Molecular mass distributions of star-branched polycondensates

Versluis, Cokki; Nijenhuis, Atze

doi:10.1002/1521-3919(20001201)9:9<735::aid-mats735>3.0.co;2-x

Cited by 6 publications

(6 citation statements)

References 4 publications

(5 reference statements)

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“…In a practical situation, however, it is likely that, depending on the kinetics and thermodynamics of the reaction, linear molecules will also be present in the reaction mixture. [15] The linear fraction can easily be incorporated into the equations for the span-length pdf by the following substitution with f linear þf star ¼ 1 where f linear is the (number) fraction of molecules without a coupling molecule, f star is the (number) fraction of molecules with a coupling molecule, and m 0 L (z) is the span-length pdf that includes the two species of molecules (monomer unit and coupling molecule). The substitution for the weight-based distribution is done similarly.…”

Section: Discussionmentioning

confidence: 99%

Span-Length Distributions of Star-Branched Polymers

Versluis

Souren

Nijenhuis

2002

Macromol. Theory Simul.

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Many relations between the physical, rheological or mechanical properties of linear polymers and their molar mass are well known. For disperse polymers, parameters that express these relations are typically related to (a combination of) the moments of the molar‐mass distribution. Properties of branched, nonlinear polymers have been far more difficult to describe in the form of general relations. Monodisperse star polymers or regular stars, with a distinct number of arms and equal arm length, are the simplest member of the family of branched polymers and have served as model compounds in many studies. For these regular stars, the relation between zero shear viscosity and arm or span length has been determined. To establish equivalent relations for disperse star‐branched polymers, it is important to assess the span‐length distribution and its moments; these parameters can be calculated when the distribution of the molar mass of the arms of a star‐branched polymer is known, for instance, for a known polymerization mechanism.

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Section: Discussionmentioning

confidence: 99%

Span-Length Distributions of Star-Branched Polymers

Versluis

Souren

Nijenhuis

2002

Macromol. Theory Simul.

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“…The system “A1B1 + B6” forms a mixture of linear and branched polymeric molecules. The branched ones have a “B6” at their core and are star shaped, with as many arms (composed of solely “A1B1” units) sprouting from the core as there are reacted B groups on the “B6”.…”

Section: From Polynomial Equation ψ(Xq(x)) = To Msdmentioning

confidence: 99%

“…For those systems and certainly for systems ''AfiBgi'' with d > 4, in Section 4.3, we present a new method to calculate the full MSD. The system ''A1B1 þ B6'' [4,5] forms a mixture of linear and branched polymeric molecules. The branched ones have a ''B6'' at their core and are star shaped, with as many arms (composed of solely ''A1B1'' units) sprouting from the core as there are reacted B groups on the ''B6''.…”

Section: From Polynomial Equationmentioning

confidence: 99%

“…We-and some other authors-have done so before. [1][2][3][4][5][6][7] However, the method proposed here: (i) is applicable to arbitrary order-2 systems, (ii) calculates the exact distribution (subject to the assumptions stated above), (iii) for the more simple systems, it yields explicit expressions for the MSD curve, and (iv) is really fast (when compared to our previous papers on the subject: [7,8] the recurrence is of constant order).…”

Section: Introductionmentioning

confidence: 99%

“…In the sections to come, we will present an algorithmic method to compute the fraction of molecules with size s ( s = 1,2,3,…), i.e., the molecular size distribution (MSD). We—and some other authors—have done so before …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Step-Growth Polymerized Systems of General Type “AfiBgi”: Generating Functions and Recurrences to Compute the MSD

Hillegers¹,

Slot

2015

Macromol. Theory Simul.

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General step‐growth polymerization systems of order 2 are considered, i.e. systems of type “AfiBgi”. We describe an algorithmic method to calculate the molecular size distribution (MSD). Input to the algorithm is the “recipe”: a list of the monomers involved stating their A and B functionalities and their molar amounts, and the degree of conversion. Output is the MSD and its moments. Three main steps lead from input to output: (i) setting up a polynomial equation for the generating function that generates the MSD, (ii) transforming this polynomial equation to a differential equation, and (iii) transforming the latter one further to a recurrence equation. The recurrence yields the MSD and is of constant order.

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A Fast Method to Compute the MSD and MWD of Polymer Populations Formed by Step‐Growth Polymerization of Polyfunctional Monomers Bearing A and B Coreactive Groups

Hillegers¹,

Blokhuis

Slot

2012

Macro Theory & Simulations

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General step‐growth polymerization systems of order 2 are considered, i.e., systems of type “AfiBgi”, and a fast algorithmic method is presented to compute, at a given degree of conversion, the MSD and the MWD. The complete distribution is calculated; not just statistical averages of the polymer population such as $\overline {M} _{{\rm n}} $ or $\overline {M} _{{\rm w}} $. For the computation of the low‐ and intermediate size/weight parts of the distribution curves, a set of recurrence relations is used. The high‐molecular size/weight parts of the curves (right tails) are computed using an accurate approximation derived from generating functions. In a previous paper, we applied our method to general order‐1 systems, i.e., systems of type “Afi”. magnified image

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Molecular mass distributions of star-branched polycondensates

Cited by 6 publications

References 4 publications

Span-Length Distributions of Star-Branched Polymers

Span-Length Distributions of Star-Branched Polymers

Step-Growth Polymerized Systems of General Type “AfiBgi”: Generating Functions and Recurrences to Compute the MSD

A Fast Method to Compute the MSD and MWD of Polymer Populations Formed by Step‐Growth Polymerization of Polyfunctional Monomers Bearing A and B Coreactive Groups

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