wA U Mo wB Mo pB U wB0 Mo pB0 U 2-109a 2-109b 2-109c

Pdf417 2d Barcode reader on .netUsing Barcode Control SDK for .net framework Control to generate, create, read, scan barcode image in .net framework applications.

MOLECULAR WEIGHT DISTRIBUTION IN LINEAR POLYMERIZATION

PDF417 maker on .netgenerate, create pdf-417 2d barcode none with .net projects

where

VS .NET barcode pdf417 recognizerfor .netUsing Barcode decoder for Visual Studio .NET Control to read, scan read, scan image in Visual Studio .NET applications.

U 2wiA 2Mo pB Mo pB0 Mo 1 p2 p2 0 =2 B B 2-110

Visual .net barcode readerin .netUsing Barcode reader for .net framework Control to read, scan read, scan image in .net framework applications.

The weight-average molecular weight, obtained by a weight averaging of wA , wB , and wB0 , is given by

Receive bar code with .netuse .net framework crystal barcode generating todevelop bar code in .net

Mw wA wB wB0 2 4 4 2-111

Control barcode pdf417 image with c#.netgenerate, create pdf417 2d barcode none in c# projects

which yields

Web.net pdf417 generatorin .netuse aspx.net barcode pdf417 generation toaccess pdf-417 2d barcode on .net

Mo Mw 4 ( 2 pB pB0 2 1 p2 p2 0 =2 B B ) 2-112

Control pdf417 2d barcode data with vb.netto encode pdf417 2d barcode and pdf-417 2d barcode data, size, image with vb.net barcode sdk

on substitution for wA, wB , and wB0 . The number-average molecular weight, obtained by dividing the total number of moles of reactants initially present divided by the total present at any time, yields

Build 2d barcode for .netusing .net vs 2010 crystal toreceive matrix barcode for asp.net web,windows application

Mn Mo 1 pA 2-29

VS .NET Crystal pdf417 integratingfor .netgenerate, create pdf417 none for .net projects

It is useful to introduce the fractions of unreacted A, B, and B0 functional groups

EAN / UCC - 14 drawer on .netuse .net framework crystal ean 128 integrated toassign ucc-128 in .net

a 1 pA b 1 pB g 1 pB0 2-113a 2-113b 2-113c

Postnet 3 Of 5 encoder on .netuse .net framework crystal postnet 3 of 5 writer todraw usps postnet barcode on .net

For the case where B and B0 groups have the same reactivity:

Rdlc Report barcode encoderwith .netusing barcode printing for rdlc reports control to generate, create barcode image in rdlc reports applications.

g b 2-114

.net Vs 2010 bar code encodingin visual basic.netgenerate, create bar code none for visual basic projects

Combination of Eqs. 2-108, 2-112 through 2-114, and 2-29 yields the polydispersity index as

Linear Barcode barcode library in office wordgenerate, create linear barcode none on word documents projects

PDI 2 a 2 2 b2 g2 =2a 2-115

UPC Symbol drawer with c#using barcode generation for .net winforms crystal control to generate, create upc-a image in .net winforms crystal applications.

Equation 2-115 yields PDI as a function of conversion in a straightforward manner without having to solve differential equations to obtain the number- and weight-average molecular weight distributions. One need only take a set of b values and then calculate the corresponding g, a, and PDI values from Eqs. 2-114 and 2-115. The limit of PDI at complete conversion pA 1; a 0 is 2 as for the Flory distribution. The Macosko-Miller method has also been applied to other polymerizations, including the A plus A0 0 system. In B B addition to being a simpler method for obtaining the average properties compared to the Flory and similar methods, it more readily allows an evaluation of the effect of various reaction parameters such as unequal group reactivity or nonstoichiometric amounts of reactants on M n , M w , and PDI (see Sec. 2-7e).

Control qr-code size on vb qr code 2d barcode size in vb

STEP POLYMERIZATION

Insert ean13 in javausing barcode integrating for java control to generate, create ean13 image in java applications.

2-7e 2-7e-1

2d Matrix Barcode barcode library on .netusing barcode implement for sql database control to generate, create 2d barcode image in sql database applications.

Effect of Reaction Variables on MWD Unequal Reactivity of Functional Groups

Add ean 13 with .netusing barcode printer for .net winforms control to generate, create ean-13 supplement 5 image in .net winforms applications.

The molecular weight distribution and/or PDI has been described for several cases where the assumption of equal reactivity of functional groups is not valid. Unequal reactivity is easily B handled by the Macosko Miller method. For the A B B0 0 system described in A B the previous section, we simply rede ne the relationship between b and g by

g bs 2-47

(which was derived previously in Sec. 2-2d-2) where s is the ratio of rate constants for reaction of B0 and B groups [Ozizmir and Odian, 1980]. The polydispersity index increases (for conversions <100%) when the reactivities of B and B0 groups are different compared to the case where the reactivities are the same. The opposite trend is found for the A B 0 system [Gandhi and Babu, 1979, 1980]. There A B is a basic difference between the two- and the three-species reaction systems. In the threespecies system, when B0 groups have higher reactivity than B groups, the B0 0 monomer B continues polymerization with A monomer, independently of the B monomer, to form A B large-sized polymer chains. In the two-species system, long chains cannot be formed without participation of B groups in the polymerization process. The extents of the broadening and narrowing effects in the two systems increase as the difference in reactivities of B and B0 become larger. The effects are signi cant at low conversions; for instance, PDI is 2.10 at 50% conversion for the three-species system when B0 is 20-fold more reactive than B compared to a PDI of 1.50 for the equal reactivity case. However, the PDI at complete converson equals 2 in both the two- and three-species systems, which is the same limit as for the equalreactivity case.

2-7e-2

Change in Reactivity on Reaction

An increase in the reactivity of one functional group in a bifunctional reactant on reaction of the other functional group results in an increase in PDI [Gandhi and Babu, 1979, 1980]. The PDI at complete conversion exceeds 2 when there is a greater than twofold increase in reactivity. PDI decreases when there is a decrease in reactivity of one functional group on reaction of the other group but the PDI at complete conversion is 2. The same trends are found but are more exaggerated when functional group reactivity varies continuously with molecular size [Gupta et al., 1979a,b; Nanda and Jain, 1968].

2-7e-3