A more convenient test method for testing the crosslinking density of thermosetting polymers

P.J. Flory
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used statistical techniques in its benchmark paper to associate the elastic mod of a rubber-phased polymer network with the number of effective elastic chains and to characterte the crosslink density of the polymer. The author also explains a method used to calculate an effective elastic chain link (v) based on rubber pre-polymer molecular weight (Mn) and reaction group molecular weight (Mc).
V s 2 (cross-link number) s v0 (1-2Mc/Mn)
This Mn correction comes from the fact that reaction groups on some polymers are involved in chain growth reactions in infinite long chains . In the intermediate state of this conceptualized infinite molecular weight, each prepolymer chain link reacts with 2 other prepolymer chain joints without a stereoscopic crosslinking reaction. Only the chain grows and only one effective elastic chain. Other reactions will form the intersection within this infinite long chain. He points out that all crosslinking reactions occur in the same (infinite) long chain, contradicting the argument that in-chain interlinking (in this case, within the same pre-cluster) has a weakening effect. Flory also discusses the non-participation of the overhanging chain at the end of the chain section in this model. However, he did not make additional corrections to the equations of its pre-polymer molecular weight and elastic mods for the end chains on these chains. In addition to this omission, Flory's hypothesis about the number of effective chains, or the intersection density and mod, obtains an excellent correlation and further corrects the molecular weight of the infinite long chain.
this, J. Scanlan
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continues to use statistical techniques to try to calculate the contribution of end chains formed during the chain growth phase, resulting in results that differ little from Flory's original predictive model. In the same article, Scanlan also began to calculate some probability of reacting to non-network strengthening.
D. R. Miller and C. W. Macosko
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the probability theory of Scanlan to the pre-cluster chain theory with different levels of official energy (f). They use statistical techniques as a basis for obtaining a programme for incomplete responses. However, in a 100% response, their conclusions were answered in the same way as Flory's original model. Non-network-enhanced reactions also require the creation of an infinite molecular weight. Graesley
the
the theory in his article , Advances in Polymer Technology.
L. W. Hill
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applied Scanlan, Miller and Macosko's research to thermo-solid coatings. However, the equation used by L. W. Hill does not contain a correction to the molecular weight of infinity. Finally, based on a single experimental data point, he suggests that corrections to polymer ernatic levels, such as infinity molecular weight, may be unnecessary.
same time, Berger and Huntjens
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developed an easier way to get closer to the approach that this article will propose.
to date, all methods require that the official energy of each polymer in the system is a known integer. Although this is always right at the molecular level, for most resins the distribution of molecular weight and ernatic groups results in an average official energy that is not an integer. In this paper, unlike the method of calculating effective elastic chains, the cross-linking of unit weights will be calculated directly based on the easy-to-use resin constant. If necessary, this result can be easily converted into an effective elastic chain molar number per unit volume, v/NV=2 (XLD)ρ, where, ρ is density, N is the Avogadero constant. Finally, we will compare our results with the methods mentioned in the foreword. We will also use the experimental data to re-verify the validity of the infinite molecular weight correction, and then we will extend this concept to UV curing coating systems and dynamic chain lengths.
the crosslink density discussed in this paper comes mostly from the correlation of high-elastic polymer stretching mods, as Flory did in 1944. In many cases, the crosslink density of these systems is 2-3 orders of magnitude greater than Flory's vulcanized polysoprene. However, the mod of the high-ballistic platform area is still associated with the estimated number of chains or crosslink density. The rationale of the Flory method shows that the structural entropy (and the resulting energy) of long-chain polymers increases linearly as the length of deformation increases. This is based on the use of a fewer purpose structures to complete the lift of the distance between the first and last ends. This linear relationship between distance and energy is a new Hook entropy spring.
although high-ballistic modality is often used to measure crosslink density, there is little interest in using it to measure coating performance, as most coatings are mostly used in transparent areas. However, cross-link density is also closely related to other properties. Most importantly, due to its impact on chain mobility and thus on the glass transition temperature Tg,
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. Other important properties include break energy
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and plastic flow grades of
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.
model of a thermosolytic polymer
For thermosolytic polymer, the molecular weight of the reactive group is usually known and is treated as an equivalent. It is sometimes expressed in various units such as acid values, hydroxy values, percentages of weight of hydroxyls, or percentages of weight of isocyanate root NCO, etc. These can be converted to equivalents. For thermoso-solid polymer systems, there are typically two different types of polymers, each containing a ernical energy group that can react with the ernobsive energy group contained in the other polymer. For example, polycyanate and polyols. In calculating the number of bridges between polymer chains, the contribution of each official energy group to the bridge is 1/2. We assume a 1:1 reaction group chemical metering ratio and carefully do not refer to the bridge association as crosslinking. Therefore, Equation 1 gives the number of bridges per unit weight in a curing paint film with a 100% reaction.
, however, it is clear that this equation is not suitable for calculating the number of intermediary bridges in polymer chains that require the formation of infinite molecular weights. Each polymer chain can be deducted from 2 reaction groups to calculate this adjusted equivalent EW', as shown in Equation 2. This adjustment is directed at each polymer in the system.
this is a simple chemical metering-based equation that Flory uses statistical techniques to correct. We will subsequently confirm that the technique of deducting 2 reaction groups from each polymer chain is effective for the different levels of molecular energy of prepolymers. A typical example: an equivalent EW is 400, the average molecular weight Mn is 2000 acrylic hydroxyl hydroxy-energy resin produced and adjusted equivalent EW' is 667g/mol (g/mole)please note that this is the number of graphs per gg of the final network structure. Therefore, if there is a loss of residual groups at the end of the cross-linking reaction, the weight of these residual groups needs to be deducted from the total molecular weight Mn, the unaljusted equivalent EW and the percentage of paint film polymer weight. As for some crosslinking agents such as melamine and melamine, the excess reaction group will shrink. In this case, by simply adjusting their weight percentage to their non-chemical metering values, the over-the-crosslinkers on the chemical meter can be applied to this calculation.
if a polymer's reaction is incomplete, whether due to unbalanced chemical metering or due to inadequate curing of two polymer systems, this adjustment can be easily made in Equation 2. For example, if the reaction is only 80% complete, the number of moles of the reaction group is 0.8 times the total number of moles of the reaction group. Thus, the first scenario in Equation 2 is adjusted to equation 4 applicable to both polymers., the system's response level can be reduced to the bottom of the zero crosslink density to find out how much it reacts when the gel point or infinity molecular weight is needed.
based on easy-to-obtain weight percentage information for most polymers combined with polymers, and chemical metering ratios obtained from coating formulations, we have listed a series of simple algetric equations for calculating crosslink density. In addition, this method can be used in cases where the average number of groups per polymer chain is a non-integer value (this is often the case).
we will now review some of the official energy combinations of the pre-cluster chain to ensure that the removal of the two reaction groups of each reaction chain can be applied in all situations. In each case, we will consider the number of groups on each polymer and its effect on the formation of mesh infinity molecular structures, as well as the number of crosslinks formed.
two reaction groups on the A polymer and two reaction groups on the B polymer
through the above discussion, it is clear that such a system will not be interlinked. This is confirmed by the calculations in Table 1. In the case of chemical metering of 1:1, the system can only form an infinite molecular weight. Such a system represents many thermoplastic polymers such as polyamides (e.g. PA6.6) and polyesters.
A polymer has 3 reaction groups and B polymer has 3 reaction groups
which provides a clear example of transition from infinite molecular weight to cross-networked structure. At a 1:1 chemical metering ratio, two-thirds of the groups participate in the reaction, and the system reaches an infinite molecular weight without any crosslinking. The reaction between the third reaction group of A polymer and the third reaction group of B polymer provides one-and-a-quarter of the crosslink contribution of the final crosslinking network, as shown in Table 2. the same situation, it is easy to infer that each chain has 4 official groups, 5 official groups and so on. Now we're going to consider the case where two polymers have different numbers of errations.
A polymer has 6 reaction groups and B polymer has 2 reaction groups
this system can represent a 6 degrees of melamine and a polyester binary alcohol. Such a system would be more challenging in conceptualizing infinity molecular weight. When each (6 degrees of energy) melamine reacts twice, and only one-third of the binary alcohol molecules react twice, there is an infinite molecular chain. But two-thirds of the binary alcohol chains did not respond because they were three times more likely to have a binary alcohol chain than melamine molecules. if each of these unresponsive binary alcohols reacts with melamine at only one end, the infinity molecules and gel points are reached. Crosslinking can only be obtained if the other end of these unresponsive binary alcohols also begins to react with melamine.
this situation will be slightly different, but the results will be the same. We re-reacted twice from each melamine, and only one-third of the binary alcohol chains reacted to this node, after which one binary alcohol at both ends and two different melamine reactions were completed, one one-way interlinking was completed. However, one-way crosslinking comes from one-half of the crosslinks provided by two melamine molecules, which do not occur on binary alcohol molecules.
, the performance of binary alcohol in this example is the same as in the first example, the contribution to crosslinking is zero. This provides us with a very important experience for mesh cross-linking design: only those chains with more than two official groups can cross-link. This assertion applies to resins for any such application. However, if this kind of dual-official chain and senior officials can be paired with co-reactants, then cross-linking can occur through co-reactants. We now need to consider another unbalanced system.
A polymer has 4 ernocity groups and B polymer has 3 official groups
at 1:1 chemical metering, the number of chains and the number of official groups on each chain link are inversely inversely. So there are three molecules of the A polymer on each of the four molecules of the B polymer. Thus, when the A-poly
hydrant of each molecule reacts twice, only three-quarters of the B-polymer chains react twice, and still a quarter of the B-polymer strands do not respond, as shown in Figure 1. Unresponsive clusters appear as open-loop states, while reactive clusters or bridges appear as closed-loop states. as a result of one of the reaction group reactions on the last B polymer molecule and the A polymer molecule, an infinite molecular weight is obtained, and the two reaction groups are consumed, as shown in Figure 2. However, as in the case above, one group is the "crosslink" group (the third base group of the A polymer), while the base group on the two dimensions of the B polymer is consumed by only one dimension. Thus, algethotics dealt with this situation in different ways (the two errations of the B polymer were deducted from the algege science) and the same result was obtained. Either way, the other two clusters are consumed to obtain an infinite molecular weight (Table 4). In the next system, we will introduce a single-role group reactor, or monosome. 。 A polymer has 6 reaction groups, B polymer has 2 reaction groups, C monomer has 1 reaction group
the system is configured to allow both B polymer and C monomer to react with A polymer. We used a 50/50 B polymer to a molar ratio of the C monomer. We copied Table 3 and Table 5 together for comparison. The first change that needs to be recorded is that the adjusted equivalent of EW for the C monosume is negative because it virtually eliminates the system's potential crosslinking. We can still use binary alcohol to react twice with each melamine molecule, as we demonstrated in the 6:2 example, which in turn will result in four unreactive groups on each melamine molecule. In the case of the 6:2 example, each of the four unreactive groups formed a one-in-two interlink by a bridge with binary alcohol, so that each melamine molecule formed two interlinks. Here, three of the four melamine unreactive groups react with the C monomer, resulting in no crosslinking. The remaining unresponsive group of melamine and binary alcohol had a bridge reaction that formed a one-in-two intersection. In all cases at 6:2:1, we have one-in-two intersections for each melamine molecule, and at 6:2, we have two interlinks for each melamine molecule. As a result, adding this monosome cost us 75% of our crosslinks. This is consistent with the results we calculated below.
many paint chemists like to evaluate crosslinking by looking at Mc of the cross-linked paint film. For infinity molecular weight,