GENERAL DISCUSSION Dr. M. J. Blandamer (University of Leicester) said: The two-phase model for water in aqueous gels as discussed, for example, by Derbyshire and Duff is supported by the kinetics of aquation of an iron(I1) complex, specifically the Fe(5-NO,-phen) + cation, in water, sol and gel systems (fig. 1). Previous work has shown that the rate constant for this aquation is sensitive both to added salt (e.g., potassium bromide and tetra-n-butylammonium bromide) and added co-solvent (e.g., t-butyl alcohol). However, the data reported here,l (fig. 1) indicate that in so far as the kinetics are concerned, the reactant in the gel system is present in an aqueous phase where the local solvent structure closely resembles that in ordinary water. -2.01 + -4.0 3.2 3.3 3.4 3.5 103K/T FIG.1.-Dependence of first order rate constant, k, on temperature for the aquation of tris-(5-nitro- l,l0-phenanthroline) iron(I1) in water (a), 0.1 % agar sol (x), 0.2 % agar gel (O), 1 % gelatin solution (0) and 3 % gelatin gel (A). (Kinetics obtained from spectra at 475 nm in systems con- taining -2 x mol dm-3 iron complex and 0.2 mol dm-3 NiS04 or ZnS04). Prof. P. L. Indovina (Rome) said: I have two remarks concerning the paper of Duff and Derbyshire. The first one has to do with the hydration value. In your paper you compare the amount of hydrated water in the agarose+ water system with the value obtained by Woessner and others (ref. (12)). But Woessner performed his measurements in the agar + water system so that the value of the hydration in the agar + water may be quite different from the agarose + water system.Furthermore, one has to remember that agar is a rather complex substance containing also agaro- pectine and several ions in appreciable concentration. Unpublished work by Dr. L. Guidoni and myself shows that the shape and magnitude of n.m.r. line width associa- ted with gelling processes is quite different in agar + water and agarose + water systems. M. J. Blandamer, J. Burgess and J. R. Membrey, unpublished data. 275276 GENERAL DISCUSSION Measurements are in progress in order to show the nature of this difference and the effect of ions present in controlled concentration. The second remark concerns some possible limitation of the exchange model. You interpreted your results using an exchange model based on the two-phase theory (bound water and free water) and I agree with you on the presence of the exchange but, in order to explain the sol-gel transition and the hysteresis it is necessary in my opinion to consider some cooperative effects.These effects are supposedly responsible for the onset of “gelled water phase ”. At this onset a diversification of correlation frequencies occurs as shown in the work by Dr. E. Tettamanti and myself quoted in a paper presented at the Inter- national Conference on Physicochemical State of Ions and Water in Living Tissues and Model Systems, held by the New York Academy of Sciences on January 10,ll and 12, 1972. This paper (published in Ann. N. Y. Acad. Sci., 1973,204,134) by Prof. M. U. Palma and his group contains serious misprints; corrected copies may be obtained from the authors.Prof. W. Prim (Syracuse University) said: I have two comments on the paper by Segeren et al. : (1) the application of a x value determined in dilute solution, to gel-data at much higher polymer concentration is rarely found to be reliable. The parameter x is only a semi-empirical one and often depends strongly on the Concentration. A better procedure would be to measure both equilibrium swelling and modulus. This will yield both x and M, according to accepted ideal gel-theory. After calibration in this way for x, swelling measurements can subsequently be used to determine M,. (2) I would suggest that measurements of the birefringence as a function of time be undertaken to determine the extent of rearranging taking place among the non- covalent crosslinks during stress relaxation.Dr. A. J. M. Segeren (Unilever) said : What Prins proposes is essentially another method of interpreting the same experimental data. This will, however, give no better reliable values for x, because of the finite extensibility of the chains. At lower cross-link densities the suggestion will be helpful, but what is needed here is a gel theory accounting not only for finite extensibility but also for variations in the number and strength of cross-links by deformation or swelling. Optical studies are being considered as a possible tool in further work. Prof. P. J. Flory (Stanford) said: The constants A and B in the theoretical equation of state for the elasticity of an ideal tetrafunctional Gaussian networks should equal t .This holds, however, only for tetrafunctional networks. Larger values are predicted for both A and B for networks of greater functionality, such as would be formed by aggregation of two-strand helices. In support of Prins’ comment, it is certainly well established that the parameter x depends on composition. Hence, in applying the swelling equation for the estimation of the degree of cross linking one should indeed use the value of x applicable at the concentration occurring in the gel. Recent work in our laboratory demonstrates accurate agreement between x values from the swelling equation (for networks of polyisobutylene and of poly-dimethylsiloxane) and those obtained from chemical potentials of solutions of the corresponding linear polymers at the same concentration.However, for the complex systems investigated by Segeren, Boskamp and van den Tempel, which must necessarily be treated in approximation, the refinement probably is not of importance. see e.g., M. llavsky and W. Prins, Macromolecules, 1970, 3, 315 ; M. Ilavsky and W. Prins, Macromolecules, 1970, 3, 425.GENERAL DISCUSSION 277 Dr. A. J. M. Segeren (Unilever) said : We are convinced that our estimates have no exact molecular significance, and we have used them only in comparative studies. Prof. M. Gordon (University of Essex) said : In this paper, Segeren et al. argued that rubber elasticity theory is inapplicable to very lightly cross-linked (critically branched) gels. As I suggested after the paper by Beltman and Lyklema, all that is needed to render it applicable, is to generalise the notion of elastically active network chain (EANC) as suggested by Scanlan and by Case.Not only is the theory applic- able, but as Dobson and Gordon pointed out, the critically branched region is the one most favoured for verification of rubber elasticity theory for the following reasons : (1) The mean length of EANC’s diverges to infinity as cross-link density is reduced back to the gel point. In the present instance of the cross-linking of primary chains, a Scanlan-Case type of EANC is not confined to a segment between two neighbouring cross-links on a primary chain, but extends over numerous primary chains and cross- links. (Of course, at high cross-link density the Scanlan-Case EANC will converge to the usual notion of a segment between neighbour cross-links).The divergence of the mean EANC length guarantees that Gaussian chain statistics are an excellent approximation (as found). The finite-extensibility theory for interpreting fig. 2 then needs reconsideration. (2) The concentration of non-relaxable entanglements is proportional to the square of the EANC concentration, and goes to zero as cross-link density is reduced towards the gel point. We may add : (3) The critically branched region is richest in information because of the non- linearity of relevant response effects-see my remark to Smidsrard’s paper. Dr. A. J. M. Segeren (Unilever) said : Our interpretation of fig. 2 relies not only on finite extensibility theory, but also on an increased number cross-links by shear.We agree that studies in the critically branched region will be helpful, and we intend to do more work at the gel point. Dr. D. J. Walsh (University of Manchester) said: Eqn (1) and (2) in the paper by Segeren et al. are based on equations for the free energy of deformation of a network which is not strictly proven. Also they have ignored the effect of network defects. The molecular weight between crosslinks and other para meters calculated based on this treatment might well be out by a factor of 2 or 3 depending on the equations used and assumptions made. When quoting a value of M, one must state the particular equation on which the estimate is based. This should then only be used for comparative studies and not be expected to have any exact molecular significance.Mr. H. Beltman and Prof. J. Lyklema ( Wageningen) said : Segeren’s explanation of the curve in fig. 2 is based on the formation of more and stronger crosslinks under stress. If this picture is correct one would expect hysteresis in the stress-shear experiment behaviour. Was such hysteresis observed? Dr. A. J. M. Segeren (Unilever) said : Our stress-strain experiments were carried on until the gels broke down; no hysteresis has been measured. It would certainly be of interest to study such hysteresis (or rather : time-) effects in connection with the proposed mobility of cross-links.278 GENERAL DISCUSSION Mr. H. Beltman (Wageningen) said : (1) Flory found for butyl rubber, as we did for PVA-congo red gels, a dependency of the modulus of ridgidity on the number average DP(DP,).It is easily understandable tha.t the number of network defects (chain ends) is a function of the number of molecules. That DP,, in fig. 8 of Smidsrard’s paper, nevertheless stands in relation with G, is due to the fact that between DP, and DP, may be a rather fixed ratio. Very likely DP, will give a much better fit of the curve, while G, plotted against DP; will give a straight line. (2) In a paragraph below fig. 6 he attributes the higher volume of gels with MG- blocks to the higher water binding capacity of these blocks. However, in general water binding does not play an important role ing gelling, usually only a small amount of water ( < 5 %) is adsorbed at the molecule. One can doubt if the difference between MM, GG and MG blocks in water binding capacity is great enough to explain the difference of gel volume.An alternative interpretation could be that MG blocks are not able to form junction points, hence increase the percentage of chain elements between the crosslinks, leading to a less compact gel. Dr. 0. Smidsr+d (University of Trondheim), said: In answer to Beltman; (1) We have measured the weight average degree of polymerization by light scattering, and the number average degree of polymerization (in the lower range of molecular weights (by analysis for end-groups1 In the range where we have both DP, and DP,-measure- ments, the ratio DP,/DP,, appears constant with a value of 3. This is reasonable from the known difference in the rate of hydrolysis of the different glycosidic linkages in alginate and from our knowledge of the block structure in alginate.Since DP, can be obtained over a wider range and with much higher accuracy than DP,, we have chosen to correlate the modulus with DP,. Exact determination of the molecular weight distribution for these non-randomly degraded alginate samples would be of interest, not only in connection with fig. 8, but also because it can yield information about the block structure. Gel filtration experiments carried out by Kirsti Granath, at Pharmacia AB, Uppsala, Sweden, are promising in this re~pect.~ For two different alginate samples differing widely in molecular weight she got DP,JDP, close to 3. (2) In the paragraph below fig. 6 I am saying that the function of the MG blocks probably is more to bind water than to form junctions.I am not thinking of firmly bound water. Some preliminary n.m.r. studies on alginate gels suggest that only a few water molecules per monomer unit are firmly bound to the alginate chain. We have no reason to suggest that these few water molecules contribute much to the total volume of the gel. We also at present know nothing about any different tendency of the three blocks in binding water molecules firmly. My suggestion was based on the thought that since the MG-blocks are more flexible, the entropy of mixing would be large compared to the MM-blocks, and that this could explain the higher volume of gels of alginate rich in the MG-sequence. Ir. Th. H. M. Snoeren (Netherlanh Institute for Dairy Research) said: I should like to make some comment on Smidsrard’s communication dealing with alginates in the gel state and his remark about the close resemblance between alginates and carra- geenan s .Recently I have characterized fractionated kappa-carrageenan samples in the 0. Smidsrsd and A. Haug, Acta Chem. Scand., 1968,22,797. K. Granath, personal communication. H. Grasdalen, I. Svare and 0. Smidsrsd, to be submitted to Actu Chem. Scund. * 0. Smidsrsd, B. Larsen, T. Painter and A. Haug, Acta Chem. Scand., 1969,23, 1573.GENERAL DISCUSSION 279 molecular weight range from 17 OOO to 700 OOO by physical methods such as light- scattering, viscosimetry and ultracentrifugation. The kappa-carrageenan samples were obtained from different sources. For the relation between the intrinsic viscosity and the weight-average molecular weight obtained by light scattering I found which suggests that the kappa-carrageenan molecule in a 0.12 ionic strength solution (NaCl) behaves as a rather stiff random coil.In agreement with this conclusion the light scattering second virial coefficient was found to decrease slightly with increasing molecular weight. At a molecular weight of 700 000 the value of this parameter was found to be 1.8 x From the molecular weights and the radii of gyration measured, the length of the Kuhn statistical segment was calculated to be about 300 A at 0.12 ionic strength. By application of the Rice-Harris theory the electrostatic expansion of the polyelectrolyte was found to be completely suppressed at this ionic strength, which indicates that the relative high value of the segment length is due to the bulkiness of the poly- saccharide skeleton.From the intrinsic viscosities and the root-mean-square end-to-end distance of the molecule the so called Flory viscosity constant 4 was calculated. This parameter was found to increase with molecular weight and at molecular weight at 700 000 its value is 0.4 x lo2'. This indicates a more or less free draining coil. [r](lOO ml g-l) = 1.39 x M$*93 mol cm3 g-2. Comparison of viscosity and sedimentation data yields 1 /S*(ds/dc)/[q] = 0.53 which in accordance with the theory of Creeth and Knight indicates again an extended molecule with a stiff and free-draining conformation. The molecular characteristics of the kappa-carrageenan, therefore, appear to resemble closely the alginates.Dr. J. W. Janus (Kodak) said : The fact that the rigidity of a polymer gel increases as the molecular weight increases is a wholly insufficient ground for assuming that the elasticity is entropic. The chance of association of macromolecules will obviously increase as their length increases. It is, thus, difficult to imagine any kind of gel structure which will not show a molecular weight dependence of this kind, at least in the low molecular weight region. Rubber-like or flexible single chain networks do have properties which distinguish them from other structures, for example, the positive temperature coefficient of elasticity. These criteria should be applied before claiming performance in accord with rubber theory.In fact, I know of no aqueous system which conforms to the thermodynamic behaviour of rubber elasticity except in rather atypical and narrow ranges of conditions. The more we learn of aqueous gels through direct study, such as electron microscopy, confirms the presence of fibrils and other structural elements to which molecular network theory is no longer appropriate. Prof. P. J. Flory (Stanford) said: Contrary to the Janus contention, the results presented in Smidsrard's fig. 8 are of the form to be expected if the concentration of cross-linkages is fixed while the primary molecular weight is increased. The results, therefore, support the explanation given by Smidsrard. Dr. 0. Smidsr+d (University of Trondheim) said: In response to Janus' doubt concerning the significance of the results in fig.8 I should like to mention that very280 GENERAL DISCUSSION similar results have been obtained with an alkaline modified K-fraction of carrageenan prepared from Chondrus crispus. The results are given in fig. 1 together with the results on alginate. The difference between the maximum values of the modulus in the two cases could be thought to have its origin in a difference in flexibility among the two 1000 2 0 0 0 DPW FIG. 1.-Modulus of rigidity, Gc= 3, against weight average degree of polymerization, DPw. x , Alginate from Laminaria digitata in 0.34 M CaCl, ; a, alkaline modified K-carrageenan in 0.1 M KCl. chains, and a student at our Institute, Knut R u t h , has studied the relationship between [qJ, RG and Mw for the Ic-fraction in order to characterize the extension of the chain.In the molecular weight range between 10 000 and 170 000 the following Mark-Houwink relation was obtained in 0.1 M LiI [q](100 ml/g) = 2.4 x MgQ8. The plot of log[q] against log Mw had some curvature above Mw = 170 000, indicating a lower exponent for the high molecular weight samples. For a sample with Mw = 500 000 we obtained [q] = 6.6 and RGz = 1500 A. This corresponds to a Kuhn statistical segment length, A , = 390 A, and a Flory constant, @ = 0.3 x The second virial coefficient was found to be 1.7 x Those values are very similar to those previously obtained for the alginate sample used in fig. 1, suggesting that the difference between the gel strengths instead is due to a difference in the number or the strength of the junctions in the two substances.Prof. M. Gordon (University ofEssex) said: With reference to fig. 8 of Smidsrard’s paper, we easily discern two regions : a final long horizontal region and the initial steeply ascending region. The latter is more interesting, because full of information. It is the critically branched region of the gelation process. The dialysis procedure ensures that the number of cross-links is held constant, while DP, of the primary chain is varied along the abscissa. When this DP, is very low, but high enough to produce a gel, most of the cross-links introduced into the material are still wasted from the point of view of elastic response. Thus the initial steep rise in fig. 8 is theGENERAL DISCUSSION 28 1 counterpart to the slow initial rise of modulus against cross-link density in fig.6 of Covas et al., fig. 7 of Burchard et al., or, in my interpretation, of the related bottom plot in fig. 4 by Beltman and Lyklema (all in this Discussion). The gel point, where Smidsrard’s curve starts in fig. 8, plus the ascending part of the curve, have in principle ample information for fitting one additional parameter, viz. the mean number of Ca2+ involved in a cross-link. Prof. F. Franks (Unilever) said: In summarizing the Discussion and introducing the final Discussion session it strikes me how relevant has been Flory’s classification of gels, all four types have been described in the papers presented at this meeting. Broadly speaking the problems discussed can be divided into two groups-those associated with the ideal, covalently linked networks and those dealing with non- covalent, reversible gels.Interest in the former group has centred on the properties of ideal networks, possibilities of achieving ideal cross-linked polymeric systems and ways of allowing for deviations from ideality, e.g., loops and entanglements. This has led to attempts to define the critical branched state and particularly to more detailed studies of the dynamics of polymer chains and networks. Quantitative treatments of non-covalently linked gels are not yet at an advanced stage of development, one of the main concerns relates to the mechanisms whereby non-covalent junction zones are formed, and their proper characterization. These gels are thermally reversible and do not only swell but dissolve in excess solvent, and they are often solvent-specific. The types of cross-links are diverse, highly specific and of finite length. From my reading of the two days’ Discussion several important unresolved problems stand out : 1. Development of modifications of classical (entropic) theories relating the rheological properties of a network and its geometry and topology, to make these treatments applicable to reversible gels. 2. Mechanisms involved in the intramolecular processes which turn apparently random polymers into gel precursors ; specific solvent and ion effects. 3. A theoretical treatment of the critically branched state. 4. Topological problems associated with polysaccharide reorganization during 5. Effects of polydispersity on the thermodynamics of gel formation, e.g., the 6. A microscopic description of reversible gel cross-links and the solvent implica- gelling. concept of the van’t Hoff average molecular weight. tion in the necessary conformational rearrangements.