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4 Exergy and Life-Cycle Assessment

4 Exergy and Life-Cycle Assessment

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Energy Efficiency and Renewable Energy. Just the Basics—Diesel Engine. 2003. Washington,

DC, U.S. Department of Energy, http://www1.eere.energy.gov/vehiclesandfuels/­


Higman, C. and M. van der Burgt. 2003. Gasification. Burlington, MA: Elsevier (Gulf

Professional Publishing).

Szondy, D. 2012. Liquid piston unveils 40-bhp X2 rotary engine with 75 percent thermal

­efficiency. Gizmag, http://www.gizmag.com/liquidpistol-rotary/24623/

Tester, J.W., E.M. Drake, and M.J. Driscoll et al. 2005. Sustainable Energy. Choosing Among

Options. Cambridge, MA: MIT Press.

Winterton, N. 2011. Chemistry for Sustainable Technologies. A Foundation. Cambridge, UK:

RSC Publishing.


Polymers and

Sustainable Energy


Polymers are an integral part of all aspects of sustainable energy solutions. Everything

from wind turbine blades to biomass is made up of polymers, the high molecularweight macromolecules that are a ubiquitous part of our lives. This chapter presents

the basics of polymer chemistry with a few examples in the realm of CO2 separation

(Section More depth is provided in the context of the composite polymers

used in the fabrication of wind turbine blades. Additional applications of polymer

chemistry in sustainable energy are introduced in later chapters in the context of fuel

cells (Chapter 6), solar photovoltaics (Chapter 7), and biomass (Chapter 8).

Unlike typical small molecules studied in introductory chemistry courses, polymers are macromolecules with molecular weights hundreds of times larger, typically

in the range of 10,000 and 1,000,000 amu. They may be synthetic (e.g., polystyrene) or

natural (e.g., cellulose) or they may be characterized by their behavior: thermoplastics

soften when heated and return to their original state by cooling, whereas thermosetting

polymers do not become pliable with heating. The difference in this behavior is due

to differences at the molecular level: in thermoset polymers, the individual polymer

chains have been covalently cross-linked and covalent bonds must be broken for the

material to flow. Vulcanization of rubber is an example of cross-linking. In thermoplastics, intermolecular forces are primarily responsible for their behavior; addition

of heat merely overcomes these intermolecular interactions that reform upon cooling.

Regardless of whether it is a thermoplastic or a thermoset polymer, these macromolecules are made up of hundreds to thousands of small-molecule monomers that

are linked together, with the common name of the polymer stemming from the name

of the monomer. For example, the monomer that makes up polyvinyl chloride (PVC)

is, aptly enough, vinyl chloride (Figure 4.1; n = a large number, where * indicates

that the polymer chain extends indefinitely). PVC is an example of a homopolymer,

that is, a polymer made from a single monomer. Copolymers, in contrast, are made

from more than one monomer. A protein would be an example of a natural copolymer

that is made up of a variety of amino acid monomers. Most polymers are made up

of a regular repeating unit that is equivalent to the monomer. In the case of PVC, the

repeat unit is the –CH2CHCl– segment. The polyamide nylon 6,6 is a regular copolymer made up of two monomers—1,6-­hexanediamine and adipoyl chloride—that

combine to make the adipoyl hexanediamine amide repeating unit (see Figure 4.2).

Reference is also often made to oligomers, which are simply short fragments of a

polymer, often consisting of just a few repeating units.



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Polyvinyl chloride

Vinyl chloride


FIGURE 4.1  Polyvinyl chloride.








Adipoyl chloride O










Repeating unit

FIGURE 4.2  Synthesis of nylon 6,6.

A key feature of synthetic polymers that makes their properties and behavior different from that of small molecules is the fact that a synthetic polymer is not a single,

unique molecule: it is a conglomerate array of many molecules of varying lengths

and (to some degree) structures. Some individual chains are shorter, some longer.

Some may be branched, whereas others are linear. For each polymer, there is an

associated statistical distribution of individual chains in the bulk sample. Unlike a

small molecule, then, a typical polymer does not have a unique molecular weight or,

even, a single determinate structure.

The bulk behavior of a polymer, therefore, encompasses the properties of all

of the molecules that make up the sample. The statistical distribution and chemical heterogeneity, the length and structure of the individual units, the presence or

absence of cross-linking, and the conformational flexibility all impact a polymer’s

properties such that polymers range from clear, brittle plastics to sticky adhesives

or bouncy elastomers. Furthermore, given the sheer size of polymers, intermolecular forces play an outsized role. For example, a polymer may be elastic as a

result of low intermolecular forces and chains with good conformational flexibility

(styrene–­butadiene rubber is a good example, Figure 4.3). If bulky substituents or

stronger intermolecular forces are present, the polymer is likely to behave more like

a ­“typical ­plastic.” Very high intermolecular forces (e.g., hydrogen bonding) and

crystallinity (as a result of the symmetry of the molecules) can lead to a polymer with


Polymers and Sustainable Energy

FIGURE 4.3  Styrene–butadiene rubber.










Kevlar 

FIGURE 4.4  A para-substituted polyaramide, Kevlar®.

excellent mechanical strength (as in Kevlar™, Figure 4.4, a material used in bulletproof f­ abrics) (Billmeyer 1984).

The average molecular weight of a polymer can be calculated by taking into

account the average degree of polymerization (DP) and the molecular weight of the

repeating unit. The degree of polymerization is equivalent to the number of repeat

units, n. Thus, the average molecular weight of a strand of nylon 6,6 with n = 10,000

would be approximately 2.26 × 106 amu because the repeat unit C12H22N2O2 has a

molecular weight of 226.

More commonly, the molecular weight of the bulk polymer is reported as a

statistical average that takes into account the distribution of individual chains.

This “molar mass distribution” is most commonly reported as either the number-­

average (Mn) or the weight-average (Mw) molecular weight. Imagine a hypothetical

polymer consisting of 100 individual chains with the following molecular weight


10 chains @ 80 amu

10 chains @ 100 amu

10 chains @ 120 amu

60 chains @ 140 amu

10 chains @ 160 amu

The number-average molecular weight for this hypothetical polymer is the simple

arithmetic mean, as given by Equation 4.1, where ni is the number of chains with

molecular weight Mi and Σni is the total number of individual chains.

Mn =

Σni Mi




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In this example, the number-average molecular weight Mn is 130 (Equation 4.2).

(10 × 80) + (10 × 100) + (10 × 120) + (60 × 140) + (10 × 160)


13, 000



= 130


Mn =

As a simple counted quantity, Mn reflects the number of discrete particles in the

sample and can, therefore, be determined by measuring colligative properties such

as vapor pressure lowering, boiling point elevation, freezing point depression, or

osmotic pressure for a very dilute solution of the polymer. More commonly, Mn is

determined along with a complete molecular weight profile using size-exclusion

chromatography (SEC) (vide infra).

The mathematical representation of weight-average molecular weight (Mw) is

shown in Equation 4.3, where wi = niMi = the weight of the chains with molecular

weight Mi.

Mw =

Σwi Mi

Σni Mi2



Σni Mi


In this case, the weight average of our hypothetical polymer sample would be 145

as shown in Equation 4.4.


(10 × 6400) + (10 × 10, 000) + (10 × 14, 400) + (60 × 19, 600) + (10 × 25, 600)

(10 × 80) + (10 × 100) + (10 × 120) + (60 × 140) + (10 × 160)

1, 740, 000


= 145


12, 000

Mw is always greater than Mn since larger chains weigh more than smaller chains

and molecular weight is squared in the Mw calculation. Thus, the higher-molecularweight chains skew the average to a higher value (Figure 4.5). The weight-average

molecular weight Mw can be determined using light-scattering techniques, ultracentrifugation or, as for Mn, by using the liquid chromatographic technique of SEC (vide


Why are Mn and Mw important properties? It is the ratio of Mw to Mn (Mw/Mn;

the polydispersity of the polymer) that gives an idea of the breadth of the molecular

weight distribution and thus insight into the bulk properties of the polymer, including

tensile strength, elasticity, hardness, and resistance to stress and cracking. For example, if a polymer contains many low-molecular-weight chains, those molecules can

act like a plasticizer and soften the polymer. In contrast, higher-molecular-weight

chains have a tendency to tangle more, increasing the viscosity of the polymer’s liquid melt. If Mw = Mn, then the polymer is monodisperse, characteristically true in the

case of natural polymers. Synthetic polymers range from narrowly to very broadly

polydisperse, as shown below (Billmeyer 1984).


Polymers and Sustainable Energy

Number average, Mn

Amount of polymer

Weight average, Mw

Molecular weight

FIGURE 4.5  Distribution of molecular weights in a typical polymer. (Billmeyer, F.W.

Textbook of Polymer Science, p. 17. New York: Wiley-Interscience. 1984. Copyright

­Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

Type of Polymer

Monodisperse polymer

Actual monodisperse “living” polymer

Addition polymer (terminated by coupling)

Addition polymer (termination by chain

transfer) or condensation polymer

High conversion vinyl polymers

Branched polymers








The determination of polymer molecular weights and distribution of individual

chain lengths are perfectly suited to the liquid chromatographic technique known

as SEC. SEC (or the more specific term gel permeation chromatography, GPC, as

it is referred to by material scientists) sorts particles (molecules) in solution according to their size. Like any liquid chromatographic technique, the method consists

of a solid phase and a mobile phase, but unlike chromatographic techniques that

rely on the adsorption of the analyte to the adsorbent, SEC separates the analytes

in solution by mechanical means: the different-sized particles are sieved through a

stationary phase “gel” (hence, gel permeation) consisting of cross-linked polymer

beads. This gel is made up of millions of porous particles through which the dissolved analyte passes (see Figure 4.6). Larger polymers move through the gel more

quickly as the smaller particles permeate the pores and are retained. Thus, polymers

of different sizes exhibit different retention times, and a chromatogram that can be

converted into a molecular mass distribution (MMD) results (Figure 4.7). The higher


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Gel polymer


FIGURE 4.6  A cartoon of the gel permeation process.

the retention time of the molecular weight distribution, the lower the average molecular weight. The breadth and retention time(s) of the MMD are inextricably related

to the physical properties of the final polymer product. It is important to note that,

unlike the c­ olligative measurements or light-scattering experiments that provide a

direct measure of molecular weight, the use of GPC requires careful construction

of a calibration curve using known molecular weight standards. If the polymer of









Elution volume/cm3

FIGURE 4.7  Molar mass distribution from gel permeation chromatography. (From

Nicholson, J.W. 2006. The Chemistry of Polymers. 3rd ed. Cambridge: Royal Society of

Chemistry. Reproduced by permission of The Royal Society of Chemistry.)


Polymers and Sustainable Energy

interest and those used in the calibration curve are different, this method can only

provide relative molecular weight values.


Given that the properties of a polymer are related to the distribution of the individual

chains that make up the bulk sample, a quick overview of the synthesis of polymers

is necessary to help us understand how and why the dispersity of these materials can

vary. There are several types of polymer synthesis but we will primarily focus on

only the two most general: step or chain growth. A third area, coordination polymerization, takes advantage of transition metal organometallic catalyst systems. While

it is an exceptionally powerful method for the polymerization of alkenes, it is arguably less relevant in the context of sustainable energy processes and so will not be

covered in this text.

4.2.1  Step-Growth Polymerization

Step-growth polymerizations are usually (but not always) condensation reactions,

where a small molecule is expelled in the reaction between monomers. For example,

the synthesis of polyethylene terephthalate (PET, a plastic often used in carbonated beverage bottles) is a typical esterification reaction in which water is expelled

(Figure 4.8). The only difference between this polymerization and a small-molecule

esterification is that the reacting species are polyfunctional, allowing for multiple

reaction sites. The nature of the mechanism for step-growth polymerizations means

that the polymer molecular weight will increase in a slow, step-like manner as the

reaction proceeds. Hence, dimers form initially, then dimers can link to form tetramers, tetramer joins tetramer to form octomers, and so on. Of course, the real scenario is not so strictly regimented; a monomer can react with a dimer or a tetramer

with a dimer, and so on. In any case, in order for a high-quality, high-molecularweight polymer to be obtained, enough time must pass to allow the reaction to proceed to completion (or nearly so).

Polycarbonates (Figure 4.9a) are examples of polymers that can be synthesized by

step-growth methods. These polycarbonates prepared with aromatic monomers such

as bisphenol A (BPA, Figure 4.9b) are tough and transparent “engineering plastics”

used as lenses, in CDs and DVDs, as construction materials, and as components in

automobiles and aircraft (Pescarmona and Taherimehr 2012). The C1 unit of polycarbonates makes them excellent prospects for the utilization of captured CO2 (Section





Ethylene glycol

(n mols)

– n H2O





p-phthalic acid

(n mols)





Polyethylene terephthalate (PET)

FIGURE 4.8  Synthesis of polyethene terephthalate via condensation.



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Generic polycarbonate



Bisphenol A polycarbonate

FIGURE 4.9  Examples of polycarbonate structures. and indeed, an environmentally friendly (i.e., green; Section 4.6) industrial

synthesis of polycarbonate has been developed via the scheme shown in Figure 4.10

(Fukuoka et  al. 2003). Not only can this synthesis use captured CO2 as one of

the starting materials, it replaces the use of the highly toxic C1 reagent, phosgene

(ClC(O)Cl). The chemists developing this industrial route found that it was difficult

to make the polymerization progress beyond a degree of polymerization of about

20 due to an extreme increase in the viscosity of the reaction mixture as the polymerization continued (a DP of 30–60 is required for the polycarbonate to possess the

desired properties). This problem was remedied by developing a unique solid-state

polymerization process utilizing a novel gravity-fed reactor, making this industrial

process of polycarbonate manufacture especially benign (Fukuoka et al. 2003). It is

worth noting here that aliphatic polycarbonates can be prepared from the reaction of

CO2 plus any of a number of epoxides. However, these polymers have lower rigidity and poorer thermal stability than aromatic polymers such as the BPA copolymer

described above (Kember et al. 2011).



+ CO2









Diphenyl carbonate




Dimethyl carbonate









Bisphenol A polycarbonate


Bisphenol A



FIGURE 4.10  A green polycarbonate synthesis using captured CO2.




Polymers and Sustainable Energy






Ph = C6H5







FIGURE 4.11  Polymerization of styrene by radical chain growth.

4.2.2  Chain-Growth Polymerization

Chain-growth polymerization is mechanistically distinct from stepwise polymerization. A classic example of chain polymerization is the radical-initiated polymerization of styrene to make polystyrene, well known as the familiar foam carry-out

container (Figure 4.11). A wide variety of olefin monomers can be polymerized by

the radical chain mechanism. As with all chain reactions, the reaction proceeds by

three mechanistic steps: initiation, propagation, and termination. Unlike stepwise

polymerizations, in chain-growth polymerizations, the monomer itself is generally

unreactive: some sort of initiation is required to form the reactive intermediate. Note

that chain polymerization can proceed via anionic (R–) or cationic (R+) intermediates as well as by radicals. For example, the synthesis of poly(p-phenylenevinylene)

(PPV), a conjugated polymer with the potential for use in organic photovoltaics, is

shown in Figure 4.12 (Cosemans et  al. 2011). When the reaction is carried out in

tetrahydrofuran, it proceeds by the anionic mechanism shown.

A significant difference between step-growth and chain-growth polymerization

is that in chain polymerization, high-molecular-weight chains are formed virtually

instantaneously as the monomer is rapidly added sequentially to the reactive terminus of each growing chain during the propagation. Thus while the yield increases

with time, the molecular weight distribution is fairly stable over the course of the

reaction. The polymerization is complete when all of the monomer is consumed or

the reaction terminates. Termination can occur by the addition of a quenching agent

or the active radicals can dimerize or react in a chain transfer reaction (see Figure

4.13). In contrast, in step-growth polymerization, the molecular weight increases

steadily over the course of the reaction.

4.2.3  Block Copolymers and CO2 Separation

It is often desirable to modify the properties of a polymer by incorporating other

monomers into the polymer product to give a copolymer. This can take place during either the synthesis (copolymerization) or postsynthesis (by grafting additional

molecular material to the already prepared polymer, giving a graft copolymer).

Copolymers can be random (e.g., A–B–B–A–A–B–A–B–A–B–A–A–A), regular

(e.g., A–B–B–A–B–B–A–), or block (e.g., A–A–A–A–B–B–B–B–). Block copolymers can be diblock, triblock, or even multiblock. The sulfonated polybenzophenone/poly(arylene ether) shown in Figure 4.14 is an example of a block copolymer

synthesized for use in polymer electrolyte membrane fuel cells. The block nature of

the copolymer leads to hydrophobic and hydrophilic domains that can lead, as we

will see in Chapter 6, to good fuel cell performance (Miyahara et al. 2012).

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