Monte Carlo Simulation Studies of the Size and Shape of Regular Three Generation Dendrimers

Wawrzyńska, Edyta; Eisenhaber, Stephan; Parzuchowski, Paweł G.; Sikorski, Andrzej; Zifferer, Gerhard

doi:10.1002/mats.201300159

Cited by 6 publications

(5 citation statements)

References 86 publications

(166 reference statements)

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“…Thus, as the scaling relation for linear chains is also valid for star‐branched chains and ring‐shaped polymers, it is expected that mean square dimensions of dendrimers of given complexity (i.e., fixed value of G and F ) will exhibit the same scaling relation (with identical scaling exponent), too . In our previous communication for G = 3 with functionalities up to F = 6, the validity of relation Equation (11) has been demonstrated. Thus, present dendrimers are treated in the same way, i.e., prefactors

C_{x, G}^{}

in the limit of infinite chain length as well as the short chain correction terms

D_{x, G}^{}

are taken from linear regressions of

true〈 x^{2} true〉 true/ n^{1.176}

versus

1 true/ \sqrt{n}

omitting “small” dendrimers with either m < 32 and/or n < 2 048.…”

Section: Resultsmentioning

confidence: 99%

“…It should be noted that linear chains already exhibit

g^{'} \approx 1.06 > 1

; this effect is enhanced in case of star‐branched chains as the expansion of arms increases with increasing functionality . For three‐generation dendrimers

g^{'}

and

g^{normal″}

are still larger and again increase with increasing functionality . Likewise, expansion of dendrimers increases with increasing number of generations keeping the functionality at a constant value (see Table ).…”

Section: Resultsmentioning

confidence: 99%

“…Thus, the g ‐factor of any random walk may be represented in terms of W

g_{R W} = {true〈 s^{2} true〉}_{R W} true/ {true〈 s^{2} true〉}_{lin, R W} = W true/ W_{lin}

and, as the Wiener index for linear chains reads as

W_{lin} = N true(N^{2} - 1 true) true/ 6

the following scaling law in the limit of an infinite chain length is obtained:

W = g_{R W} \cdot W_{lin} = g_{R W} \cdot N true(N^{2} - 1 true) true/ 6 \approx true(g_{R W, \infty} true/ 6 true) \cdot N^{3}

Thus, as the scaling exponent of the squared radius of gyration of any athermal random walk with respect to chain length reads as 1.176, the following scaling law of

true〈 s^{2} true〉

with respect to W is expected

true〈 s^{2} true〉 = C_{s} \cdot {true(W true/ true(g_{R W, \infty} true/ 6 true) true)}^{1.176 true/ 3} = true[C_{s} \cdot {true(6 true/ g_{R W, \infty} true)}^{0.392} true] \cdot W^{0.392}

as long as the Wiener index is controlled exclusively by the chain length keeping the structure constant. The combined prefactor of the scaling law can be easily calculated for regular dendrimers using the closed relation for

g_{R W, \infty}

given in our previous communication, derived from closed analytical form for W ,…”

Section: Resultsmentioning

confidence: 99%

“…We recently studied regular dendrimers built of spacers of equal length connecting branching points by means of computer simulations . In the present paper, we extended this model by the introduction of the irregularity to these dendrimers.…”

Section: Introductionmentioning

confidence: 99%

“…Dynamic Monte Carlo simulations were carried out to determine the structure of the systems studied. The algorithm used consisted of Verdier–Stockmayer type local changes of chain's conformation and the pivot motions . The scaling behavior of polymer size, symmetry, and the structure of the studied chains was determined and discussed.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo Simulation Studies of Regular and Irregular Dendritic Polymers

Wawrzyńska

Sikorski

Zifferer

2015

Macro Theory & Simulations

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A dynamic Monte Carlo method was employed to study regular as well as irregular dendrimers with up to G ¼ 8 generations with functionality F ¼ 3 under athermal conditions. The size of dendrimers showed the same scaling law with respect to chain-length n as linear chains, keeping G at a constant value. If n was varied via G at fixed spacer-length m its scaling behavior was similar to that of collapsed globules, at least for large values of G. Asphericity strongly decreased with an increase of G. The composition of irregular dendrimers remained unchanged with respect to F and G but the spacer-lengths were distributed according to several models. Quite generally, distributions became broader, size larger and shape less symmetric compared to the regular case. These effects increased with an increase of dispersity of the branches.

show abstract

C_{x, G}^{}

in the limit of infinite chain length as well as the short chain correction terms

D_{x, G}^{}

are taken from linear regressions of

true〈 x^{2} true〉 true/ n^{1.176}

versus

1 true/ \sqrt{n}

omitting “small” dendrimers with either m < 32 and/or n < 2 048.…”

Section: Resultsmentioning

confidence: 99%

“…It should be noted that linear chains already exhibit

g^{'} \approx 1.06 > 1

; this effect is enhanced in case of star‐branched chains as the expansion of arms increases with increasing functionality . For three‐generation dendrimers

g^{'}

and

g^{normal″}

Section: Resultsmentioning

confidence: 99%

“…Thus, the g ‐factor of any random walk may be represented in terms of W

g_{R W} = {true〈 s^{2} true〉}_{R W} true/ {true〈 s^{2} true〉}_{lin, R W} = W true/ W_{lin}

and, as the Wiener index for linear chains reads as

W_{lin} = N true(N^{2} - 1 true) true/ 6

the following scaling law in the limit of an infinite chain length is obtained:

W = g_{R W} \cdot W_{lin} = g_{R W} \cdot N true(N^{2} - 1 true) true/ 6 \approx true(g_{R W, \infty} true/ 6 true) \cdot N^{3}

Thus, as the scaling exponent of the squared radius of gyration of any athermal random walk with respect to chain length reads as 1.176, the following scaling law of