Chain Elasticity, Shape Resistance, and Switchability

Characteristic Behavior of Polysaccharides

Polysaccharides are fundamental compounds of the living systems and known as the first biological polymers. The glucopyranose ring, with the most stable chair conformation, transforms itself into a chair-boat conformation when it passes over an energy barrier with the influence of an external force. a-(l,4) and /3-(l,3) linkages of glucose residues are shown to have an influence over transitional energy during the elongation of polysaccharides.30 Li et al. and Marszalek et al. found that the little difference between the primary structures of two isomers CM-amylose and CM-cellulose causes a huge difference in their elongation properties.35,36

CM-amylose shows a shoulder-like plateau on its force curve at about 300 pN. There is 0.08 nm elongation and

7.3 kT of required energy for conformational transition is observed per glucose residue.35 CM-cellulose has a sudden increase in its force curve and shows no plateau.

The mechanical property of the polysaccharide chain is intensely affected by different linkages; each successive /?-(!,4)-linked glucose residue can readily flip 180” to an extended conformation by an external force effect; however, a-(l,4)-linked glucose residues readily adopt a chair-boat transition in order to achieve an extended conformation during the elongation process. CM-amylose has its authentic property of conformational transition. Marszalek et al. also pointed out that the range between two glycosidic oxygen molecules that determines the length of a monomer of polysaccharide is likely to vary with the pyranose ring. Stretching the polysaccharide chain seems to help conformations and provides further separation of glycosidic oxygen molecules parallel to the extension of the molecule.35,36 Cellulose has /HI,4) linkages. In their ab initio calculations glycosidic oxygen vector (0,04) is already at its maximum value in the chair conformation. Therefore, a cellulose molecule not showing a plateau region in its force curve indicates the conformational transition of the ring structure. These results correspond to the known rigidity of cellulose.

Xu et al. performed a control experiment with a set of carrageenan-bearing oxygen bridges and oxygen bridges not bearing carrageenan. They worked with the Л-carrageenan, к-carrageenan, and L-carrageenan, which are identical in primary structure at the 1,3-linked p- D-pyranose ring of the repeating unit. However, k- carrageenan and L-carrageenan have an oxygen bridge over 1,4-linked a-D-galactopyranose in their other repeating part. Л-Carrageenan showed a shoulder-like plateau as a sign of the conformational transition process, but this process was prohibited by the effect of an additional oxygen barrier in к-carrageenan and L-carrageenan (Fig. 4.4) 37

Normalization of the force curves obtained on (а) Л-, (b) к-, and (c) L-carrageenan

Figure 4.4 Normalization of the force curves obtained on (а) Л-, (b) к-, and (c) L-carrageenan.

Effect of Small-Molecule Polymer Interaction on Switchability

It has become easy to study small molecule-polymer interactions in changing buffer by applying the SMFS technique at the solid-liquid interface in a liquid cell. Alternation of single-chain elasticity in the presence of small molecules proves the interaction between molecules and polymers.30

Wang et al. made a comparative study of the singlechain elasticity of PDMA and poly[2-(diethylamino)ethyl methacrylate] (PDEA) with SMFS. These two polymers have the same backbone structure with varying substitutions in AMinked groups. Various buffer conditions, that is, aqueous NaOH and aqueous urea solutions of 2 M and 8 M, were applied. The contour lengths of PDMA varied due to the polydisperse nature of the polymer and the uncontrolled stretching point of the AFM cantilever. The F-E curves of the polymer for different contour lengths were normalized, and the superimposed force curves are shown in Fig. 4.5a.38

It is observed that the low stretching force and rupture with no hysteresis between stretching and relaxing processes refers to the equilibrium condition. Wang et al. used the M-FJC model to describe the elasticity of a single PDMA polymer chain. Figure 4.5b shows the similar results of the PDEA sample experiments. However, a single PDEA chain is observed to be stiffer in the high-force region. This difference is attributed to the effects of side groups on the polymer backbone. When the concentration of aqueous urea was higher the stiffness of the PDMA increased. This is attributed to the formation of hydrogen bonds in PDMA. To understand the mechanisms of the interaction between

(a) Several typical force-extension curves of PDMA in an

Figure 4.5 (a) Several typical force-extension curves of PDMA in an

aqueous solution (pH 9), one of which is fitted by a modified FJC (M-FJC) curve. The fit parameters are /|< (1.3 nm, К segment) 12,000 pN/nm. The normalized force curves are superimposed and plotted in the inset, (b) Comparison of modified FJC fits and normalized force curves of PDMA and PDEA in aqueous solutions.

PDMA and urea, they measured the infrared (IR) spectra of PDMA and 8 M mixture and the 2 M urea mixture. In the case of the 2 M urea solution, Fourier-transform infrared (FTIR) spectra show similar results.

Figure 4.6a shows the similar results for the PDEA tests. The results of the dependence of the urea concentration of the PDMA and PDEA single-chain elasticity in 2 M

Comparison of normalized force curves of (a) aqueous solution and 2 M and 8 M urea buffer solutions for PDEA (b) PDMA and PDEA in 2 M urea solution (c) PDMA and PDEA in 8 M urea solution

Figure 4.6 Comparison of normalized force curves of (a) aqueous solution and 2 M and 8 M urea buffer solutions for PDEA (b) PDMA and PDEA in 2 M urea solution (c) PDMA and PDEA in 8 M urea solution.

solution are compared in Fig. 4.6b. In the 8 M concentration of urea buffer solution, the chains show no discrepancy (Fig. 4.6c).

These results suggest that sufficiently high concentrations of urea determine the elasticity of the singlepolymer chain. In many water-soluble polymers, such as polyethylene glycol) (PEG) and poly(vinyl alcohol) (PVA), hydrogen bonds are the controlling factor.39,40 Oesterhelt et al. performed an experiment to elongate the PEG molecule and observed a resistive force as the elongation function in different solvents. All the cases have given a fully reversible molecular response corresponding to the thermodynamic equilibrium.

The hexadecane PEG shows the ideal entropy spring behavior and fits perfectly to the definition of FJC in the water-based solution. The force curves show a remarkable deviation in the middle force region, which indicates suprastructure deformation within the polymer. A nonpla- nar suprastructure formed by PEG and stabilized by water bridges in an aqueous solution that is predicted through ab initio calculations agrees well with the analysis based on elastically coupled Markovian two-level systems, and the obtained binding free energy is 3.0 ± 0.3 KT.39 Also Li et al. investigated PVA at the nanoscale with SMFS and found that the elastic properties of PVA molecules scale linearly with their contour lengths. PVA shows deviation at force spectra, and this deviation may indicate a suprastructure in PVA in NaCl solution.40

Liu et al. investigated PVPr single-chain nanomechanical properties in water, ethanol, and THF solvents using the SMFS technique. The F-E curve of PVPr is noticeably deviated in water due to the provided water bridge between the carbonyl groups of pyrrolidone rings. The single chain requires more energy because this water bridge

(a) Typical force curve of the elongation of a single PVPr chain in DI water

Figure 4.7 (a) Typical force curve of the elongation of a single PVPr chain in DI water. The dotted line is the fitting curve on using the M-FJC model. Fit parameters are ly 0.63 nm and Kq 41,580 pN. (b) Comparison of the normalized force curves of the elongation of a single PVPr chain in DI water, ethanol, and THF. Fit parameters are ly 0.31 nm and Ко 38,000 pN.

needs to break for a specific amount of stretch of PVPr (Fig. 4.7).

Liu et al. also studied the PVPr-I2 force signal in the KI and KI3 aqueous solution. While the elastic properties of KI3 were significantly influenced by specific interaction, I2 and I- did not influence and this effect is analyzed by using IR. The stretched and relaxed motions repeatedly applied without rupture did not show any hysteresis (Fig. 4.8).41

Polymer-Solvent Interaction

In general, the interactions of the polymer with the appropriate solvent result in either dissolution or swelling. In the case of flexible polymer chains, units or segments of the chains can displace with solvent molecules. The dependence of the interaction energy on the intermolecular distance explains why loosely packed polymer molecules have weaker interchain interaction and increased polymer solubility.12

(a) Stretching and relaxing traces of the identical PVPr chain in aqueous KI3 solution. For clarity the two curves are offset, (b) FTIR spectra of PVPr and its mixture with KI3 at 1750-1600 cm

Figure 4.8 (a) Stretching and relaxing traces of the identical PVPr chain in aqueous KI3 solution. For clarity the two curves are offset, (b) FTIR spectra of PVPr and its mixture with KI3 at 1750-1600 cm-1: curve a, PVPr film; curve b, PVPr film under the existence of excess KI3.

In solvents of good thermodynamical characteristics polymer/segment-solvent interactions are the most active and the chain will expand to improve these interactions while reducing the polymer-polymer interaction excluded volume (EV] effect. In contrast in a solvent with poor thermodynamical features, the chain contracts to minimize the impractical polymer-solvent interactions.15

Luo et al.42 were the first ones to discover the notable influence of the EV effect on single-chain mechanics of PEG. They used four different organic solvents, including tetrachloroethane (TCE, C2H2CI4), n-nonane (C9H20), n- dodecane (C12H26). and n-hexadecane (C16H34), as liquid media in their study. In the experiment with relatively the smallest-size-solvent TCE they observed typical F-E curves, and with normalization superposed F-E curves were obtained, which is a sign of single-chain elasticity of PEG. The plateau that was observed in aqueous solution- based normalization F-E curves is not presented in TCE. The freely rotating chain (FRC) model is the proper way to describe chain elasticity of PEG as it is considered to be a flexible polymer and all C-C and C-0 bonds rotate freely. The chain structure of PEG corresponding to the quantum mechanical-freely rotating chain (QM-FRC) model calculation results suggests that the PEG chain is not influenced by the EV interaction of TCE molecules. IV-hexadecane, ~7 times larger than TCE, is used in experiments also. In Fig. 4.9 a comparison of F-E curves of PEG in TCE and n-hexadecane is shown.

Lower energy requirement for the elongation of the PEG chain in an n-hexadecane solvent than the TCE obtained is a result of the molecular size difference. Figure 4.10 shows the interaction effect on the polymer chain conformation schematically. Because of the large range in size scale between TCE and n-hexadecane two other organic solvents, n-nonane (C9H20) and n-dodecane (C12H26), were also investigated.

Comparison of the single-chain F-E curves of PEG obtained in hexadecane (cyan) and TCE (red). The dotted line is the QM-FRC fitting curve at/ь = 0.146 nm (black)

Figure 4.9 Comparison of the single-chain F-E curves of PEG obtained in hexadecane (cyan) and TCE (red). The dotted line is the QM-FRC fitting curve at/ь = 0.146 nm (black).

The schematic of the EV effect on the conformation of a polymer chain. The small and large spheres represent the solvent molecules of different sizes

Figure 4.10 The schematic of the EV effect on the conformation of a polymer chain. The small and large spheres represent the solvent molecules of different sizes.

Figure 4.11 shows single-chain F-E curves obtained from four tested solvents. As these results indicate, a nonpolar solvent can be evaluated in two classes: small-sized organic solvents in which PEG elasticity stays novel and middle- sized solvents giving F-E curves different from those of the

The normalized single-chain F-E curves of PEG obtained in organic solvents with different molecular sizes

Figure 4.11 The normalized single-chain F-E curves of PEG obtained in organic solvents with different molecular sizes.

small-sized solvents due to their EV effect on the singlechain mechanics of PEG.42

Polymers and low-molecular-weight solvents should have close affinity (hydrogen or donor-acceptor bonds) with each other, and the polymer swells before it dissolves, that is, the low-molecular-weight liquid is absorbed and inevitably changes occur in the polymer structure leading to mass and volume increase.12 A swelling occurs not only in the liquid phase but also in the gas phase, and the swollen polymer in the liquid also reacts with the gas phase of the same liquid. Even though the swelling in the gas phase is slow, it is equal to the same equilibrium state as the swelling degree in the liquid phase.12 The measurement of the swollen polymer can be monitored gravimetrically or volumetrically.

Table 4.1 Hildebrand parameters of selected solvents and polymers

Solvent

S [(MPa)1'2]

H-bonding tendency

Acetone

20.3

Medium

Butylenes (iso)

13.7

Poor

Ethyl alcohol

26

Strong

Methanol

29.7

Strong

Toluene

18.2

Poor

Water

47.9

Strong

Polymer

Poly(ethylene)

16.6

Poly(vinyl alcohol)

25.78

Poly(vinyl chloride)

19

Poly(vinylidene fluoride)

23.2

Here, a is equal to the swelling rate, V is the volume of the swollen polymer, and Vo is the volume of the unswollen polymer.

In a study that examined the mechanical behavior of a single-polymer chain in the presence of a nonsolvent in the liquid environment, Horinaka and his colleagues used a polystyrene (PS) chain in a mixture of different volumes of dioxane and methanol. According to their study in good and theta solvents F-E curves show an FRC-like tendency and good reproducibility. Nonsolvent-based experiments gave such results as F-E curves dependent on the extension speed, for example, at a relatively lower speed of 200 nm/s FRC-like was behavior observed while saw-toothed curves were obtained at 2000 nm/s. The shape of the saw-toothed curves was varied due to different measurements. A force relaxation was also seen under a fixed extension distance with 2000 nm/s extension. The mechanical behavior in the nonsolvent points to an inhomogeneous deformation in the PS chain due to a reduction in the chain mobility.

Force-extension curves for a PS chain in a liquid of

Figure 4.12 Force-extension curves for a PS chain in a liquid of

1. The extension rate was (a) 200 nm/s and (b) 2000 nm/s. The solid lines are fitted curves by the m-FJC model with the same parameters.

Because dioxane is a good solvent for PS and methanol is not, tp = 1, 0714, 0.35, and 0 dioxane volume mixtures were used, tp = 0.714 is reported to be a theta solvent for PS at 25°C.43

0.35 and tp = 0 are nonsolvents. Experimental work suggests that at tp = 1 the curve profile is independent of the extension speed (Fig. 4.12). In tp = 0.35 there is an obvious difference in F-E curves due to the extension speed, the FJC-like nature at 200 nm/s, and the saw-toothed shape at 2000 nm/s in Fig. 4.13. This data can be expressed in general as follows: the deformation is homogenous under the conditions of small deformation rate and chain motion time characteristic of products, but it is inhomogeneous when the product is large enough.44

Latent solvents exhibit little or no solvent properties at room temperature in polymer systems. However, they can become solvents at high temperatures or with appropriate solvent mixtures. For instance, acetone is used as a latent solvent for the PVDF polymer 45

Force-extension curves for a PS chain in a liquid of

Figure 4.13 Force-extension curves for a PS chain in a liquid of

0.35. The extension rate was (a) 200 nm/s and (b) 2000 nm/s. The solid line in (a) is a fitted curve by the m-FJC model.

Schematic depiction of the swelling of a polyvinyl fluoride particle by its latent solvent

Figure 4.14 Schematic depiction of the swelling of a polyvinyl fluoride particle by its latent solvent.

As a good illustration, in Fig. 4.14, poly(vinyl fluoride) (PVF) films are obtained from the dispersion of PVF using propylene carbonate or other latent solvents (especially ketones), such as iV-methyl pyrrolidone (4.1 D), y-butyrolactone (4.27 D), sulfolane (4.8 D), and dimethyl acetamide (3.7 D). PVF is insoluble at high temperatures with its latent solvent; instead it swells with the diffusion of solvent particles.46,47

 
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