the samples studied, indicating that multiple scattering was insignificant. RESULTS A N D DISCUSSION DIFFUSION COEFFICIENTS AT INFINITE DILUTION (Do) The values of diffusion coefficients at infinite dilution were obtained by manual extrapolation of diffusion coefficients obtained at non-zero concentrations (outlined1214 DIFFUSION OF DEXTRAN 0 10 20 30 40 50 channel number FIG. 3.-(a) Variation of the field, autocorrelation function with channel number (sample time 1.85 ps per channel) for dextran FDR7783 at a concentration of 28.0 kg m-3.Experimental data (a), quadratic cumulant fit (-). (b) As (a) with dextran FDR7783 at a concentration of 132 kg m-3. below), as we have no prior knowledge of the manner of their concentration dependence. The results obtained from the three techniques used, i.e. r i m . , P.C.S. and intradiffusion, are presented in table 2. The error associated with measurements of r.i.m. and P.C.S. was < 5%. However, owing to the relatively strong concentration dependence of 0: values at low concentrations (outlined below), the error in the (D +)o values was near 10%. The Do values obtained by r i m . and P.C.S. (table 2) were found to be in excellent agreement. For the range of polydispersity encountered with these samples, the diffusion coefficients are relatively insensitive to the different weighted averages of Do that arise from r.i.m.and P.C.S. Since gel-chromatographic analysis did not reveal any clear indication of degradationPRESTON, COMPER, HUGHES, SNOOK AND VAN MEGEN 1215 TABLE 2.-DIFFUSION COEFFICIENTS AT INFINITE DILUTION diffusion coefficient (Do)/ 10-l' m2 s-l dex tran from classification from r.i.m. from P.C.S. intr diffusion T10 9.9 8.9 10.9 T20 6.7 6.7 T70 3.5 3.3 4.5 Tl5O 2 . 2 2.2 3.7 FDR7783 2.19 2.2 3.7 of the dextran following the labelling procedure, it is suggested that the difference between ( D + ) O and Do may be due to a non-uniform distribution of label in the preparation. Scaling the values of Do obtained from r i m .gives the relations DO = (1 -62 & 0.07) x 10-4j@;0-552( k0.005) DO = (1.15+0.50) x 10--4M-0.543(+0.045) and Do values from P.C.S. gives the relation D o = (1.17+0.3) x 10--4&f--0.521(k0.021). In the latter case, values of the exponent are found to be higher than that obtained from the P.C.S. data of Sellen24 on the diffusion coefficients of dextran in dilute solution, where he obtained an exponent value of 0.45. These differences are probably within experimental error, as his Do values are similar to those obtained in his study. The most significant difference between our data and Sellen's corresponds to measurements on the T10 sample. As pointed out by Sellen,24 his relatively lower values of Do for low-molecular-weight dextrans are probably the result of inadequate clarification of his samples. We have also found that clean preparations are absolutely necessary to arrive at a reproducible value for D as measured by P.C.S.The theoretical value of the molecular-weight exponent evaluated by various theoretical treatment^^^ is 0.6, which is reasonable agreement for value for dextran in this study. CONCENTRATION DEPENDENCE ON THE INTRADIFFUSXON COEFFICIENT The concentration dependence of the intradiffusion coefficient, D:, of [3H]T10, [3H]T70 and [3H]FDR7783 is shown as a log-log plot in fig. 4. The intradiffusion coefficient decreases significantly with increasing dextran concentration for all dextran samples studied. An approach to the interpretation of DF is through the treatment of de Gennes.This treatment predicts that above a critical concentration, C*, the flexible polymer chains begins to entangle. Calculation of C* may be made through eqn (5). The values of RG have been obtained through the relationships Do = RTl5.11 x 61q0RGN where qo is the solvent viscosity and Nis Avogadro's number. Values of hydrodynamic radius R, have been obtained from the Stokes-Einstein expression. The calculated values of RG are in good agreement with the measured value of R, for dextran obtained by Granath28 (see table 3). The use of R, to estimate C*, as suggested by1216 DIFFUSION OF DEXTRAN I 0.6 0.8 l m 0 8 0 m o 9 ' 0 8 0. o o 00. 1.0 1 I 0 I I 0 10 100 C/kg rne3 FIG. 4.-A log-log plot of the reduced intradiffusion coefficient D;/(D;)" for tritium-labelled dextrans T10 (a), T70 (0) and FDR7783 (m) against dextran concentration. Adam and Del~anti,~' gives too high a range of C* values.de Gennes predicts that the intradiffusion coefficient, Or, should be independent of concentration up to a value approaching C* and above C* should follow the relationship 0; K C-1.75. This behaviour is commonly handled with a log-log plot as in fig. 4, for which the critical C* is identified with an apparent discontinuation of the variation of 0; with C.Jt is emphasized, however, that such analysis has come under criticism,2s as the nature of the plot lends itself to ambiguous interpretation. In any case, in pursuing the de Gennes treatment we find (contrary to expectations) that 0; values certainly exhibit coilcentration dependence below the critical concentrations evaluated in table 3.In fact, the relative change of 0; with concentration appears maximal at a concentration of 0-30 kg m-3 for T70 and FDR7783. The scaling treatment as applied to the results in fig. 4 is inconclusive as (a) deviations from linearity in the plots appear at relatively high concentrations and (b) the value of the exponent, when an attempt is made to linearise that data, is in the range of 0.7-0.8 for the various dextrans; this value is considerably lower than would be predicted for the movement of a flexible polymer. We also note that the magnitude of the exponent is not sensitively related to the chemical composition and flexibility of molecules under study. Similar values of thePRESTON, COMPER, HUGHES, SNOOK AND VAN MEGEN 1217 TABLE 3.-ESTIMATES OF THE CRITICAL CONCENTRATION, c*, FOR DEXTRANS C*/kg m-3 dextran classification RG/nm R,/nm rangea (RG) rangea (Rh) T10 3.26 2.16 1 18-498 407-1 716 T20 4.83 3.20 7 1-300 256-1030 T70 9.24 6.12 35-146 120-503 FDR7783 14.76 9.78 20-8 1 67-28 1 a Range calculated from eqn (5). exponent have been obtained for the intradiffusion of poly(ethy1ene glycol) and poly(viny1 alcohol) (unpublished) and from a reanalysis of the intradiffusion of albumin.g Indeed the dynamic behaviour of these polymers closely parallels the predicted behaviour of the concentration-dependent movement of spheres and compact particles through networks, where the exponent has a value of 0.75. Experimental values in the range 0.6-0.65 have been obtained for the sedimentation of various spherical particles, including albumin, in poly(ethy1ene oxide) and the transport of albumin in hyaluronate networks30 when reanalysed on the basis of the scaling law.2g There has been one report by Hervet et aL31 which gave the predicted value of the exponent as 1.75 in studies of monodisperse polystyrene in benzene solutions by forced Rayleigh scattering.However, we draw attention to the earlier studies of Park,l* utilizing an albeit more polydisperse polystyrene sample in toluene, where an exponent value of 0.68 was found through measurements of intradiffusion using an open-ended capillary technique (as in this study). There is no clear reason why these two studies should yield such substantially different results. CONCENTRATION DEPENDENCE OF THE MUTUAL DIFFUSION COEFFICIENT COMPARISON OF DIFFUSION COEFFICIENTS OBTAINED BY R.I.M. AND P.C.S.Values obtained by r i m . of the mutual diffusion coefficients of the various dextran fractions, as a function of dextran concentration, are shown in fig. 5. The diffusion coefficients have been measured in solutions covering a concentration range from 1 to 250 kg m-3. For dextrans of molecular weight (uw) > 7 x lo4 a marked concen- tration dependence of D is evident ; with increasing concentration the mutual coeffi- cient becomes greater. On the other hand, for dextrans in the Mw range (1-2) x lo4 the mutual diffusion coefficient is essentially constant. For experiments utilizing similar solutions the diffusion coefficient obtained by P.c.s., as evaulated by the cumulant-fit method, for the various dextran fractions are included in fig.5 (a)-(& There is good agreement between the D values obtained by the P.C.S. and r i m . over the complete concentration range for the T10 and T20 samples, for higher-molecular-weight samples with C < 50 kg m-3, and particularly for FDR7783 at C > 50 kg m-3. In general, the good agreement between the D values obtained using P.C.S. as compared with the boundary relaxation r.i.m., for all four dextran samples measured over a wide range of concentration, immediately establishes the nature of the diffusion coefficient associated with the initial decay of the correlation function as that of a mutual diffusion coefficient. A similar conclusion can be made in the comparison 40 FAR 11218 DIFFUSION OF DEXTRAN l o b O 0 0 0 0 0 0 0 0 t I I I 1 I I I I 1 I 0 (cl 0 0 0 0 0 0 6 6 5 0 0 0.0 50 100 150 200 Clkg m-3 FIG.5.-The mutual diffusion coefficient D of dextran as a function of the mean concentration for dextran T10 (a), T20 (b), T70 (c) and FDR7783 (d): 0, values of the mutual diffusion coefficient obtained by rim.; 0, values of D obtained by P.C.S. as evaluated by second-order cumulant-fitting procedures. of the mutual diffusion coefficient of bovine serum albumin as measured in the ultracentrifuge9 and the diffusion coefficient obtained by quasielastic laser light-~cattering.~~ EFFECT OF POLYDISPERSITY O N THE DIFFUSION COEFFICIENT In that the P.C.S. and boundary relaxation methods yield two different types of average diffusion coefficient, the agreement between the two techniques remains remarkably good.While the prediction of the difference between the two averaged cgefficients is complex and difficult at this stage, the experimentally determined values from the two techniques demonstrate that these differences are not great for the polydisperse samples used in this study. This was confirmed by the P.C.S. analysis of two dextran samples, namely T150 and FDR7783, with approximately the same weight-average molecular weight (1 50000) but with very different values of M,/Mn (1.80 and 1.32, respectively). These results are shown in fig. 6. In this case, values of D for T150 were slightly lower than that obtained for FDR7783, particularly at higher concentrations.PRESTON, COMPER, HUGHES, SNOOK AND VAN MEGEN 1219 v v o 0 0 0 8 0 0 50 100 Clkg m-3 FIG.6.-The effect of polydispersity on the diffusion coefficients, D, obtained by P.C.S. The values of D evaluated by the cumulant-fitting method for dextran T150 and FDR7783 are represented as ('I) and (a), respectively. INFLUENCE OF CONCENTRATION We have provided evidence in this paper that the concentration dependence of the mutual diffusion coefficient of dextran in a good solvent is a function of the molecular weight of the sample. Dextran preparations of T10 and T20 showed effectively no concentration dependence, whereas T70 and FDR7783 exhibited an increase in D with increasing concentration. On the other hand, all the dextran preparations exhibited a marked decrease in the intradiffusion coefficient Dr with increasing concentration.The C* values theoretically predicted and given in table 3 appear too high as applied to the T70 and FDR7783 dextrans. We find no evidence to suggest a 'critical' crossover point between dilute and semi-dilute regions for D measurements outlined in fig. 5. In utilizing the scaling law for mutual diffusion, D cc C", the value of the exponent v is approximately zero for T10 and T20,0.27 for T70 and 0.29 for FDR7783. The values of the exponent are considerably lower than predicted (v = 0.75) for 'cooperative diffusion ' associated with semi-dilute polymer Knowing the virial coefficients of dextran from table 1, we may evaluate the reduced quantity (D/D;t)calc from eqn (4). The variation of the predicted value of (D/Dt)calc is a continuously increasing quantity with increasing dextran concentration.Note that in this evaluation the third virial coefficient dominates the magnitude of the reduced parameter at concentrations > ca. 50 kg m-,, so that the quantity (D/Dt)calc is extremely sensitive to errors in A,, a parameter which is intrinsically difficult to measure. The experimental measurement of the reduced parameter (D/Dt),,p, may be compared with (D/D;t)calc in order to test eqn (4). Owing to the difference in ( D + ) O and Do values outlined in table 2, we have estimated the normalized reduced parameter DID: x (D;t)"/D0 to compare with (D/Dt)calc. For T10 dextran [fig. 7(a)] excellent agreement is obtained between these two reduced parameters up to a concentration of 150 kg m-3.On the other hand, we find for the higher molecular weight dextrans, 40-21220 DIFFUSION OF DEXTRAN 0 50 100 150 0 50 100 Clkg m-3 Clkg m-3 FIG. 7.-Variation of DID;' against dextran concentration for dextran T10 (a), T70 (b) and FDR7783 (c). The solid line is the estimate of (D/Dl+)celc with the use of virial coefficients in table 1 and eqn (4). The use of D from rim. was made in the estimate of DID: x (D;')O/D0 [ =(D/Df),,,J. These values of (D/D:)expt are presented as (0). the parameter D/D: x (D;t>,/Do is consistently less than (D/D;t),,l,. Similar findings were made by ,Laurent el aZ.l0 These authors qualitatively suggested that this discrepancy was the result of the inconsistent use of different averaged parameters describing molecular weight, virialcoefficientsand diffusion coefficients forpolydisperse samples of dextran.However, this observed discrepancy together with conclusions on the scaling treatment of 0;' may also suggest that the value of 0;' is too high for T70 and FDR7783 or that the assumptions involved in the derivation of eqn (4) are not valid for these polymers.PRESTON, COMPER, HUGHES, SNOOK AND VAN MEGEN 1221 This project was supported by the Australian Research Grants Committee (grant nos. D68/16898, D2 73/14137, B78/15168 and DS 79/15252). We acknowledge the expert technical assistance of Gregory Checkley, Wayne Connors and Geoffrey Wilson. W. D. Comper and T. C. Laurent, Physiol. Rev., 1978, 58, 255. B. N. Preston, T. C. Laurent and W. D. Comper, in Glycosaminoglycan Assemblies in the Extracellular Matrix, ed.D. A. Rees and S. Arnott (Humana Press, to be published). J. G. Albright and R. Mills, J. Phys. Chem., 1965, 69, 3120. R. J. Bearman, J. Phys. Chem., 1961,65, 1961. A. G. Ogston, Arch. Biochem. Biophys., 1962, suppl. 1, 39; E. Edmond and A. G. Ogston, Biochem. J., 1968, 109, 569. H. Yamakawa, Modern Theory of Polymer Solutions (Harper and Row, New York, 1971). ' R. Bergman and L. 0. Sundelof, Eur. Polym. J., 1977, 13, 881. L. 0. Sundelof, Ber Bunsenges. Phys. Chem., 1971, 83, 329. R. G. Kitchen, B. N. Preston and J. W. Wells, J. Polym. Sci., Polym. Symp., 1976, 55, 39. lo T. C. Laurent, L. 0. Sundelof, K. 0. Wik and B. Warmegird, Eur. J. Biochem., 1976, 68, 95. M. Daoud, J. P. Cotton, B. Farnoux, G. Jannink, G. Sarma, H. Benoit, R. Duplessix, C. Picot and P. G. de Gennes, Macromolecules, 1975, 8, 804. l2 R. G. Kitchen, Diffiion in Model Connective Tissue Systems (Thesis) (Monash University, 1975). l3 P. G. de Gennes, Macromolecules, 1976,9,587; and review article, P. G. de Gennes, Nature (London), l4 E. Edmond, S. Farquhar, J. R. Dunstone and A. G. Ogston, Biochem. J., 1968, 108, 755; H. Vink, l5 W. E. Trevelyan and J. S. Harrison, Biochem. J., 1952,50, 298. l6 J. M. Creeth, J. Am. Chem. SOC., 1955, 77, 6428. L. J. Gosting and H. Fujita, J. Am. Chem. Soc., 1957, 79, 1359. G. S . Park, Symp. Macromolecules, IUPAC Meeting, Weisbaden, 1959, vol. 11, paper AS. 1979, 282, 367. Eur. Polym. J., 1971, 7, 1411. lD J. S. Anderson and K. Saddington, J. Chem. Soc., 1949, S381. 2o L. Nanis, M. Litt and J. Chen, J. Electrochem. Soc., 1973, 120, 509. 21 R. J. Pecora, J. Chem. Phys., 1968, 49, 1036. 22 M. B. Weissman, J. Chem. Phys., 1980, 72, 231. 23 P. N. Pusey, Milan ConJ Light Scattering Fluids of Macromolecular Solutions, ed. V. Giogo, M. Corti and N. Cigilio (Plenum Press, New York, 1980); K. Gaylor, I. Snook and W. van Megen, J. Chem. Phys., 1981, 75, 1682. 24 D. B. Sellen, Polymer, 1975, 16, 561. 25 M. Daoud and G. Jannink, J. Phys. (Paris), 1976, 37, 293; S. F. Edwards, Proc. Phys. SOC., 1965, 28 K. Granath, J. Colloid Sci., 1958, 13, 308. 27 M. Adam and M. Delsanti, Macromolecules, 1977, 10, 1229. 28 G. D. Patterson, J. P. Jarny and C. P. Lindsay, Macromolecules, 1980, 13, 668. 29 D. Langevin and F. Rondelez, Polymer, 1978, 19, 875. 30 T. C. Laurent, and A. Pietruszkiewicz, Biochim. Biophys. Acta, 1961, 49, 258. 31 H. Hervet, L. Leger and F. Rondelez, Phys. Rev. Lett., 1979, 42, 1681. 32 B. D. Fair and A. M. Jamieson, J. Colloid Interface Sci., 1980, 73, 130. 85, 613. (PAPER 1/859)