provides a reliable measurement of the ratio of the two functions. The ratios of the integral of the peak
centered at 12 ppm (methyl group of the octyl side chain) and of half of that at 22 ppm (the two methyl
groups of the isopropyl side chain) to the sum of the integrals of unmodified and modified carboxylates
yield, respectively, the grafting ratios of octyl and isopropyl side chains, which are comparable to the
estimates obtained by
1 H NMR.
Further estimation of grafting ratios can be obtained by elemental analysis and by pH-metry
(estimation of free carboxylates), the latter being performed in 80:20 v/v ethanol/water.
Protocol prepared by Fabrice Giusti on the basis of Tribet et al. (1996), Gohon et al. (2004,
2006), Giusti et al. (2014), and laboratory notes.
4.6
Annexes
4.6.1
Annex 4.1. Determining and Expressing the Average Mass and Dispersity
of Polymers
Determining the average mass of synthetic polymers is challenging, the main issue being that, whatever the synthesis
pathway, a polymer preparation will always present a more or less broad molecular mass distribution. Synthetic polymers
result from the successive incorporation of units called monomers, which react on themselves to form a macromolecular
chain, much like, in vivo, amino acids associate one with another to yield the primary structure of a protein. However, at
variance with biomacromolecules, whose number of units (sugars, amino acids, nucleotides, isopentenyl, etc.) and
sequence are usually well-defined, the number of monomers that form a synthetic macromolecular chain can only be
approximated by an average value and a rough estimation of deviations from this average. This is a consequence of the
fact that chemical synthesis of long polymers cannot be controlled step by step, as most biological syntheses are, but
comprises many sources of length variation.
4.6.1.1 The Origin of Dispersity
Polymerization reactions fall into two main categories, chain-growth polymerization, where the reaction produces only
macromolecular chains, and step-growth polymerization, where the reaction produces macromolecular chains and
by-products called condensates (Flory 1953). Polycondensation (such as a diol or diamine reacting with a diacid,
yielding respectively polyester and polyamide, with water as the condensate; Fig. 4.36A) is an example of step-growth
process, whereas radical and ionic (cationic or anionic) polymerization are examples of chain-growth processes
(Fig. 4.36B).
Both methods lead to heterogeneous mixtures. As an example, we will consider the case of free radical
polymerization, a chain-growth process, with monomers endowed with a vinyl group (Fig. 4.37). Polymerization is
initialized by an initiator (Ini 2 ), whose decomposition generates two free radicals (Ini
•
). The radicals react with a
monomer (M) to form the first reactive adduct initiator monomer (Fig. 4.37, Step 1) (Mayo et al. 1951). Next, each
adduct reacts with another monomer to form a di-adduct, which in turn reacts with yet another monomer, yielding a
tri-adduct, etc., leading to the formation and growth of a macroradical. The growth step is called propagation (Fig. 4.37,
Step 2). One would be tempted to postulate that the final size of the polymer can be simply defined by the ratio of the
initial concentration of the monomer to that of the initiator. However, reality is more complicated, the growth of the
macroradicals being limited by several random phenomena, namely the efficiency of the initiator, the randomness of
growth from one polymer to the next, transfer reactions, and the vagaries of reaction termination.
The efficiency of the initiator is related to the fraction of Ini
• radicals that do react with a monomer to initiate the
polymerization, which is not 100%. Further, the growth of the chains can be stopped by transfer reactions, which occur
between a macroradical and a second partner, which can be either the solvent, a monomer, an initiator, or an impurity
(Fig. 4.38). Those reactions that generate a macromolecule and a new free radical affect the size of the macromolecule in
formation, without stopping the polymerization process, as the newly formed radical reacts with unreacted monomers to
yield another macroradical. The process of polymerization is stopped by disappearance of the free radicals. This may
occur according to various mechanisms, among which chain disproportionation and combination (Fig. 4.37, Step 3).
Chain disproportionation involves the transfer of an atom (hydrogen, essentially) from a macroradical donor to a
macroradical acceptor, which combination entails the covalent coupling of two macroradicals. Given the existence of
these various factors, the final preparation is necessarily polydisperse.
210
4 Chemical Structure, Synthesis, and Physical-Chemical Properties of Amphipols
centered at 12 ppm (methyl group of the octyl side chain) and of half of that at 22 ppm (the two methyl
groups of the isopropyl side chain) to the sum of the integrals of unmodified and modified carboxylates
yield, respectively, the grafting ratios of octyl and isopropyl side chains, which are comparable to the
estimates obtained by
1 H NMR.
Further estimation of grafting ratios can be obtained by elemental analysis and by pH-metry
(estimation of free carboxylates), the latter being performed in 80:20 v/v ethanol/water.
Protocol prepared by Fabrice Giusti on the basis of Tribet et al. (1996), Gohon et al. (2004,
2006), Giusti et al. (2014), and laboratory notes.
4.6
Annexes
4.6.1
Annex 4.1. Determining and Expressing the Average Mass and Dispersity
of Polymers
Determining the average mass of synthetic polymers is challenging, the main issue being that, whatever the synthesis
pathway, a polymer preparation will always present a more or less broad molecular mass distribution. Synthetic polymers
result from the successive incorporation of units called monomers, which react on themselves to form a macromolecular
chain, much like, in vivo, amino acids associate one with another to yield the primary structure of a protein. However, at
variance with biomacromolecules, whose number of units (sugars, amino acids, nucleotides, isopentenyl, etc.) and
sequence are usually well-defined, the number of monomers that form a synthetic macromolecular chain can only be
approximated by an average value and a rough estimation of deviations from this average. This is a consequence of the
fact that chemical synthesis of long polymers cannot be controlled step by step, as most biological syntheses are, but
comprises many sources of length variation.
4.6.1.1 The Origin of Dispersity
Polymerization reactions fall into two main categories, chain-growth polymerization, where the reaction produces only
macromolecular chains, and step-growth polymerization, where the reaction produces macromolecular chains and
by-products called condensates (Flory 1953). Polycondensation (such as a diol or diamine reacting with a diacid,
yielding respectively polyester and polyamide, with water as the condensate; Fig. 4.36A) is an example of step-growth
process, whereas radical and ionic (cationic or anionic) polymerization are examples of chain-growth processes
(Fig. 4.36B).
Both methods lead to heterogeneous mixtures. As an example, we will consider the case of free radical
polymerization, a chain-growth process, with monomers endowed with a vinyl group (Fig. 4.37). Polymerization is
initialized by an initiator (Ini 2 ), whose decomposition generates two free radicals (Ini
•
). The radicals react with a
monomer (M) to form the first reactive adduct initiator monomer (Fig. 4.37, Step 1) (Mayo et al. 1951). Next, each
adduct reacts with another monomer to form a di-adduct, which in turn reacts with yet another monomer, yielding a
tri-adduct, etc., leading to the formation and growth of a macroradical. The growth step is called propagation (Fig. 4.37,
Step 2). One would be tempted to postulate that the final size of the polymer can be simply defined by the ratio of the
initial concentration of the monomer to that of the initiator. However, reality is more complicated, the growth of the
macroradicals being limited by several random phenomena, namely the efficiency of the initiator, the randomness of
growth from one polymer to the next, transfer reactions, and the vagaries of reaction termination.
The efficiency of the initiator is related to the fraction of Ini
• radicals that do react with a monomer to initiate the
polymerization, which is not 100%. Further, the growth of the chains can be stopped by transfer reactions, which occur
between a macroradical and a second partner, which can be either the solvent, a monomer, an initiator, or an impurity
(Fig. 4.38). Those reactions that generate a macromolecule and a new free radical affect the size of the macromolecule in
formation, without stopping the polymerization process, as the newly formed radical reacts with unreacted monomers to
yield another macroradical. The process of polymerization is stopped by disappearance of the free radicals. This may
occur according to various mechanisms, among which chain disproportionation and combination (Fig. 4.37, Step 3).
Chain disproportionation involves the transfer of an atom (hydrogen, essentially) from a macroradical donor to a
macroradical acceptor, which combination entails the covalent coupling of two macroradicals. Given the existence of
these various factors, the final preparation is necessarily polydisperse.
210
4 Chemical Structure, Synthesis, and Physical-Chemical Properties of Amphipols