Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational and Structure Analysis by Rietveld Refinement

*Mercedes Pérez Méndez, José Fayos Alcañiz and Marc Meunier*

## **Abstract**

Molecular modeling techniques are applied to polyesteramides designed as PNOBDME (C34H38N2O6)n and PNOBEE (C26H22N2O6)n, synthesized and characterized as cholesteric liquid crystals -through the condensation reaction between 4 and 4<sup>0</sup> -(terephthaloyl- diaminedibenzoic chloride (NOBC) and racemic glycol: DL-1,2 dodecanediol, or DL-1,2-butanediol, respectively, being chemical modifications of precursor multifunctional cholesteric LC polyesters, adding new properties but holding their helical macromolecular structures. Although the starting raw materials were racemic, these cholesteric LC polymers exhibit unexpected optical activity and chiral morphology. For that reason, conformational analysis is studied on the monomer models of PNOBDME and PNOBEE. Four helical conformers models, experimentally observed by NMR, are proposed for each cholesteric polyesteramide: R*gg*, R*gt,* S*gg*, S*gt*. Polymerization of the monomeric conformers, with minima energies, have been simulated and used to reproduce the crystalline fraction observed by x-ray diffraction. Three orders of chirality are observed in the structure of the polymer chains: One due to the asymmetric carbon atoms, a second chirality due to the two successive rotations of the benzene groups, along the main chain, within the monomer which implies the formation of helical molecules, for both *R* and *S* chirality and still, a third chirality corresponding to the twisting of the rigid/semirigid cholesteric LC polymer chains. All these factors contributing to the net optical activity observed in these materials. Crystal packing is simulated in triclinic primitive P1cells, with molecular chains oriented parallel to the *z*-axis (*c* lattice parameter equal to the pitch length of each simulated polymer helix) and parameters *a*, *b, α, β* and *γ,* obtained by Pawley refinement from the known structures of precursor polyesters. The simulated x-ray diffraction patterns of the proposed crystal models fit, after successive Pawley and Rietveld refinement cycles, the experimental WAXS. Powder Quantitative Phase Analysis applied to an ideal mixture with the four possible helical conformers, for each degree of polymerization, allows to refine their relative weight and determine the major phase relative amount. These results would confirm the theory of a preferable recrystallization, among the four possible helical diastereoisomers, depending on the synthetic conditions.

**Keywords:** Cholesteric Liquid-Crystal Polyesteramides, Molecular modeling, WAXS synchrotron radiation source, Conformational Analysis, Rietveld refinement, Crystal polymeric chains models

## **1. Introduction**

In 1953, K. Ziegler discovered a catalytic system to obtain industrially linear crystalline polyethylene at mild temperatures and pressures (based on titanium halides and organoaluminium compounds). In 1954, G. Natta developed crystalline polypropylene and proved the unprecedented regularity of its molecules and helical form of its crystals. In 1963 both scientists shared the Nobel Prize in Chemistry by having created the science of "regular polymers and stereospecific polymerization" [1].

Wallace Carothers had stated in 1929, working at the DuPont company, the aim to prepare polymers of particular structure through the use of established organic reactions and he had demonstrated the relationship between structure and properties for some polymers: polyesters, polyamides, neoprene, etc. He had first claimed that structural and stereochemical factors will usually be more important factors than others, such as temperature, in bifunctional condensation reactions, explained in terms of a step-growth of bi-functional monomers reacting to first form dimers, then trimers, longer oligomers and eventually long-chain polymers [2].

The problem arose of the relationship between the conformation of stereoregular macromolecules in the crystalline state and in solution, as well as between stereoregularity and conformation. The research in this field stimulated the synthesis of optically active polymers, particularly vinyl polymers, with the hope that optical activity might be of help in investigating the conformation of macromolecules in solution [3].

Since then, the synthesis and application of optically active synthetic polymers and their structure control have attracted growing interest. Three major groupings can be established among them: polymers with optical activity arising from asymmetric centers in the side or main chain; polymers with optical activity arising from both asymmetric centers and macromolecular asymmetry based on the secondary structure (i.e., a helix); and polymers with optical activity arising entirely from conformational asymmetry (macromolecular asymmetry) when the polymers are prepared by helix-sense selective polymerization [4].

Chirality is essential for life and chiral phenomena play significant roles in nature. Most of the naturally occurring molecules/macromolecules, such as nucleic acids, proteins, and polysaccharides are chiral and optically active. This situation can be very obviously seen if we look at the chirality of nearly 800 drugs (about 97%) derived from natural sources. Only 2% are racemates and only 1% is achiral [5].

The parallel behavior between liquid-crystals in materials science and lipids in life science was pointed out by Ringsdorf in 1988, based on their common amphiphilic nature, being both self-organizing systems [6].

In 1992 the International Union of Crystallography re-defined the concept of crystal as: "Any solid which has a diffraction pattern essentially discrete" (Fourier space) [7]. The *Crystal Family* was accepted to be composed of: *Periodic* and *aperiodic crystals*. Liquid-crystals (LC) belonging to the last group.

DNA behaves as a liquid-crystal with a cholesteric mesophase, described as the special array of nematic planes, containing complementary base pairs, stacked in a superstructure with chiral helical symmetry of charge distribution [8–10].

Two polyesteramides designed as PNOBDME (C34H38N2O6)n and PNOBEE (C26H22N2O6)n in **Figure 1a** and **b**, have been synthesized and characterized as *Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

#### **Figure 1.**

*The monomeric unit of polyesteramides: (a) PNOBDME; (b) PNOBEE. The three different zones of the monomer:* mesogen*,* spacer *and* flexible side chain *are indicated. The asterisk indicates the chiral center (12C\*) in PNOBDME and (4 C\*) in PNOBEE, both in the flexible spacer. Torsion angles* <sup>φ</sup>, *along with the 11C-12C\* bond and <sup>3</sup> C-<sup>4</sup> C\* bond, respectively, are indicated. Aromatic-end acid and aliphatic-end alcoholic groups are also specified.*

cholesteric liquid crystals -through the condensation reaction between 4 and 40 -(terephthaloyl- diaminedibenzoic chloride (NOBC) and racemic glycol: DL-1,2 dodecanediol, or DL-1,2-butanediol, respectively [11–13], being chemical modifications of precursor multifunctional cholesteric LC polyesters PTOBDME [C34H36O8]n and PTOBEE [C26 H20 O8]n [14–16], shown in **Figure 2**, with newly added properties but holding their helical macromolecular structures. All of them have been shown to be biocompatible against macrophages and fibroblasts cellular lines and behave as both thermotropic and lyotropic. Besides, they can interact with biomacromolecules such as lipids (both neutral and cationic) and with

#### **Figure 2.**

*Monomeric unit of precursor cholesteric liquid-crystalline polyesters PTOBDME (m = 9) and PTOBEE (m = 1). The asterisk in the spacer indicates the chiral center (12C\*) in PTOBDME and (4 C\*) in PTOBEE.*

polynucleotides and nucleic acids. They have proved to be able to act as non-viral vectors in gene therapy [17, 18].

Although the starting raw materials were all racemic, the studied cholesteric LC polymers exhibit unexpected optical activity and chiral morphology.

According to our previous experience, each enantiomeric polymer shows two independent sets of signals, observed by conventional NMR techniques, attributed to two diastereomeric conformers: *gg* and *gt*, differentiated with the apostrophe (') and without it (). They have been related with two possible staggered conformations of the torsion angle *φ*- containing the asymmetric carbon atom in the spaceralong the 11C-12C\* bond in PNOBDME and <sup>3</sup> C-<sup>4</sup> C\* bond in PNOBEE respectively, with two possible helical screw sense of the polymer chain.

Chirality observed in racemic precursor polyesters was proposed to be due to the kinetic resolution of a preferable helical diastereomer, such as *Sgt*, concerning the possible four forms, while the *R*/*S* ratio of asymmetric carbon atoms remained 50/50.

The same behavior has been observed in six similar functionalized cationic cholesteric liquid crystal polymers also synthesized in our lab [19].

Molecular models of all these LC polymers had always shown helical polymeric chains with stereoregular head-tail, isotactic structure, explained as being the result of the higher reactivity of the primary hydroxyl OH-groups concerning the secondary ones, in the glycol, through the condensation reaction. In agreement with Carothers, the structural and stereochemical factors are crucial elements in the progress of polymer structure through the condensation reaction [2].

The structural fragment, including chiral secondary alcohol and a primary alcohol group (a beta-chiral 1,2 diol) is particularly interesting since it is present in many relevant natural products, such as sugars, nucleosides, glycerides) [20], chiral nanostructures from helical polymers and metallic salts [21].

A detail of the spacer is visible in **Figure 3**, showing the secondary alcohol group bonded to chiral 12C\* in PNOBDME (to <sup>4</sup> C\* in PNOBEE) and the primary alcohol bonded to 11C (to <sup>3</sup> C in PNOBEE).

Tetrahedral carbon atoms **11C**, allocated in *α* with respect to the asymmetric carbon atom 12C\* (**Figure 1a**), and **<sup>3</sup> C** in PNOBEE, in *α* with respect to chiral <sup>4</sup> C\* (**Figure 1b**), are *prochirals*, since both could be ideally converted to a chiral centre by arbitrarily changing only one attached H group to a deuterium atom (D with higher priority than H). Depending on the configuration, R/S, of the so created chiral centre, the H atom ideally deuterated, would be labeled as *pro-R*/*S*.

The two hydrogen atoms Ha and Hb, bonded to *prochiral 11C carbon atom,* in PNOBDME, can be described as *prochiral hydrogens*, also designated as *diastereotopic*. Their indistinguishable signals by <sup>1</sup> H-NMR split then into two signals easily differentiated. The same effect is observed for Hd and He, bonded to prochiral 10C, and for Hf and Hg, bonded to prochiral <sup>9</sup> C. Equally the two hydrogen atoms on

#### **Figure 3.**

*Scheme of the* spacer *in PNOBDME including the two alcohol groups with* R *absolute configuration of 12C\*.*

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

*prochiral <sup>3</sup> C carbon atom* Ha and Hb, and Hd, He bonded to *<sup>2</sup> C* in PNOBEE, are considered as *prochiral hydrogens.*

Besides chirality due to the asymmetrical carbon atom, a second chirality due to the helical conformation is predicted by the molecular models of polyesteramides PNOBDME and PNOBEE.

According to Ute *et al.* [22–24], when an isotactic polymer with asymmetric carbon atoms carries non-identical end-groups (R1 6¼ R2), each polymer can have two enantiomers, *e.g.*, R1-*RRR*���*R*-R2 and R1-*SSS*���*S*-R2 isomers. Each enantiomer with two *helical conformations*, right-handed and left-handed, being diastereomeric structures whose energies differ from one another (i. e. dG 6¼ 0). Each helical state can be observed by NMR as an independent set of signals, while enantiomers are not distinguishable by NMR.

In the case of PNOBDME, the presence of the chiral carbon atom 12C\* in the repeat unit and the different end groups for the aliphatic-end (-OH) and aromaticend (-COOH) promotes the presence of two helical conformations *gg* and *gt*, experimentally observed in the NMR spectra as two independent sets of signals differentiated as (´) and () for each isotactic stereoregularity R, R, R, and S, S, S, that implies four possible diastereoisomers. **Figure 4** shows the four helical conformers of PNOBDME and PNOBEE through the 11C-12C\* bond and <sup>3</sup> C-<sup>4</sup> C\* (torsion *φ*), respectively.

The existence of these two independent conformers had also been observed for PTOBDME and PTOBEE by Raman experiments [25] and by NMR [26]. The combination of a helix with two screw senses and the two absolute configurations providing four diastereomeric structures. It was also related to the presence of helical structures, the Cotton effect and the sign of the helicity in the case of 1–2 di-O-benzoylated sn-glycerols [27–29].

Details of molecular models for *gg* and *gt* conformers of a dimer of PNOBDME are shown in **Figure 5**, projected along with the 11C-12C\* bond, torsion *φ*, (perpendicular to the paper) with 12C\* (bonded to Hc) having *R* and *S* absolute configuration, in yellow, behind 11C (bonded to Ha and Hb).

**Figure 4.**

*The relationship between the four helical conformations* gg *and* gt *of PNOBDME, and PNOBEE through the 11C-12C\* bond, and <sup>3</sup> C-<sup>4</sup> C\* (torsion* φ*), respectively.*

#### **Figure 5**.

*Molecular model details of a PNOBDME dimer. View along 11C-12C\* bond (perpendicular to the paper), with (*R*) and (*S*) absolute configuration of 12C\* (in yellow behind 11C) for: (a)* Rgg*-diastereoisomer; (b)* Sgg*- diastereoisomer; (c)* Rgt*- diastereoisomer; (d)* Sgt *diastereoisomer.*

## **2. Molecular mechanics simulation and conformational analysis of PNOBEE and PNOBDME**

Molecular Mechanics modeling was performed with Materials Studio® v.2021 [30]. COMPASS-III forcefield was used for the monomer, assigning both atomic masses and partial charges. The total energy was then minimized and geometry optimized with FORCITE module.

Within the monomer repeat unit, a *Head* (CHead) and a *Tail* (OTail) *atoms* were defined. The extended length *(l)* of the bonds in the chain between CH and OT, *backbone atoms*, including double bonds and rings, is ≈ 23 Å, following the notation by Flory of the spatial representation of a single bonded carbon chain skeleton [31], **Figure 6**.

**Figure 6**. *Spatial representation of a single bonded carbon chain after Flory [31].*

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

#### **Figure 7**.

*Monomeric repeat units of PNOBDME (a)* Rgg*-diastereoisomer; (b)* Sgg*- diastereoisomer; (c)* Rgt*diastereoisomer; (d)* Sgt *diastereoisomer.*

According to Flory, the configuration of a chain molecule in space is determined by the lengths *l* of the bonds of the chain skeleton, by the angles *θ* specifying the difference between the directions of successive bonds, and by the angles *φ* of rotation, or torsion, about these bonds. It is possible to consider the lengths of the bonds in the chain and the angle between successive bonds to be fixed quantities for a given structure.

The presence of the chiral centre (C\*) atom was considered, including both *R* or *S* chirality.

The monomeric repeat units of PNOBDME, are modelized in **Figure 7**, for the four helical conformations: (a) R*gg*; (b) S*gg*; (c) R*gt*; (d) S*gt*, with the defined *Head atom* (CHead) selected in blue and the *Tail atom* (OTail) selected in red, and the backbone atoms colored in pink. HproS and HproR are also labeled.

Since the mesogen of PNOBDME and PNOBEE consists of three planar rigid groups: one terephthalamide and two benzoates, limited by parenthesis in **Figure 8**, connected by amide and ester groups, a simplified model could be reduced to the three articulated planes I, II and III, in the molecular scheme of **Figure 9**, connected

**Figure 8.** *Monomeric repeat unit of PNOBDME and PNOBEE.*

**Figure 9**. *A simplified model of the monomeric repeat unit of PNOBDME and PNOBEE.*

**Figure 10.**

*A simplified model of the monomeric repeat unit of precursor polyesters PTOBDME and PTOBEE.*

by torsions **CN1**, **N1CB** between Plane I and Plane II, and **N2C**, **CBN2** between Plane II and Plane III. A similar simplified model has been defined for the monomeric repeat unit of precursor polyesters PTOBDME and PTOBEE, in **Figure 10** [25].

Four more independent torsions were considered within the flexible spacer as **Phi (***φ)***,** which defines the head orientation to the mesogen, **Tau** which determines the lateral chain orientation to the mesogen, the **torsion CO** along with the CcarbonylOester bond (i.e. 13C in PNOBDME and <sup>5</sup> C in PNOBEE), close to 180°, and **C\* -CHead.** These torsions were the independent variables for Conformational Analysis (CA). Similar notations has been considered in precursor polyesters PTOBDME and PTOBEE, **Figure 10**.

## **2.1 Conformational analysis of PNOBEE and PTOBEE**

The molecular model of the monomeric repeat unit of polyesteramide PNOBEE, with a shorter lateral chain, can be seen in **Figure 11a** after its energy was minimized by performing a geometry optimization with the Forcite module of Materials Studio® [30], compared to that of monomeric precursor polyester PTOBEE, with also a shorter lateral chain, in **Figure 11b**.

The independent torsion values of PNOBEE monomer, are given in **Table 1**. They can be compared to those of PTOBEE monomer in **Table 2**. PNOBEE exhibits higher CN1 and N2C absolute values than PTOBEE (CO1 and O2C) but lower N1CB and CBN2 absolute values than O1CB and CBO2.

Conformers of PNOBEE with torsions N1CB and CBN2 with the same sign, that means, with two successive rotations of the benzene groups in the same direction, along the main chain axis (i. e. between planes I, II and III): around +35°; +35° or 35°; 35°, promote the formation of a helix with a triangular cross-section

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

**Figure 11.**

*Molecular models of the optimized monomeric PNOBEE (a) and PTOBEE (b).*


#### **Table 1.**

*Conformational analysis of PNOBEE monomer. Torsional angles (°) for the possible conformers.*


#### **Table 2.**

*Conformational analysis of PTOBEE monomer. Torsional angles (°) for the possible conformers.*

(marked with Δ in **Table 1**), either with *S* or *R* chirality. This is also observed in PTOBEE with O1CB and CBO2: +44°; +44° or �44°; �44°, also signaled with a triangular cross-section (Δ) in **Table 2**.

In conformers of PNOBEE with two successive rotations of the benzene groups in the opposite direction, means torsions N1CB and CBN2 with opposite sign: �35°; +35°; or +35°; �35°, promotes a helix with planes I and III parallel along with the backbone atoms -cross-view- (section 6¼ in **Table 1**) for both *S* or *R* chirality. They

have been differentiated with //. This is also observed in PTOBEE with O1CB and CBO2 values: 44°; +44°; or + 44°; 44° in **Table 2**.

The two successive rotations of the benzene groups within the monomer imply the formation of helical molecules, involving a second order of chirality, even without presence of a chiral atom. In **Figures 12** and **13** the respective sectional

#### **Figure 12**.

*Conformers of monomeric PNOBEE with both* R *and* S *chirality, with a triangular sectional view (a); and with parallel Planes I and III (b).*

#### **Figure 13**.

*Conformers of monomeric PTOBEE with both* R *and* S *chirality, with triangular sectional view (a); and with Planes I and III parallel (b).*

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*


**Table 3.**

*Torsional angles (°) for the four possible helical conformations of PNOBDME and PTOBDME monomers: R*gg*, R*gt*, S*gg*, S*gt*, after energy minimization.*

views of the monomeric conformers of PNOBEE and PTOBEE are represented along with the backbone atoms with the three benzene groups forming a triangular cross-section (a); and with Planes I and III parallel (b), for both *R* and *S* chirality.

## **2.2 Conformational analysis of PNOBDME and PTOBDME**

**Table 3** shows the independent torsional values of the four possible staggered conformers of PNOBDME monomer: R*gg,* R*gt*, S*gg*, S*gt*, compared to those of PTOBDME, after energy was minimized by geometry optimization.

All the torsion angles values of PNOBDME R*gg* conformer are quite similar to those of conformer S*gg* but with opposite signs. The same is observed between R*gt* and S*gt* values.

PNOBDME R*gg* and R*gt* conformers exhibit the same torsions sign and even similar values of the head torsions within the spacer: CO, Phi, Tau and C\*-CH. The same similarity is observed between S*gg* and S*gt* but with opposite signs.

A systematic Conformational Analysis (CA) applied to the PTOBDME monomer for the **two** torsions (CO1, CBO1) in one terephthalate ester bridge, had given four equi-energetic minima, observed in the (CO, CBO) map, **Figure 14**, at points: **A** (163°; 44°), **B** (163°; 44°), **C** (163°; 141°), **D** (163°; 141°) [25], very close values to those found for PTOBEE in **Table 2**. Other secondary minima were found at **E**(42°; 36°) and **F**(41°; 144°) with slightly higher energy. The same results were obtained in the CA of the second terephthalate ester group with the two torsions (CO2, CBO2).

The systematic CA for the four torsions defined for the spacer (head) in PTOBDME monomer, CO (i.e., CcarbonylOester), Phi, Tau, and C\* CH, had given 57 sterically allowed conformations after removal of duplicates, with an energy threshold of 10 kcal/mol. The three optimized conformers with the lowest energy, E = 74,2 kcal/mol, resulted in a unique solution at (CO, Phi, Tau, C\* CH) = (177°; 77°; 64°; 179,75°) [25]. These values are quite similar to those found for the four staggered diastereomeric conformers of PNOBDME in **Table 3**.

An ordinary molecular dynamics simulation had also been carried out with the PTOBDME monomer, including all torsions, imposing temperatures between 1600 and 500 K, followed by Quenching or Annealing. The lowest energy minima found

#### **Figure 14.**

*Systematic conformational search map for torsions: 1 = CO1,* ح *2= C* ح *BO1 in PTOBDME, after [25].*

included the head torsions (175°; 77°; 57°; 174°) [25]. Similar to those found for PTOBEE (172,6°; 72,88°; 51,9°; 163,8°) in **Table 2**.

## **3. Polymer chains**

Homopolymerization of the monomers with minimized energy was then simulated with Materials Studio® [30] by imposing Head-to-Tail orientation, torsion angle between monomers fixed to 180° and isotacticity to the polymer chain.

Helical rigid/semirigid chains models were obtained in all LC polymers with the chiral groups located in the spacer along the main backbone chain, and with the flexible lateral chains located either far or near the helix, one of the major types of macromolecules forming the cholesteric mesophase [32], as schematized in **Figure 15**. The total energy of the polymer models was also minimized and their geometry optimized with Forcite module of Materials Studio® [30].

The lowest energy helical molecular model of Poly(PTOBEE-S //)25 with pentagonal cross-section is shown in **Figure 16** as an example.

Molecular models of the four helical conformers of polyesteramide (PNOBDME)10, oriented parallel to the *z-*axis, are shown in **Figure 17**. Sectionalcross view, along the *z*-axis, of Poly(PNOBDME R*gg*)10; Poly(PNOBDME S*gg*)10; Poly(PNOBDME R*gt*)10 and Poly(PNOBDME S*gt*)10*.*

The main structural difference among the PNOBDME conformers is the different positions of the lateral chains. In conformers R*gg* and S*gg* the side chains are allocated among the benzoyl groups, with the result of its restricted mobility, in agreement with the positive NOE values obtained for precursor PTOBDME [16]. While in R*gt* and S*gt* conformers the lateral chains are placed outside the mesogenic benzoyl groups, exhibiting higher mobility, with a negative NOE.

**Figure 15**.

*Schematic representation of the cholesteric LC polymer type, with a rigid or semirigid helical chain with flexible branches.*

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

**Figure 16**. *Sectional cross-view of Poly(PTOBEE-*S *//)25.*

### **Figure 17**.

*Molecular model of the four diastereoisomer polymer chains of PNOBDME. Cross-view, along* z*: (a) Poly(PNOBDME\_R*gg*)10; (b) Poly(PNOBDME\_S*gg*)10; (c) Poly(PNOBDME\_R*gt*)10; (d) Poly(PNOBDME\_S*gt*)10*.

The same effect has been observed for polyester PTOBDME S*gg* and S*gt* conformers. Their lateral view and cross-section can be seen in **Figure 18**.

The four helical conformers models of polyesteramide (PNOBDME)100: Poly(PNOBDME\_R*gg*)100; Poly(PNOBDME\_S*gg*)100; Poly(PNOBDME\_R*gt*)100 and Poly(PNOBDME\_S*gt*)100, are simulated in **Figure 19**, along the *z*-axis (sectional cross view).

Their lateral view is reproduced in **Figure 20**. A third order of chirality corresponding to the twisting of the rigid/semirigid cholesteric LC polymer chain can be observed.

## *Liquid Crystals*

#### **Figure 18.**

*(a) Lateral view of PolyPTOBDME\_S*gg *conformer along* Z *axis and (b) cross section; (c) lateral view of PolyPTOBDME S*gt *conformer along* Z *and; (d) cross section.*

**Figure 19**.

*Cross-view of the four helical conformers models of (PNOBDME)100: (a) Poly(PNOBDME\_R*gg*)100; (b) Poly(PNOBDME\_S*gg*)100; (c) Poly(PNOBDME\_R*gt*)100 and (d) Poly(PNOBDME\_S*gt*)100.*

## **4. Crystalline structure and morphology modelization of precursor polyesters PTOBEE and PTOBDME**

## **4.1 Crystal structure simulation of precursor polyester PTOBEE**

Crystal packing of helical molecular chain model of (PTOBEE-*R*)8 (as defined in **Table 2**) has been simulated, with Materials Studio® [30], in a triclinic primitive P1 unit cell, **Figure 21b**, with parameters: *a* = 5,6 Å, *b* = 4,65 Å, *c* = 177,2 Å (equal to the pitch length of **each** simulated polymer helix), *α* = 90°, *β* = 120°, and *γ* = 88°.

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

**Figure 20**.

*Lateral view of the polymer models of the four helical conformers of (PNOBDME)100. (a) Poly(PNOBDME\_R*gg*)100; (b) Poly(PNOBDME\_S*gg*)100; (c) Poly(PNOBDME\_R*gt*)100 and (d) Poly(PNOBDME\_S*gt*)100.*

Polymer molecular models were oriented with their main chain parallel to the *z*-axis. Only one cell has been drawn. Its content is repeated in the *x* and *y* directions with *a* and *b* translational vectors to build a 3D polymer crystalline model.

The calculated X-ray diffraction pattern of PTOBEE from the crystal model is shown in **Figure 21d** compared to the experimental Synchrotron X-Ray diffraction pattern of PTOBEE under dynamical conditions in **Figure 21c**, where two reflections always present throughout the experiment at *2θ* 16° and 24° were associated with the mesophase state and another two at 19° and 28° with the crystal formation. The relative intensity of peaks assigned to crystal presence is lost, after the temperature of the transition crystal to liquid-crystal is reached, at about 150°C, during the heating process; and they almost do not recover after the cooling process as compared with isothermal crystallization. The molecular model of the polymer (PTOBEE-*R*)66 (in **Table 2**) is displayed in **Figure 21e**, exhibiting square cross-section, and the twisting of the helical chain at higher level. Experimental microphotographs of PTOBEE single crystals are shown in **Figure 21f** and **g**.

## **4.2 Crystal structure simulation of precursor polyester PTOBDME**

The helical molecular model of Poly(PTOBDME)n could be packed in one triclinic primitive P1 unit cell with parameters: *a* = 5,5 Å, *b* = 4,7 Å, **c** (helical pitch length depending on the model) =222,1 Å for Poly(PTOBDME\_R*gg*)40, *c* = 169,8 Å for Poly(PTOBDME\_R*gt*)15, *c* = 171,5 Å for Poly(PTOBDME\_S*gg*)15, *c* = 277,5 Å for Poly(PTOBDME\_S*gt*)40, *α* = 92°, *β* = 112°, and *γ* = 90°.

**Figure 21.**

*Structure of precursor polyester (PTOBEE)8: (a) monomer model (C26H20O8); (b) simulated crystal structure; (c) experimental synchrotron X-Ray diffraction pattern of PTOBEE under dynamical conditions: Heating range between 30°C and 180°C at 10°C/min,5 min, kept isothermally at 180°C, and cooling range from 180–30°C at 10°C/min; (d) Calculated X-ray diffraction pattern of PTOBEE from the crystal model, refined to match the experimental; (e) molecular model of (PTOBEE-*R*)66 (in Table 2) with square cross-section and with helix writhing at a higher level; (f) and (g) experimental crystal photographs of PTOBEE.*

The morphology of the polymer crystal model was further simulated also with Materials Studio® [30]. The simulated crystal morphology appears in **Figure 22b** with a rombohedrical pink shape. It is in good agreement with the rhombohedral

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

#### **Figure 22.**

*Structure of precursor polyester (PTOBDME)20: (a) monomer model (C34H36O8); (b) crystal packing and morphology simulation; (c) recalculated WAXS; (d) optical micrograph of experimental rhombohedral crystals of PTOBDME dispersed in mesophase matrix; (e) experimental WAXS pattern of PTOBDME, in the heating range, with synchrotron radiation source; (f) WAXS pattern in the cooling range.*

crystals observed by optical microscopy, dispersed within the mesophase matrix, **Figure 22d**.

Experimental XRD patterns of PTOBDME registered during heating and cooling ranges, with synchrotron radiation source, are given in **Figure 22e** and **f** respectively. Two XRD peaks, at *2θ* 16° (d100 = 5,5 Å) and 24° (3,71 Å), always present in the entire temperature range, were assigned to the cholesteric mesophase. The third one at *2θ* 19° (d010 = 4,7 Å) and a small one at *2θ* 22,5° (3,95 Å), disappearing at 240°C during the heating range and appearing again at about 150°C while cooling, were interpreted as due to the presence of a three-dimensional (3D) order, in agreement with the crystalline stability temperature, DSC curves. This means that a cholesteric mesophase is always present and coexists with the crystalline phase.

## **5. Crystalline structure and morphology. Modelization of polyesteramide PNOBDME**

### **5.1 Experimental simultaneous SAXS/WAXS patterns of PNOBDME**

The powder SR diffraction data were registered at 16.1 beamline at Daresbury Laboratory, Warrington, U.K., during the heating range from 30–200°C, with a monochromatic beam (λ = 1,4 Å), **Figure 23**. Both SAXS and WAXS detectors were

#### **Figure 23**.

*Experimental simultaneous SAXS (a)/WAXS (b) patterns of PNOBDME with synchrotron radiation source; (c) projection of all superimposed WAXS patterns.*

lineal. Wet collagen (rat tail tendon, *d* = 676,08 Å) was used to calibrate the *q-*axis (Å�<sup>1</sup> ) of the SAXS detector. The WAXS detector was calibrated with HDPE, with the scattering angle defined by *2θ*. The experimental patterns were corrected for background scattering, with the help of ATSAS 3.0 [33].

The SAXS spectra in **Figure 23a** show two sharp order reflections at *q* value of 0,018 Å�<sup>1</sup> (55,5 Å) and 0,029 Å�<sup>1</sup> (34,48 Å).

Four WAXS peaks, **Figure 23b** at *2θ* ffi 18,39° (*d* = 4,38 Å); 18,83° (*d* = 4,28 Å); 35,17° (*d* = 2,31 Å) and 40,75° (*d* = 2,01 Å) are systematically observed in the entire temperature range, and were assigned to the cholesteric mesophase.

While peaks at *2θ* ffi 26,39° (*d* = 3,07 Å); 50,71° (*d* = 1,63 Å) disappearing at about 90°C during the heating range are attributed to crystal 3D phase.

## **5.2 Crystal structure simulation of polyesteramide PNOBDME**

Crystal packing for each of the four helical diastereoisomer polymer chains of Poly(PNOBDME)10 has been simulated, with Materials Studio® [30], in triclinic primitive P1 unit cells, with their main chains oriented parallel to the *z*-axis, **Figure 24**. Only one unit cell has been drawn. Its content is repeated in the *x* and *y* directions with *a* and *b* translational vectors to build a 3D polymer crystalline model.

Crystal models have also been simulated for the four PNOBDME diastereoisomers with different degrees of polymerization, *n* = 10, 30, 60, 100, and optimized by energy minimization with the Forcite module [30], as shown in **Table 4**.

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

#### **Figure 24**.

*Crystal model details of the four helical conformers of PNOBDME: (a) Poly(PNOBDME\_R*gg*)10; (b) Poly(PNOBDME\_S*gg*)10; (c) Poly(PNOBDME\_R*gt*)10; (d) Poly(PNOBDME\_S*gt*)10*.

#### **5.3 Structure refinement**

From the different simulated crystal models, their theoretical powder diffraction patterns can be calculated, and the polymer structure refined until the simulated spectra match the experimental diffraction pattern of PNOBDME, in **Figure 23b**. Changes in positional parameters cause changes in structure-factor magnitudes and therefore in relative peak intensities, whereas atomic displacement (thermal) parameters have the effect of emphasizing the high-angle region (smaller thermal parameters) or de-emphasizing it (larger thermal parameters). It is usually advisable to start the refinement of structural parameters with the positions of the heavier atoms and then to try those of the lighter atoms. If the latter refinement converges, all atomic positions in the model can then be refined simultaneously. At this point, the refinement of the somewhat trickier parameters can be attempted [34, 35].

### *5.3.1 Pawley refinement*

Crystal\_Poly(PNOBDME\_R*gg*)10 model, with a minimized total energy = 244 kcal/mol, has been first refined by successive Pawley cycles, by


**Table 4.**

 *Pawley refinement optimized results, minimized E, refined lattice cell parameters, agreement indices (R values).*

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

optimizing the *Lattice Parameters* (*a*, *b*, *c*, *α*, *β*, *γ*); *Pattern Parameters* (Pseudo-Voigt profile function): Peaks FWHM (U, V, W), Profile parameters (NA, NB), Line shift (Instrument Geometry Bragg–Brentano): Zero point value, Shift #1, Shift #2; *Sample parameters*: Crystallite size broadening (A, B, C).

The refined crystal model gave a lattice cell: *a* = 5,91996 ( *0,00029*) Å,

*b* = 5,04000 ( *0,00025*) Å, *c* = 55,29001 ( *0,00284)* Å, *α* = 90,57956 ( *0,00047*)°, *β* = 109,00002 ( *0,00051*)°, and *γ* = 89,50015 ( *0,00044*)°, adjusted to a

triclinic lattice cell with Space Group: P 1. The Pawley adjustment factors for Crystal\_Poly(PNOBDME\_R*gg*)10, between theoretical spectrum of the crystal model and the experimental diffraction pattern are: Final Rwp: 0,44%; Final Rp: 0,09%; Final Rwp (without background): 0,23%; Final CMACS: 0,00%. **Figure 25** displays the simulated Intensity plot *vs 2θ* for the crystal, compared to the experimental powder diffraction pattern, and the difference between them.

In **Table 4** the optimized results are given for the crystals built from the four helical conformers: Crystal\_Poly(PNOBDME\_R*gg*)n, Crystal\_Poly(PNOBDME\_R*gt*)n*,* Crystal\_Poly(PNOBDME\_S*gg*)n and Crystal\_Poly(PNOBDME\_S*gt*)n, at different degrees of polymerization, *n* = 10, 30, 60, 100, with minimized energy, after Pawley refinement cycles of the lattice cell parameters and agreement indices values: Rwp, Rp, Rwp (without background and Final CMACS. Slightly higher *a* and *b* cell parameters are observed for R*gg* and S*gg* conformers with broader chain diameters.

## *5.3.2 Rietveld refinement*

Starting from the best Pawley refined model, the first cycle of *Rietveld* is accomplished by optimizing the *Cell Lattice Parameters* (*a*, *b*, *c*, *α*, *β*, *γ*) into a triclinic unit cell with Space Group P1; *Pattern Parameters* (Pseudo-Voigt peak Profile Function): FWHM (U, V, W), profile parameters (NA, NB), Line Shift parameters (instrument Geometry Bragg–Brentano): Zero point, Shift #1, Shift #2, Asymmetry (Rietveld correction) P parameter, Background coefficients (Polynomial order = 20); *Sample Parameters*: Crystallite Size broadening (A, B, C), Preferred Orientation (Function Rietveld-Toraya): (a\* , b\* , c\* , G1, G2), Atomic Temperature Factors applied; *Structure* parameters, 30 torsions being refined (hydrogen atoms used); *Atoms* Temperature Factors set to anisotropic, first for only the N and O atoms and after for all the atoms, Occupancies are also refined.

#### **Figure 25**.

*Pawley refinement of synchrotron powder diffraction pattern of Crystal\_Poly(PNOBDME\_R*gg*)10. Observed intensities-magenta-line, calculated intensities-blue points. Green ticks are reflection positions. The difference (observed-calculated) curve-black line.*

#### **Figure 26**.

*Final Rietveld refinement of Crystal\_Poly(PNOBDME\_R*gg*)10 with fine-convergence and anisotropic temperature factors set for all the atoms.*

Convergence is set from coarse (1 cycle), medium (2 cycles) to fine (4 cycles). The refined unit cell parameters for Poly(PNOBDME\_R*gg*)10 are: *a* = 5,915 ( *0,05811*) Å, *b* = 5,03 ( *0,05061*) Å, **c** = 55,29 ( *0,55878*) Å, *α* = 89,38 ( *0,18356*)°, *β* = 109,01 ( *0,26747*)°, and *γ* = 88,91 ( *0,23494*)°. The adjustment factors: Final Rwp: 15,83% Final Rp: 10,41% Final Rwp (without background): 52,92% Final CMACS: 6,62%, in **Figure 26**.

## **5.4 Powder quantitative phase analysis**

The Powder Quantitative Phase Analysis module of Materials Studio® [30] has been used to determine the relative amounts of different phases in a mixture from a powder diffraction pattern of the mixture.

An approximation has been made considering ideal mixtures with the four helical conformers crystal structures of Crystal\_Poly(PNOBDME)n as pure component phases, for each degree of polymerization, n = 10, 30, 60, 100, their relative amounts being determined from *Experimental PNOBDME Powder diffraction pattern*, **Figure 23c***.*

The Refined weights for Crystal\_Poly(PNOBDME)10 pure phases: R*gg*, *Sgg*, R*gt* and S*gt* in, **Figure 27**, gave Crystal\_Poly(PNOBDME)10\_S*gg* as preferable major phase (90,79%) and Crystal\_Poly(PNOBDME)10\_R*gg* in lower proportion (9,199%).

The Refined weights for Crystal\_Poly(PNOBDME)30 pure phases: R*gg*, *Sgg*, R*gt* and S*gt*, in **Figure 28**, gives Crystal\_Poly(PNOBDME)30\_R*gg* as major phase (86,45%), with Crystal\_Poly(PNOBDME)30\_R*gt* (13,54%).


#### **Figure 27.**

*Refined weights on ideal mixture of Crystals\_Poly(PNOBDME)10 pure phases: R*gg*,* Sgg*, R*gt *and S*gt*.*

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*


#### **Figure 28.**

*Refined weights of Crystal\_Poly(PNOBDME)30 pure phases: R*gg*,* Sgg*, R*gt *and S*gt*.*


### **Figure 29.**

*Refined weights of Crystal\_Poly(PNOBDME)60 pure phases: R*gg*,* Sgg*, R*gt *and S*gt*.*


### **Figure 30.**

*Refined weights of Crystal\_Poly(PNOBDME)100 pure phases. R*gg*,* Sgg*, R*gt *and S*gt*.*

The Refined weights for Crystal\_Poly(PNOBDME)60 four pure phases, in **Figure 29**, gives Crystal\_Poly(PNOBDME)60\_S*gt* as major component (100%).

The Refined weights for Crystal\_Poly(PNOBDME)100 pure phases, in **Figure 30**, gives Crystal\_Poly(PNOBDME)100\_S*gt* as major component (100%).

These results would redound to the previously postulated kinetic resolution of a preferable helical diastereomer, with respect to the four possible, the R/S ratio of asymmetric carbon atoms remaining 50:50, depending on the synthetic conditions and the degree of polymerization.

The results presented here are only indicational; more refinement cycles would be needed to improve accuracy.

## **6. Conclusions**

Conformational and Structure Analysis has been performed on polyesteramides PNOBEE and PNOBDME compared to those of polyesters precursor.

Since the mesogen of PNOBDME and PNOBEE consists of three planar rigid groups: one terephthalamide and two benzoates, connected by amide and ester

groups, a simplified model could be reduced to three articulated planes I, II and III, in the molecular scheme.

Three orders of chiralities are observed: One due to the asymmetric carbon atoms, a second chirality due to the two successive rotations of the benzene groups within the monomer, along the main chain, which imply the formation of helical molecules with either the three benzene groups forming a triangular cross-section (Δ) or with Planes I and III becoming parallel (//), for both *R* and *S* chirality. Moreover, a third chirality corresponds to the twisting of the rigid/semirigid cholesteric LC polymer chain LC polymer.

Four helical conformer models are proposed for each cholesteric polyesteramide: R*gg*, R*gt,* S*gg*, S*gt*, experimentally observed by NMR.

Polymerization of the monomeric conformers, with minima energies, have been simulated and used to reproduce the crystalline fraction observed by x-ray diffraction.

Crystal models of the four PNOBDME diastereoisomers have been simulated with different degrees of polymerization, *n* = 10, 30, 60, 100, and optimized by energy minimization with the Forcite module.

Crystal packing was simulated in triclinic primitive P1cells, with molecular chains oriented parallel to the *z*-axis (with *c* lattice parameter attained from simulated "polymerization" and parameters *a*, *b, α, β and γ,* obtained by Pawley refinement from the known structures of precursor polyesters.

Successive Pawley refinement cycles optimized the lattice cell parameters for all the simulated polymers, obtaining excellent adjustment factors for Crystal\_Poly(PNOBDME\_R*gg*)10, between theoretical spectrum of the crystal model and the experimental diffraction pattern are: Final Rwp: 0,44%; Final Rp: 0,09%; Final Rwp (without background): 0,23%; Final CMACS: 0,00%. Sequential Rietveld cycles refined the structures with fine-convergence, by changing positional parameters 30 torsion angles, causing changes in structure-factor magnitudes, relative peak intensities, and atomic displacement (thermal parameters) set first isotropic for all the atoms and after set to anisotropic for only the N and O atoms and then for the rest. Occupancies are also refined. Final Rwp: 15.83% Final Rp: 10.41% Final Rwp (without background): 52.92% Final CMACS: 6.62.

Optimized results are given for the crystals built from the four helical conformers: Crystal\_Poly(PNOBDME\_R*gg*)n, Crystal\_Poly(PNOBDME\_R*gt*)n*,* Crystal\_Poly(PNOBDME\_S*gg*)n and Crystal\_Poly(PNOBDME\_S*gt*)n, at different degrees of polymerization, *n* = 10, 30, 60, 100, with minimized energy, after Pawley refinement cycles of the lattice cell parameters and agreement indices values: Rwp, Rp, Rwp.

Crystal structure models are proposed whose simulated x-ray diffraction patterns fit the experimental WAXS, after successive Pawley and Rietveld refinement cycles.

A Powder Quantitative Phase Analysis approximation has been made considering ideal mixtures with the four helical conformers crystal structures of Crystal\_Poly(PNOBDME)n as pure component phases, for each degree of polymerization, n = 10, 30, 60, 100, their relative amounts being determined from *Experimental PNOBDME Powder diffraction pattern.*

The Refined weights for Crystal\_Poly(PNOBDME)10 pure phases: R*gg*, *Sgg*, R*gt* and S*gt*, gave Crystal\_Poly(PNOBDME)10\_S*gg* as preferable major phase (90,79%) and Crystal\_Poly(PNOBDME)10\_R*gg* in lower proportion (9,199%).

The Refined weights for Crystal\_Poly(PNOBDME)30 pure phases: R*gg*, *Sgg*, R*gt* and S*gt*, gives Crystal\_Poly(PNOBDME)30\_R*gg* as major phase (86,45%), with Crystal\_Poly(PNOBDME)30\_R*gt* (13,54%).

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

The Refined weights for Crystal\_Poly(PNOBDME)60 and Crystal\_Poly (PNOBDME)100, four pure phases, give Crystal\_Poly(PNOBDME)60\_S*gt* as major component (100%).

These results confirm the previously postulated kinetic resolution of a preferable helical diastereomer, with respect to the four possible, depending on the synthetic conditions and the degree of polymerization, while the R/S ratio of asymmetric carbon atoms remains 50:50.

## **Acknowledgements**

We thank CSIC for its facilities. We acknowledge support of the publication fee by the CSIC Open Access Publication Support Initiative through its Unit of Information Resources for Research (URICI).

## **Author details**

Mercedes Pérez Méndez<sup>1</sup> \*, José Fayos Alcañiz<sup>2</sup> and Marc Meunier<sup>3</sup>


<sup>© 2022</sup> The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

[1] McMillan F M. The Chain Straighteners. Fruitful Innovation: The Discovery of linear and Stereoregular Synthetic Polymers: The Macmillan Press LTD 1979, London.

[2] Carothers W H. Studies on polymerization and ring formation. I. An introduction to the general theory of condensation polymers. J. Am. Chem. Soc. 1929; 51, 8: 2548-2559.

[3] Pino P, Ciardelli F, Zandomeneghi M. Optical Activity in Stereoregular Synthetic Polymers Annual Review of Physical Chemistry October 1970; Vol. 21:1: 561-608. https://doi.org/10.1146/a nnurev.pc.21.100170.003021]

[4] Vogl O, Corley L S, Harris W J, Jaycox G D, Zhang J. Optical activity based on macromolecular asymmetry. Makromol.Chem., Suppl. 1985; 13 :1-12.

[5] Mallakpour S, Zadehnazari A. Advances in synthetic optically active condensation polymers – A review. eXPRESS Polymer Letters 2011; 5, (2): 142–181 Available online at www.expre sspolymlett.com. DOI: 10.3144/ expresspolymlett.2011.15

[6] Ringsdorf H, Schlarb B, Venzmer J. Molecular Architecture and Function of Polymeric Oriented Systems: Models for the Study of Organization, Surface Recognition, and Dynamics of Biomembranes. Angew. Chem. Int. Ed. Engl. 1988; 27, 113-158.

[7] International Union of Crystallography, Report of the Executive Committee for 1991, Acta Cryst. 1992; A48,922.

[8] Zanchetta G. Liquid crystalline phases in oligonucleotide solutions [thesis] University of Milan 2007

[9] Kornyshev A A, Leikin S, Malinin S V. Chiral electrostatic interaction and

cholesteric liquid crystals of DNA. Eur. Phys. J. E 2002; 7: 83-93

[10] Lai S L, Hartono D, Yang K-L. Self-assembly of cholesterol DNA at liquid crystal/aqueous interface and its application for DNA detection. Appl. Phys. Lett. 2009; 95: 153702.

[11] Pérez Méndez M. "Synthesis and Characterization of Biocompatible Polyesteramides: PNOBDME (C34H38N2O6)n and PNOBEE (C26H22N2O6)n as Cholesteric Liquid Crystals. Polymer Science 2018; 4, 2. DOI: 10.36648/2471-9935.4.2.37. https://polymerscience.imedpub.com/ synthesis-and-characterization-ofbiocompatible-polyesteramidespnobdmec34h38n2o6n-and-pnobeec26h22n2o6n-as-cholesteric-liquid-cr. php?aid=2395

[12] Pérez Méndez M. Biocompatible, Nanostructured, Chiral Polyesteramides: PNOBDME (C34H38N2O6)n and PNOBEE (C26H22N2O6)n Synthesized and Characterised as Cholesteric Liquid Crystals. International Journal of Engineering Research and Applications (IJERA) 2019*;* 9, 6 (Part �1): 52-66; ISSN: 2248-9622; DOI: 10.9790/9622- 0906015267.

[13] Pérez Méndez M, Fayos Alcañiz J. Cholesteric Liquid Crystal Polyesteramides, Non-viral Vectors. In: Liquid Crystals and Display Technology: IntechOpen; 2020. DOI: 10.5772/intechopen.9131. Available from: https://www.intechopen.com/ online-first/cholesteric-liquid-crystalpolyesteramides-non-viral-vectors.

[14] Pérez-Méndez M, Marco C. New synthesis, thermal properties and texture of cholesteric Poly[ethyl ethylene 4,4<sup>0</sup> -(terephthaloyldioxy) dibenzoate]. Acta Polymerica 1997; 48: 502-506.

*Molecular Simulation of Cholesteric Liquid-Crystal Polyesteramides: Conformational… DOI: http://dx.doi.org/10.5772/intechopen.100388*

[15] Pérez-Méndez M, Marco Rocha C. Preparing cholesteric liquid-crystals - by adding acid dichloride and butanediol to chloro-naphthalene, heating in nitrogen, decanting into toluene, etc. Patent with n° EP1004650-A; WO9831771-A; WO9831771-A1; AU9854863-A; ES2125818-A1; ES2125818-B1; EP1004650-A1; US6165382-A; MX9906732-A1; JP2001513827-W; AU739076-B; EP1004650-B1; DE69824182-E.

[16] Pérez Méndez M, Sanguino Otero J. Cholesteric Liquid-Crystal Copolyester, Poly[oxycarbonyl-1,4-phenylene- oxy - 1,4 terephthaloyl- oxy- 1,4 phenylenecarbonyloxy(1,2-dodecane)] [C34H36O8]n, Synthesized from Racemic Materials: Kinetics, Structure and Optical Characterization. International Journal of Engineering Research and Applications (IJERA) 2015; Vol. 5, Issue 7 (Part - 2): 48-62. ISSN: 2248-9622.

[17] Perez-Mendez M, Fayos J, Blanch G P and Sánchez Cortés S. Biofunctionalization of Cholesteric Liquid-Crystal Helical Polymers. Nanocarriers. ENCYCLOPEDIA OF NANOSCIENCE.AND NANOTECHNOLOGY 2011, Volume 11: 547-580, Edited by H. S. Nalwa, ACS. American Scientific Publishers, ISBN: 1-58883-160-4;

[18] Pérez Méndez M, Hammouda B. SAXS and SANS investigation of synthetic cholesteric liquid-crystal polymers for biomedical applications. Journal of Materials Science and Engineering 2013; B 3 (2): 104-115.

[19] Pérez Méndez M. Synthetic Cationic Cholesteric Liquid Crystal Polymers. In: Liquid Crystals - Recent Advancements in Fundamental and Device Technologies, Chapter 2. Dr. Pankaj Kumar Choudhury (Ed.): InTechOpen; 2018. DOI: 10.5772/intechopen.70995. https://www.intechopen.com/books/ liquid-crystals-recent-advancements-infundamental-and-device-technologie

s/synthetic-cationic-cholesteric-liquidcrystal-polymers.

[20] Freire F, Seco J M, Quiñoá E, Riguera R. The Prediction of the Absolute Stereochemistry of Primary and Secondary 1,2-Diols by <sup>1</sup> H NMR Spectroscopy: Principles and Applications. Chem. Eur.J*.* 2005; Vol. 11; Issue 19: 5509-5522.

[21] Arias S, Freire F, Quiñoá E, Riguera R.Nanospheres, Nanotubes, Toroids, and Gels with Controlled Macroscopic Chirality. Angew. Chem. Int. Edition 2014; 53, Issue 50: 13720– 13724.

[22] Ute K, Hirose K, Kashimoto H, Hatada K, Vogl O. Haloaldehyde polymers. 51. Helix-sense reversal of isotactic chloral oligomers in solution. J. Am. Chem. Soc. 1991; 113: 6305- 6306, DOI: 10.1021/ja00016a076.

[23] Ute K, Oka K, Okamoto Y, Hatada K, Xi F, Vogl O. Haloaldehyde Polymers LIII. Optical Resolution of Purely Isotactic Oligomers of Chloral: Optical Activity of the Chloral Oligomers Assuming One-Handed Helical Conformation in Solution. Polym. J. 1991; 23: 1419-1424.

[24] Ute K, Hirose K, Kashimoto H, Nakayama H, Hatada K, O Vogl O. Helix-Inversion Equilibrium of Isotactic Chloral Oligomers in Solution. Polym. J. 1993; 25, N° 11: 1175- 1186.

[25] Fayos J, Sánchez-Cortés S, Marco C, Pérez-Méndez M. Conformational analysis and molecular modeling of cholesteric liquid-crystal polyesters based on XRD, Raman and transition thermal analysis. J. Macromol.Sci.- Physics 2001*,* B40(3&4): 553-576. https://doi.org/10.1081/MB-100106177.

[26] Perez-Mendez M, Marsal R, Garrido L, Martin-Pastor M. Self-Association and Stereoselectivity in a Chiral Liquid-Crystal Cholesteric

Polymer Formed under Achiral Conditions. Macromolecules 2003; 36: 8049-8055.

[27] Tian G, Lu Y, Novak B M. Helix-Sense Selective Polymerization of Carbodiimides: Building Permanently Optically Active Polymers from Achiral Monomers. J. Am. Chem. Soc. 2004; 126: 4082-4083.

[28] Schlitzer D S, Novak B M. Trapped Kinetic States, Chiral Amplification and Molecular Chaperoning in Synthetic Polymers: Chiral Induction in Polyguanidines through Ion Pair Interactions. J. Am. Chem. Soc. 1998; 120, 9: 2196-2197.

[29] Tang H Z, Lu Y, Tian G, Capracotta M D, Novak B M. Stable Helical Polyguanidines: Poly{N-(1-anthryl)-N'- [(R)-and/or (S)-3,7-dimethyloctyl] guanidines}. J. Am. Chem. Soc. 2004; 126: 3722-3723.

[30] Materials Studio v.2021, Dassault Systemes BIOVIA, Cambridge, U.K.

[31] Flory P J. Principles of Polymer Chemistry, Cornell University Press: Ithaca (1953): p. 400.

[32] Boiko N, Shibaev V. Cholesteric polymer liquid crystals and their optical properties. International Journal of Polymeric Materials. 2000;45(3–4): 533-583

[33] *ATSAS 3.0*: expanded functionality and new tools for small-angle scattering data analysis. Manalastas-Cantos K, Konarev P V, Hajizadeh N R, Kikhney A G, Petoukhov M V, Molodenskiy D S, Panjkovich A, Mertens H D T, Gruzinov A, Borges C, Jeffries C M, Svergun D I, Franke D. J. Appl. Cryst. 2021; 54: 343-355. DOI:10.1107/ S1600576720013412

[34] Young R A, editor. The Rietveld method. IUCr Monograph on Crystallography; No. 5. Oxford:

International Union of Crystallography/ Oxford University Press 1993. ISBN 0-19-855577-6.

[35] McCusker L B, Von Dreele R B, Cox D E, Louër D, Scardie P. Rietveld refinement guidelines. J. Appl. Cryst. 1999; 32: 36-50.

## **Chapter 5**
