Modeling of Diffusion Effects on Step-Growth Polymerizations

Guzmán, Job D.; Pollard, Richard; Schieber, Jay D.

doi:10.1021/ma049469v

Cited by 31 publications

(38 citation statements)

References 27 publications

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“…4,5 We show in Figure 6 how D k scales with the mass of the cluster, M, for different values of p, by properly taking the different masses of the small and large …”

Section: Resultsmentioning

confidence: 99%

Modeling the Crossover between Chemically and Diffusion-Controlled Irreversible Aggregation in a Small-Functionality Gel-Forming System

et al. 2010

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The analysis of realistic numerical simulations of a gel-forming irreversible aggregation process provides information on the role of cluster diffusion in controlling the late stages of the aggregation kinetics. Interestingly, the crossover from chemically controlled to diffusion-controlled aggregation takes place well beyond percolation, after most of the particles have aggregated in the spanning network and only small clusters remain in the sol. The simulation data are scrutinized to gain insight into the origin of this crossover. We show that a single additional time scale (related to the average diffusion time) is sufficient to provide an accurate description of the evolution of the extent of reaction at all times.

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“…4,5 We show in Figure 6 how D k scales with the mass of the cluster, M, for different values of p, by properly taking the different masses of the small and large …”

Section: Resultsmentioning

confidence: 99%

Modeling the Crossover between Chemically and Diffusion-Controlled Irreversible Aggregation in a Small-Functionality Gel-Forming System

et al. 2010

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“…Apart from free radical polymerizations, which have been extensively studied, diffusion phenomena play also an important role in step-growth reactions, [15] although this has been less studied in literature.…”

Section: Reviewmentioning

confidence: 99%

“…The work of Oshani and Moreau [169] assumes that the influence of chain length i on the effective rate coefficient k i is dramatic in order to obtain an analytic solution for linear homo-polymerization. The effect of segmental diffusion on irreversible, step-growth polymerizations of ARB type monomers was studied by Kumar et al [167,170] Recently, Guzman et al [15] presented a detail study of diffusion effects in step-growth polymerization via a chain-by-chain simulation, meaning that they kept track of the concentration of every chain length so that additional approximations were not necessary to integrate the population balance equations. Both homopolymerization and A 2 þ B 2 step-growth polymerizations were considered.…”

Section: Diffusion-controlled Step Growth Polymerizationmentioning

confidence: 99%

“…An estimate for the number of equations required could be obtained from the analytical solution of the equal reactivity case. [15] For most simulations it was found satisfactorily to use 10 times the number average degree of polymerization meaning that for a typical value of 1 000 one has to solve simultaneously approximately 10 000 ODEs! Exactly the same model as presented in Equation (91)- (93) was later used by Yan et al [172,173] in studying diffusion effects on chain extension reactions, using carboxyl-terminated polyamide 12 with bisoxazolines.…”

Section: Diffusion-controlled Step Growth Polymerizationmentioning

confidence: 99%

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A Review of Modeling of Diffusion Controlled Polymerization Reactions

Achilias¹

2007

Macro Theory & Simulations

230

292

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A plethora of models have been developed quantifying the effect of diffusion‐controlled phenomena on polymerization reactions. The most prominent approaches are reviewed here, including innovative ones that have emerged over the last decade. Free‐radical and step‐growth polymerizations are considered in a way to show that similar models have been used in both mechanisms. In free‐radical polymerization the models proposed are subdivided according to their theoretical background into four categories: (i) based on a Fickian description of reactant diffusion; (ii) free‐volume theory based; (iii) chain‐length dependent; and, (iv) empirical. The reversible addition‐fragmentation technique is discussed, together with two industrially important case‐studies, solid state polycondensation and epoxy‐amine curing.magnified image

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“…To understand the behavior of D, consider that the overall diffusion constant is an average over particles belonging to clusters of different sizes; therefore D = k D k (kN k )/N , where D k is the diffusion constant for particles in a cluster of size k [26]. Typically, D k drops inversely to the cluster size, so that D k ≈ D 1 /k, the so-called Stokesian limit of diffusion [27,28]. In this approximation, D ≈ D 1 k N k /N = D 1 N c /N .…”

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confidence: 99%

Theoretical Description of a DNA-Linked Nanoparticle Self-Assembly

2010

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Nanoparticles tethered with DNA strands are promising building blocks for bottom-up nanotechnology, and a theoretical understanding is important for future development. Here we build on approaches developed in polymer physics to provide theoretical descriptions for the equilibrium clustering and dynamics, as well as the self-assembly kinetics of DNA-linked nanoparticles. Striking agreement is observed between the theory and molecular modeling of DNA tethered nanoparticles.The specificity, directionality, and technological control over base sequence make DNA an attractive linking unit for artificial constructs [1][2][3]. One such approach is to attach DNA strands of designed base sequence onto a nanoparticle (NP), thereby creating "molecules" that self-assemble into highly organized structures through complementary pairings of DNA [4,5]. Recent experiments have demonstrated that uniformly DNAfunctionalized NP can self-assemble into disordered [6][7][8][9] or ordered crystal structures [10][11][12][13]. NPs with a discrete number of attachments are harder to prepare, but they provide possibilities for even more diverse structures [14][15][16][17]. In addition to examining the possible equilibrium structures, it is also vital to develop an understanding for the kinetics of the self-assembly process [8,12,13,18,19], since the pathway to desired structures may depend sensitively on sample preparation.In this Letter, we build on concepts from polymer physics to provide a theoretical framework that describes both the equilibrium properties and the self-assembly kinetics of NPs functionalized with a small number of ss-DNA. We demonstrate the applicability of this theory to molecular simulations of a binary mixture where NPs are functionalized with two or three ssDNA, similar to experimentally realized systems [15].The coarse-grained molecular model we use for the DNA-functionalized NP is a modest modification of a previous model [20]. The inset of fig. 1 provides a graphical representation. The sugar-phosphate backbone is represented by connected beads with only excluded volume interactions; each bead carries an additional "sticky" site that represents a base (A, T, C, or G) and can bond only with another sticky site of complementary type (A-T or C-G pair). The size of the sticky site is small relative to the backbone beads, so that a base can bond to at most one other complementary base. A bending potential between consecutive triplets of backbone beads is included to model the characteristic rigidity of the DNA strands and to maintain the angle between ssDNA attached to the same core (120• for 3-functional NP and 180• for 2-functional NP). A more complete description of the model is provided in Ref. [20]. We consider ssDNA four bases in length with sequence A-C-G-T, chosen to enable complementary pairing between ssDNA on different NPs. To mimic solvent effects on dynamics, we simulate this model using dissipative particle dynamics [21], an algorithm known to ensure correct hydrodynamic behavior. Length is measured in ...

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Modeling of Diffusion Effects on Step-Growth Polymerizations

Cited by 31 publications

References 27 publications

Modeling the Crossover between Chemically and Diffusion-Controlled Irreversible Aggregation in a Small-Functionality Gel-Forming System

Modeling the Crossover between Chemically and Diffusion-Controlled Irreversible Aggregation in a Small-Functionality Gel-Forming System

A Review of Modeling of Diffusion Controlled Polymerization Reactions

Theoretical Description of a DNA-Linked Nanoparticle Self-Assembly

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