Crosslinking unit

Serious deviations of the polymer network structure from the ideal one can have several causes. One of them is the crosslinking agent involvement in intramolecular cycle formation. The contribution of this reaction grows with the system dilution as well as when the crosslinker units in the chain are close one to the other, i.e. its fraction in the copolymer increases. All this is in good agreement with the observed trend. 

Inorganic networks, especially glasslike gnes can be characterized by the ratio of network forming (e.g. [siO ] ) to network modifying (e.g. =Si-0 Na ) units. Network formers (e.g. SiO, B 03, A 2°3 T 2 are (in opposition to the majority of organic units) three-dimensional crosslinking units. 

Macromonomers carrying mono-, bi- or trifunctional end groups are sometimes important constituents of a network. Through them, terminating, chain-extending, or crosslinking units are introduced to modify the network... 

Thus, the effect of introducing flexible crosslinked units into DAP resins was reflected in the improved flexibility. In particular, PEGBAP having a long-chain glycol unit showed a remarkable effect ... 

In conclusion, DAP resins with improved flexibility were successfully obtained by introducing flexible crosslinked units on the surface of the microgel, i.e., by crosslinking flexibly microgels to form the macrogel. This finding may become a useful guideline for the modification of three-dimensional polymers As an extension of... 

Increases 1n X N agree well with the amount calculated for a crossUnklng mechanism Involving two crosslinker units linked by a nitrogen (Scheme 7). Inefficient formation of more sterically congested structures containing three crosslinker units per nitrogen Is also consistent with the data. 

To derive the condition for the gel point in random crosslinking of existing chains of arbitrary molecular weight distribution, let us consider a primary chain selected at random having P monomer units. If one unit of the selected chain happens to be crosslinked, the probability that this unit is a part of the selected chain is equal to the weight fraction wP of the P-mer. The expected number of additional crosslinked units in the P-mer is then q(P — 1). The mean expected number of additional crosslinked units in a chain is... 

The number of crosslinked units per primary molecule denoted by crosslinking index y is equal to qP (jP is the number average). At... 

If the sol fraction is not negligible, the fraction of crosslinked units in the gel is higher than in the whole system. For random crosslinking of primary chains with an arbitrary molecular weight distribution, the crosslinking density in the gel qb is related to the overall crosslinking density q by (55) ... 

To obtain the concentration of crosslinked units in the copolymerizing system one may proceed as follows (124,45). Denoting by Xs, mx and m2 the number of moles of doubly reacted divinyl molecules, reacted monovinyl molecules, and divinyl molecules reacted with one vinyl respectively, the crosslinking density can be expressed as... 

Without any proof it has often been assumed that C equals C so that an estimate of rcl could be obtained which could be compared with the number of chemically crosslinked units, vc. Any differences were subsequently interpreted in terms of various network defects, as e.g. entanglements, closed loops, or unreacted functionalities. 

Taken from Ref.19 b taken from Ref.69 c taken from Ref. 8 d taken from Ref.67 taken from Ref, 731 r taken from Ref.,0) phr of sulfur h % of dicumyl peroxide number of crosslinking units per weight average PMA chain j average number of repeat units between crosslinks k concentration of chains between network joints, (mole/cm3)x 104 1 methyl group rotation m segmental motion motions within the crystalline part of the polymer... 

Let us consider a system consisting of A0 polymer chains of varying length. The polymer chains are built from identical crosslinkable units, and the total number of units in the system is A If we define Ns as the number of s-meric chains in the system (for example, N is the number of monomers, N2 is the number of dimers, etc.) the number of polymer chains A0 will be... 

Since the crosslinking density a is the probability of any unit to be cross-linked, the number of additional crosslinked units on an, v-mcric chain, crosslinked to the first chain, is expected to be equal to a. multiplied by the number of remaining crosslinkable groups (.v— 1). Thus, the expected number of additional chains crosslinked to the. v-meric chain, which is crosslinked to the first randomly chosen chain, is a(s— 1). Averaging over all chain sizes will give the average expectance of additional chains v. 

It is interesting to note that the Eq. (9) is also valid for random copolymer systems consisting of both crosslinkable and non-crosslinkable units [83]. 

The probability that an, v-mcric polymer chain has p crosslinked units is given by... 

Figure 13.5 shows a diagram of photoresist film coated on a non-reflective substrate and irradiated from the front. The thickness of the photoresist is h. It is convenient to introduce a dimensionless variable z measuring the position in the film, with z — 0 on the top of the film and z = 1 on the photo-resist/substrate interface. The photoresist with density p consists of crosslinkable units with molecular weight M0, molar absorptivity e, and concentration m. At the onset of irradiation, concentration of the cross-linkable units is uniform through the film, m — m0 — p/M0, and the initial optical density of the film is D0, which is given by... 

A definite embrittlement is observed in formaldehyde-treated wood that may result from the short crosslinking unit (O—C—O) formed between formaldehyde and fibrils in the cell wall. If the inner carbon unit were longer, there would be more flexibility in this unit and the embrittlement should be reduced. 

A different mechanism is postulated for acid crosslinking, involving the liberation of both isobutanol and its formal, ultimately producing crosslinked units as ... 

Various crosslinked acrylate resists have been reported in the literature, mainly based on methacrylic acid anhydride (MANH) crosslink units. In the simplest case, the anhydride crosslinks may be formed by baking methacrylic acid (MAA) homopolymer, although this... 

Thus, sensitivity depends strongly on the crosslink density, du, which is controlled by the fraction of crosslinkable units in the material and the extent of the crosslinking reaction during baking. In the present work, the number of crosslinkable sites on each copolymer was fixed so different methods of changing the crosslink density were explored. Three approaches were used 1) the extent of the crosslink reaction was controlled by varying the bake conditions, 2) the crosslink reaction was carried out to completion and then the crosslink density was modified by a subsequent process step, 3) the total number of crosslink sites was altered and the reaction was allowed to proceed to completion. 

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