GENERAL DISCUSSION Dr. I(. DuSek (Czechoslovakia) said: (a) The indentation method for measuring the elastic moduli of gels is very simple and could be used in cases when other methods fail. I wonder whether the dependence between the load and indentation depth has been examined in terms of the free energy change of rubberlike networks bearing in mind that the local stresses may be quite high. Is the experimental ratio P/d* inde- pendent of d and what is its dependence on the degree of swelling? (b) The relation between the concentration of elastically active network chains (EANC), v, and the concentration of elastically effective crosslinks (EEC) in eqn (2) v = 2n may lead to a confusion for real systems with free chain ends. Some EEC give rise to three and others to four EANC, contributing thus by 3 and 3, respectively, to the number of EANC (cf. e.g., Dobson and Gordon, J.Chem. Phys., 1965,43,705). The correction to v in the form of eqn (5) is then valid only in the close vicinity of the gel point where all EEC are effectively trifunctional. With regard to the paper by Beinert et al., it seems to me that the deactivation of living ends in model polystyrene-divinylbenzene networks by a monofunctional termination agent (methanol) produces dead ends in divinylbenzene units and thus lowers the effective functionality of the crosslink. If, e.g., two living ends of poly- styrene chains reacted with a divinylbenzene molecule, this branch point would become bifunctional after deactivation with methanol, i.e., elastically ineffective.Would the results be different if one used a bifunctional termination agent, capable of joining two living ends of divinylbenzene units? Dr. D. J. Walsh (University of Manchester) said: (a) A lot of work has been done on this method of measuring modulus by people at the Malayan Rubber Producers Research Association in Welwyn Garden City, who find it to give answers in good agreement with other methods. We have done relatively little but think that as very small deformations can be measured, and the stress may be spread through a large part of the sample, the local stresses need not be very high. We have found the ratio P/d3 to be independent of d, which is an important point, but as we always prepare and test samples at one concentration we have no information of the effect of swelling.(b) I agree that other authors would suggest a smaller chain end correction than that calculated by Flory. Having looked into this I agree that these may be more justified. However, an alteration in the size of this correction term would have only a small effect, certainly within the limit of other uncertainties, and would not sub- stantially alter the interpretation of the results. This alteration would also take the results slightly further away, rather than sligbtly nearer to the alternative value of A = 1. Dr. J. Herz (Strasbourg) said: The answer to Dugek is no. The addition of the terminating-agent (methanol or any other ‘‘ proton donor ”) takes place when the crosslinking reaction is completed and the gel already formed. The remaining carbanionic groups are all located within the crosslinked polydivinylbenzene nodules.Deactivation of these “ living ” groups by protons cannot change the structure of the gel nor introduce, at this stage, supplementary pendent chains. Moreover the termination reaction by bifunctional or by monofunctional proton- donor is the same. Coupling reactions by bifunctional terminating agents as C0Cl2 3536 GENERAL DISCUSSION or dichlorodiniethylsiloxane should not modify the structure of the gel, since they would merely introduce further links within each nodule, and not between them. Prof. M. Gordon (University of Essex) said: Two remarks on the statistical importance of short chain segments: first random cross-linking leads to a most- probable (Flory-) distribution of segments between cross-links, in which short segments have high probability.Secondly, the situation may be illustrated by calculating the average over all cross-links of the ratio of the longest to the shortest among the four chain-segments which issue from a cross-link. (The model adopted is merely that of lightly cross-linking long primary chains). This ratio turns out to be quite high-may I challenge the audience to estimate it? Prof. W. Prim (University of Syracuse) said : Ten. Prof. M. Gordon (University of Essex) said: Yes, it is of this order. The exact value is 8-s. Very short chains will constitute a kind of network flaw. The synthetic procedures by Beinert et al. (this Discussion) avoids these. One would expect the greatest effect of their improved networks to be felt mostly in ultimate properties, where the short chains become highly strained.Dr. D. J. Walsh (University of Manchester) said : I agree with Gordon that very short chains will act as a defect, the effect of which on the modulus is difficult to esti- mate. One could estimate for instance for a system with number average degree of polymerisation between crosslinks = 150, what fraction of the chains are below 50 units long. These could be less elastically effective but only the shortest of these would be completely ineffective. I think that the effect would not be large enough to alter the conclusions reached from my results. Also the smallest of chains would be more likely to be removed in the form of closed loop defects. I also agree that the effect on ultimate properties would be far greater but these have not been examined.Dr. R. F. T. Stepto (UMIST) said : The probabilities of ring formation, for rings of the smallest two sizes, as defined by expressions (7) and (8) of Allen’s paper, are incorporated into eqn (9) to (12) as essentially (1 - r l ) (1 - r2), where r1 and r2 represent expressions (7) and (8). It would appear that the relationship between rl and r2 is rather approximate. Although the mutual concentrations of a pair of groups able to form loops of the two sizes are proportional to iVi9 and (2N3-3, there will be pro- portionately more pairs of groups able to form rings of the larger size, and P in expression (8) should be larger than P in expression (7). Approximate calculation shows that, depending upon the degree of crosslinks, up to a 4-fold increase in P in expression (8) as compared to (7) could occur.Do the authors have any knowledge of how the relative values of rl and rz affect their interpretation of the results, in particular with regard to the comparison of the curves in fig. 2 and 3? Dr. D. J. Walsh (University of Manchester) said: To take up Stepto’s point, the relative size of r2 is not easy to estimate and will not be the same as in the case of the crosslinking of a trifunctional monomer. Using a simple approach I estimate that three times the number of sites are available for forming the second type of closed loop but that it only reduces the number of effective chains by 1 (as against 2 for the first type). One of the resultant chains is in effect 2 chains both linking two pointsGENERAL DISCUSSION 37 the effect of which is difficult to estimate. The larger closed loops are also more likely to entrap other chains thus contributing to the entanglements.The conclusion is that this part of the expression can only be approximate. Fortunately the effect of r2 is extremely small over the range considered, a fact which is verified by the experimental results on networks containing none of the first type of closed loops. Mr. H. Beltman and Prof. J. Lyklema ( Wageningen) said : There appears to be some analogy between Allen's results and ours. We have found that in the early stages of gelation the extent of wasting is proportional to the squared polymer concentration c2. From our eqn (12) a c2 dependency can also be inferred, at least if one neglects the Rc2 term due to entanglements and sets c22%N,3 P2 - - P c22%N (' - =:)(' - P + ( P + cNi)(P + cN;2+) for cN3 < P.Although Allen's derivation applies to a different stage in the gelling process we would nevertheless appreciate his comment as to whether or not the observed c2 analogy is fortuitous. Dr. D. J. Walsh (University of Manchester) said: The form of the expression would depend on the number of defects one wished to consider. If only the first order closed loop was considered, for example, a first order dependence would be obtained. The observation of Beltman and Lyklema may justify the use of the two types of closed loop. The approximation made in the expression will only be valid at con- centrations lower than those we have used.Dr. R. F. T. Stepto (UMIST) said: In addition to the many syntheses suggested in the paper of Beinert et al., it would seem that model networks, within the limits defined by the authors, could be made using conventional polycondensations, pro- vided that monomers (prepolymers) of large enough molecular weight are used. For example, poly(propy1ene oxide) triols of various molecular weights can be reacted with di-acid chlorides, or diisocyanates. The triols have well-defined chemical functionalities, and, within the limits of the Poisson distribution, equal chain lengths (of 100 bonds or more) between functional groups. The materials are commercially available, and hence appear to provide a relatively easy route to model networks. Can the authors see any disadvantages of such syntheses compared to those described in their paper? Dr. J. Herz (Strasbourg) said: The reaction of OH endgroups of well characterized star-shaped poly(propy1eneoxide) triols with the difunctional compounds mentioned by Stepto should indeed lead to interesting model-networks, provided exact stoichio- metry can be obtained, and assuming that the reaction with diisocyanates is free of side-reactions, which is not always the case.