Translating Simulated Chain Length and Molar Mass Distributions in Chain‐Growth Polymerization for Experimental Comparison and Mechanistic Insight

Abstract

From an industrial point of view, it has often been claimed that MMDs need to possess a sufficiently large mass average molar mass M m (e.g., 10 6 g mol −1 ) to ensure sufficient entanglements and must be broad, requiring dispersity (Ð) values well above 1.5. [5,8] For specific applications, such as coatings, MMD bimodality has even been put forward as the primary target, leading to dispersity values higher than 4. [15][16][17] For the determination of the radical propagation, [18][19][20][21][22][23] backbiting, [24][25][26][27] and β-scission [24,28] rate coefficients or the quantification of photo dissociation quantum yields, [29] a modulated MMD trace is beneficial. In contrast to modulated and broad MMDs, the more recent chemical development of living and reversible deactivation radical poly merization (L/RDRP) mechanisms has made clear that more niche applications (e.g., drug delivery or high-end cosmetics) can benefit from lower M m values (e.g., 10 4 g mol −1 ) and narrow monomodal MMDs with Ð values below 1.5. [30][31][32][33][34][35][36] This dedicated molecular tailoring is also related to control over end-group functionality to enable the synthesis of more special polymers such as block, gradient, and star (co)polymers. [37][38][39][40][41] Therefore, a dedicated knowledge of the relationship between reaction conditions and MMD is indispensable for any polymerization mechanism.The key analytical tool for MMD characterization is size exclusion chromatography (SEC) or equivalently gel permeation chromatography (GPC) in which longer chains-so species with higher molar masses-elute first, as they have fewer interactions with the smaller pores in the packed columns. The chains with the highest molar masses are thus located at the lowest retention times (RTs) in the chromatogram so that the recorded chromatogram corresponds to a "reverse" MMD. This is illustrated in Figure 1a employing a refractive index (RI) detector, which is also known as single GPC detection. Ideally, calibration takes place with standards of the same polymer type that are characterized by very narrow MMDs (Ð values close to 1), as demonstrated in Figure 1b. In many research groups, one finally aims at a log-MMD representation, requiring a normalization on logarithmic scale. This is illustrated by the arrow between Figure 1c,d and leadsThe molar mass distribution (MMD), which is also known as the molecular weight distribution (MWD), is a key molecular property for a polymerization process, as it determines polymer strength and polymeric material deformation. Several MMD and related chain length distribution (CLD) representations are however used interchangeably, often leading to biased conclusions. Herein it is highlighted how the most interesting simulated CLD/MMD representations, i.e., the number, mass, z-based, and logarithmic CLD/MMD, can be translated into each other and how they need to be corrected to facilitate comparison with experimental size exclusion chromatography traces. Their relevance is highlighted by including case st...

A unified kinetic Monte Carlo approach to evaluate (a)symmetric block and gradient copolymers with linear and branched chains illustrated for poly(2-oxazoline)s

“…38 This correction assumes that all species are linear so that with a significant population of branched species further modifications are still required (see Modeling section). All distributions were normalized according to the best practices outlined in the recent work of Marien et al 72…”

“…Kinetic Monte Carlo principles CROP of MeOx and PhOx is simulated via kMC modeling based on previous work by Van Steenberge et al, 62 which uses as core the stochastic simulation algorithm 8 and the matrixbased extensions as highlighted by Trigilio et al 55 The kMC algorithm samples reaction events and time increments between these reaction events based on so-called microscopic MC reaction rates (s −1 ). In this way, CROP characteristics such as the (fractional) (co)monomer conversions (X M,A and X M,B ), number and mass average molar masses (M n and M m ), the dispersity (Đ), and the complete chain length distribution (CLD) or MMD 72 are calculated as a function of time or total monomer conversion.…”

“…To allow for direct comparison with experimental SEC traces, the simulated molar masses of the branched species are increased by a factor 1.1 to account for their lower hydrodynamic volume compared to linear chains of the same molar mass, as explained in previous work. 66,72 Also, SEC broadening 74,75 is applied to simulate logarithmic-molar mass distributions (log-MMDs). 72 A SEC broadening parameter within the range of 0.01-0.05 (see bottom part of Fig.…”

“…66,72 Also, SEC broadening 74,75 is applied to simulate logarithmic-molar mass distributions (log-MMDs). 72 A SEC broadening parameter within the range of 0.01-0.05 (see bottom part of Fig. S11 in the ESI †) typical for poly(2-oxazoline) systems is considered for both linear and branched chains.…”

Exploiting (Multicomponent) Semibatch and Jacket Temperature Procedures to Safely Tune Molecular Properties for Solution Free Radical Polymerization of n‐Butyl Acrylate

“…[5][6][7][8][9][10][11] Also the chain length or molar mass distribution (CLD/MMD) is greatly affected by these side reactions. [12] In particular, the (number/mass) average chain length/molar mass is reduced at higher temperatures, while the dispersity of the MMD increases. [13] Up to high but not extremely high temperatures (e.g., 333 K) both conventional dead polymer chains and macromonomer species (containing C═C moieties) are substantially formed.…”