Number-average molecular weight between

Mc number average molecular weight between crosslinks... 

Number average molecular weight between cross-links. 

The number of repeating units between crosslinks, N, a parameter appearing in equation (1), can be simply defined as the jratio of the number average molecular weight between crosslinks, Mc, to the average molecular weight of the clusters, Mq. 

There are two parameters used as a measure of cross-Unk density the number of network chains, v, usually expressed as v/ V, where V is the volume of the unstrained network and the number of cross-links (p) per unit volume, p/F. The relationship between p and v is established by knowing the number of chains starting from a particular cross-linking point, (functionality). The two most important types of network are the tetrafunctional (c ) =z 4) and the trifunctional ( = 3). Another characteristic parameter of a network is the number-average molecular weight between cross-links,... 

Me is the number-average molecular weight between polymer cross-links M is the number-average molecular weight of the uncross-Unked polymer M is a critical molecular weight between cross-links (p is polymer volume fraction n is solute radius... 

Klemm and co-workers have applied this double Diels-Alder methodology to the synthesis of novel polymers. Copolymerization of bispyrone 23 with bismaleimide 24 leads to soluble, stable polymers of number-average molecular weights between 10,000 and 34,000. The polymers are composed of coronand structure subunits 25 alternating with alkyl linkers. 

Swelling experiments and stress-strain measurements are widely used to estimate the crosslinking density in liquid-crystalline networks [101,106-108], For ideal rubbers with tetrafunctional crosslinks, these techniques allow the evaluation of the number average molecular weight between crosslinks [104, 105]. 

Based on the amount of bromine reacted, th number average molecular weight between two crosslink sites (M ) in PPO was 17,000. The theoretical of the crosslinked polystyrene was 7,260. 

The quantity Me in a polymer network (the present case) is the number-average molecular weight between cross-links. 

Here, the shear modulus of the swollen hair G = (pRT/Mc) (v2 — j)/ (1 < ) 1/3(i 2M,/M) y n is the number of segments of the network chain L x) is the anti-Langevin fimction p is the dry density of fiie sample is the number average molecular weight between crosslinks of the rubbery phase M is the primary molecular weight R is the gas constant T is absolute temperature V2 is the volume fiaction of the polymer within the gel and y is the filler effect of the HS domain that exists in the rubbery phase. Equation (3) provides y. 

In Chapter 3 of this book, L. Brannon-Peppas offered a thorough analysis of the preparation and structure of hydrogels. In that chapter. It was noted that the number average molecular weight between crosslinks. Me, and the volume equilibrium swelling ratio, Q, or its reciprocal parameter equilibrium polymer volume fraction, x>2,s. are important parameters for the characterization of the network. It is then necessary to review theories and equations used for calculation of such parameters. 

The effective crosslink density, px, is defined as the concentration of elastically active chains (chains which are deformed by an applied stress) in the polymer network, and is usually reported on the basis of moles of chains per cubic centimeter of dry polymer. Network structure can also be described with a number of closely related terms [28]. For example, when linear polymers are crosslinked, it Is often desirable to express crosslinking in terms of the number average molecular weight of the polymer before crosslinking, Mp, and the number average molecular weight between crosslinks,... 

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