Entropy Rules: Molecular Dynamics Simulations of Model Oligomers for Thermoresponsive Polymers

entropy

Article Entropy Rules: Molecular Dynamics Simulations of Model Oligomers for Thermoresponsive Polymers

Alexander Kantardjiev * and Petko M. Ivanov Institute of Organic Chemistry with Centre of Phytochemistry, Bulgarian Academy of Sciences, ul. Acad. G. Bonchev, bloc 9, 1113 Soﬁa, Bulgaria; [email protected] * Correspondence: [email protected]

Received: 20 July 2020; Accepted: 9 October 2020; Published: 21 October 2020

Abstract: We attempted to attain atomic-scale insights into the mechanism of the heat-induced phase transition of two thermoresponsive polymers containing amide groups, poly(N-isopropylacrylamide) (PNIPAM) and poly(2-isopropyl-2-oxazoline) (PIPOZ), and we succeeded in reproducing the existence of lower critical solution temperature (LCST). The simulation data are in accord with experimental ﬁndings. We found out that the entropy has an important contribution to the thermodynamics of the phase separation transition. Moreover, after decomposing further the entropy change to contributions from the solutes and from the solvent, it appeared out that the entropy of the solvent has the decisive share for the lowering of the free energy of the system when increasing the temperature above the LCST. Our conclusion is that the thermoresponsive behavior is driven by the entropy of the solvent. The water molecules structured around the functional groups of the polymer that are exposed to contact with the solvent in the extended conformation lower the enthalpy of the system, but at certain temperature the extended conformation of the polymer collapses as a result of dominating entropy gain from “released” water molecules. We stress also on the importance of using more than one reference molecule in the simulation box at the setup of the simulation.

Keywords: molecular dynamics; entropy calculation; thermoresponsive polymers; lower critical solution temperature; molecular dynamics; GROMACS—GPU calculations

1. Introduction Most synthetic macromolecules become more soluble when heated. However, there are water-soluble polymers that separate from solution upon heating (inverse temperature-dependent solubility) above the phase transition temperature (lower critical solution temperature, LCST). Such polymers are referred to as thermoresponsive polymers. This phenomenon is explained to result from the balance between the enthalpy contribution from the energy stabilization due to hydrogen bonding of the polymer with the water molecules and the entropy gain of the system at higher temperature that outweighs the enthalpy preference at lower temperatures. Hydrogen bonding between the polymer and the water molecules lowers the free energy of dissolution. This effect becomes less important at higher temperature and, accordingly, entropy effects prevail [1]. The thermoresponsive polymers are characterized by the abrupt change in their properties in response to temperature variations [2,3]. Their solubility behavior is still a fundamental and challenging problem in polymer science, but remains elusive to describe theoretically and difficult to simulate via computational methods. A major challenge is to relate structural characteristics of the polymers to this phenomenon. Besides the fundamental theoretical issues, the thermoresponsive polymers are of significant technological importance for the design of stimuli-responsive (smart) materials with adaptive properties. Promising applications in the pharmaceutical industry present drug delivery, biomedical applications, e.g., tissue engineering and smart devices [4–6]. An important prerequisite

Entropy 2020, 22, 1187; doi:10.3390/e22101187 www.mdpi.com/journal/entropy Entropy 2020, 22, 1187 2 of 18 for such applications is to fine-tune the temperature of the phase transition (e.g., aiming at the physiologically relevant human body temperature). Such control of the transition temperature point can be acquired by exploring copolymerization with other appropriate monomers. The LCST is the stringent formal thermodynamic characteristic of the thermoresponsive behavior. Below the LCST the components of the solution become miscible whatever the composition of the polymer solution. The effect at the molecular level is detected as a coil-to-globule transition of the conformation of the polymer. Polymers containing amide groups constitute the largest group among the thermoresponsive polymers. The most examined thermoresponsive polymers are poly(N-isopropylacrylamide) (PNIPAM) and poly(2-isopropyl-2-oxazoline) (PIPOZ) (Figure1). Both have an amide group in the side chain and the substantial difference between PNIPAM and PIPOZ is that the main chain of PNIPAM is nonpolar, whereas PIPOZ is with polar backbone. The amide groups of PNIPAM can be proton donors as well as proton acceptors, whereas the amide groups of PIPOZ can be only proton acceptors. We examine in this study by molecular dynamics simulations (MD) model oligomers of N-isopropylacrylamide (NIPAM) and 2-isopropyl-2-oxazoline (IPOZ).

(a) (b)

Figure 1. Schematic structures of (a) N-isopropylacrylamide (NIPAM) unit and (b) 2 isopropyl-2-oxazoline

(IPOZ) unit.

The PNIPAM polymer is the paradigmic thermoresponsive molecule. The experimental research on the PNIPAM phase behavior in aqueous solution is abundant [1–3]. Still not so well examined is PIPOZ [7–9]. The PIPOZ polymer shows thermoresponsive behavior at around the same temperature range as PNIPAM. We focused our interest both on the thermodynamics and the mechanisms at the molecular level leading to the heat induced phase transition. The interest in the PIPOZ properties is additionally fueled by its advantages, relative to the PNIPAM polymer, in relation to practical applications, especially its biocompatibility. Molecular dynamics simulations were also used to study the thermoresponsibility effect [10–22], but mostly in the case of PNIPAM and its copolymers. To the best of our knowledge only two published works report molecular dynamics simulations in the case of PIPOZ molecules [23,24]. The first one applied short atomistic MD runs of systems comprised of a single 8-mer PIPOZ molecule solvated by 500 water molecules and the focus is on the differences of the hydrogen bonding below and above the point of phase transition [23]. The other investigation applied MD simulation in vacuum in order to investigate the possible conformations of PIPOZ chains both in amorphous and crystalline states [24]. We apply in this study all-atom molecular dynamics simulations in an attempt to reproduce the phenomenology of the effect (i.e., temperature-induced collapse of the chain) for NIPAM and IPOZ oligomers in water solution aiming at getting structural and thermodynamic evidences for the cause of their heat induced phase transition behavior.

Entropy 2020, 22, 1187 3 of 18

2. Methods

2.1. Molecular Mechanics Models of the Polymer Structures The graphic antechamber [25,26] was used to build the molecular models for the PNIPAM and PIPOZ monomers. The generated structures were saved in the standard mol2 format and the files were transferred to Gaussian input files [27] for geometry optimization and subsequent derivation of RESP (Restrained Electrostatic Potential) charges [28]. The Gaussian log file, containing the electrostatic potential distribution results, was used as an input file to the antechamber RESP functionality which performed the fit of the data and generated “ac” format file (short for antechamber) containing information about the derived atomic charges. In order to obtain monomer units with charge distribution corresponding to the monomer block within the polymer, we stripped out the charges of the linking methyl groups. A special file was generated manually that contains information about the linkage definitions, i.e., rules for removing those atoms of the monomer units which got stripped out upon polymerization. Special attention was devoted to the terminal residues of the polymer chain. The head and the tail residues cap the oligomer chain at the two ends. The same procedure as with the internal residues was followed to derive charges for the terminal residues. Two manually built files were used to define the rules for connectivity of head and tail residues. The AMBER tleap procedure was used to construct the oligomer systems. From this point on the GROMACS package [29–32] was used for the simulations. The AMBER topology was converted to the GROMACS formats by using the AnteChamber PYthon Parser interfacE [33]. The AMBER-03 [25] (a third generation force field, derived from AMBER99) all atom force field port for the GROMACS molecular dynamics program was used in the simulations.

2.2. Molecular Dynamics Setup Description We conducted molecular dynamics simulations of fully atomistic models of NIPAM and IPOZ oligomers with chain lengths of 12 (12-mer), 24 (24-mer), and 30 (30-mer) monomer units in cubic simulation cells. The oligomers were solvated by filling the simulation box with water molecules using the genbox routine of the GROMACS suite. An explicit water model (TIP3P) was applied [34,35]. The systems were parameterized, assembled and equilibrated in several stages. The total energies of the isolated oligomer chains were firstly minimized, followed by minimization of the energies of the whole systems, oligomers plus model water molecules. The energy of the system as a whole was minimized by means of the L-BFGS (limited-memory Broyden–Fletcher–Goldfarb–Shanno) algorithm. The optimized structure was used as the initial configuration for the simulations at two extreme temperature regimes—at 263.0 K and 333.0 K. The simulations were executed in the NPT (constant pressure and constant temperature) ensemble. Temperature was controlled by applying the Nose–Hoover thermostat with a coupling time 1.0 ps [36,37]. Periodic boundary conditions and minimum image convention were applied. The particle–particle particle–mesh method (P3M) [38] with a real space cutoff 12.0 Å was used for evaluating the electrostatic interactions. The choice of the P3M solver was motivated for its favorable NlogN computational complexity (where N is the number of all interaction sites in the system). The integrator used to propagate the molecular dynamics trajectories was the velocity Verlet algorithm. This choice was dictated by the availability of the efficiently parallelized version for GPU systems [39]. The integration time step was 2.0 fs. The lengths of the bonds involving hydrogen atoms were constrained by the LINCS procedure [40]. Two extreme cases for the simulation cell were explored for the 30-mer structures—a box with side length 100.0 Å and a larger box with a side of 300.0 Å. Two initial geometries (an extended conformation and conformation optimized by conformational search [41]) of the NIPAM and IPOZ oligomers were used as startup conformations for the simulations of the 12-mers. For each of them five chains were randomly distributed in a cubic box (with 100.0 Å side). The multiple chain setup was deliberately designed in order to test computationally the agglomeration process concomitant with (or following) the thermoresponsive chain collapse. The specific molecular Entropy 2020, 22, 1187 4 of 18 dynamics engine driving the simulation was the mdrun program of the GROMACS package version 4.6 [32]. The visualization engine throughout this work was the VMD program [42].

2.3. Data Extraction from Molecular Dynamics Trajectories GROMACS routines were used to extract relevant structural data from the generated molecular dynamics trajectories. The dynamics of the conformational evolution of the oligomer chains were monitored by the variation with the simulation time of the end-to-end distance of the backbone chains and the radii of gyration (rg). The radius of gyration is a measure for the extent of a polymer chain and we applied it as a measure for the collapse of the polymer molecule into a globular state. An analysis of the intermolecular (oligomer ... water) hydrogen bonds was also carried out, with the purpose to correlate the hydrogen bonding patterns around the polymer molecules with the thermoresponsive behavior observed as a collapse of the polymer chain above the LCST.

2.4. Estimation of Entropy Contributions—Brief Theoretical Intermezzo

2.4.1. Stringent Formal Deﬁnition—Sampling of the Complete Phase Space Formally the entropy calculation seems straightforward—it is a logarithmic measure of the accessible volume in phase space):

S = kB ln(ρ) (1) − where ρ is the phase space density and kB is the Boltzmann constant, < > denotes ensemble average. However, in practice the direct calculation of the entropy value is infeasible. The diﬃculty stems from the entropy value dependence on the complete phase space of the system. Its evaluation requires an integral over the complete phase space which is computationally prohibitive. Z 3N 3N S = kB d xd pρ(x, p) ln[ρ(x, p)] (2) − R where x, p represent the coordinates and momenta of the particles in the ensemble.

2.4.2. Access to Phase Space Density An additional obstacle is the lack of knowledge of the phase space density. It is not directly accessible from molecular dynamics trajectories. Therefore, yet another major problem arises in the entropy calculation methods—ﬁnding a suitable approximation of the phase space density. Two approaches are relevant:

Phase space density estimation through energy and partition function • The following relation gives access to the density through energy (which is accessible in the molecular dynamics simulation): e βH(x.p) ρ(x, p) = − (3) Z where H is the Hamiltonian and Z is the partition function of the system. However, again an obstacle arises—the cost for the evaluation of the partition function Z. Thus, we resorted to another approximation—the quasiharmonic approximation.

Quasiharmonic approximation—Gaussian analytical ansatz for density • Alternatively, we can direct our thought at constructing an analytical ansatz of the density and fit it to the molecular dynamics’ trajectory. Karplus et al. [43] utilized the fact that the entropy can be decomposed into position dependent and moment dependent component. The momentum dependent component can be estimated analytically. Therefore, the bottleneck of this method is the computation Entropy 2020, 22, 1187 5 of 18 of the coordinate dependent component. Again, direct estimation is impossible. However, fitting the density as an analytical ansatz to the molecular dynamics’ trajectory is a way around this. The density near local/global minimum on the free energy surface can be approximated by a Gaussian function. More specifically the generated molecular dynamics trajectories can be used to fit the following multivariate Gaussian function:

1 1 (x x )TC 1(x x ) ρ(x, p) = e− 2 − 0 − − 0 (4) 3N/2 1 (2π) C 2 | | where C is the covariance matrix, |C| is the determinant of the covariance matrix. Actually, the ﬁt parameters are the eigenvectors of the covariance matrix C—its 3N principal components. Then the entropy (based on the ﬁtted density) can be obtained by the following formula:

3 1 h 3N i S = NkB + kB ln (2π) C (5) −2 2 | | The covariance matrix of the atomic ﬂuctuations has peculiar eigenvalue spectrum that might turn out to be problematic in realistic calculations. The problem comes from the contribution of the high-frequency motions. The solution comes from the analytic quantum mechanical treatment of the problematic degrees of freedom.

2.4.3. Quantum Mechanical Considerations and Approximations Quantum mechanical entropy of harmonic oscillator • The solution of Schlitter et al. [44] excludes the low eigenvalues by application of quantum mechanical considerations for the entropy of the harmonic oscillator at room temperature

S = κα ln(1 exp( α)), exp(α) 1 − − − h¯ω − (6) α = kT

Quantum mechanical variance is related to the frequency w of the oscillator in the above expressions. On the other hand, data from molecular dynamics simulations can be used to estimate only the classical variance (no direct access to quantum mechanical variance).

Reducing the quantum formula to the application of the classical limit of the variance • The classical limit of the coordinate variance can be substituted in the above expression of the entropy by application of the following relation [44]:

1 mkT D E = ∆x2 (7) α2 h¯ 2 cl Then the entropy calculation boils down to the estimation of the classical variance (accessible from molecular dynamics simulations). The ﬁnal expression for the entropy makes use of yet another heuristic approximation by Schlitter [44] and ﬁnally generalizing to the multidimensional case by summing over 3N degrees of freedom yields:

X3N ! 1 kBT D 2E S kB ln 1 + ∆x (8) ≈ 2 2 i cl i=1 h¯ D E where ∆x2 represent the classical variance of the ith degree of freedom. i cl In order to estimate the entropy contribution in the coil-to-globule transition, we applied a computational scheme based on these approaches—the quasiharmonic method of Karplus et al. [43] and the improvement based on Schlitter’s method [44]. The theoretical foundation and the computational Entropy 2020, 22, 1187 6 of 18 bottleneck of the procedure is the evaluation of the covariance matrix of the Cartesian positional coordinates from the molecular dynamics trajectories. The entropy is calculated from the eigenvalues obtained after the diagonalization of the mass-weighted covariance matrix. Though not fully validated, the method had been already applied for entropy estimates in simulations of polymer molecules, e.g., to examine the entropy change upon protein folding [45].

3. Results and Discussion Eight diﬀerent setups for simulations were executed (Table1). The discussion starts with examination of the structural variations with the simulation time of the 30-mer and the 24-mer NIPAM and IPOZ oligomer chains. Next, the results are presented for the multiple 12-mers (multiple chains) NIPAM and IPOZ molecules in an attempt to reproduce the temperature induced agglomeration of the multiple chains (in foil to the chain collapse). Molecular characteristics, hydrogen-bonding and polar contacts, were also determined and discussed. Special attention was devoted at the estimate of the entropy changes when passing from temperature far below (263.0 K) to temperature far above (333.0 K) the LCST point (for all cases, including 12-mer, 24-mer, and 30-mer NIPAM and IPOZ oligomers). The PNIPAM molecule undergoes a discontinuous hydration dehydration transition at around 305 K [1,2]. We consider the relatively wide span through the supposed transition temperature as necessary in order to obviate the mismatch between the temperature in the simulation settings and the real thermodynamic temperature.

Table 1. The simulation setups executed depending on the number of monomeric units, the number of oligomer molecules in a unit box and the size of the cubic box with model water molecules.

PNIPAM PIPOZ Number of oligomer molecules 1 2 5 1 2 5 in the unit box Number of monomeric units 30 24 12 30 24 12 Size of the cubic box with water 100.0 300.0 100.0 100.0 100.0 300.0 100.0 100.0 molecules [Å] Number of water molecules 11,748 294,902 11,019 10,980 11,733 294,887 11,010 10,945 Duration of the simulation [ns] 30.0 10.0 12.0 12.0 30.0 10.0 12.0 12.0

Two alternative initial setups were considered for the 30-mers with the purpose to assess the dependence of the results on the size of the solvent box, 100.0 Å and 300.0 Å side lengths, respectively. Due to computational limitations we were in a position to run only short simulations (10.0 ns) for the case of the large solvation box (300.0 Å). Although we generated additional simulation data for intermediate points along the temperature range, we report here only the results for the two extreme temperatures (263.0 K and 333.0 K). Figure2 contains data extracted from the 10.0 ns simulation of single 30-mer NIPAM and IPOZ molecules starting from an initially extended conformation. There is clear tendency for collapse of the NIPAM oligomer chain at the higher temperature as the molecule adopts supposedly a globular state, whereas the variations of the radius of gyration and the end-to-end distance at the low temperature are in support for the persistence of the extended form (Figure2a,b). The data for the 30-mer IPOZ molecule unequivocally demonstrate reproducibility of the experimentally observed LCST effect for PIPOZ solutions (Figure2c,d). To the best of our knowledge, this is the first reported fully atomistic molecular dynamics reproduction (using adequate solvation and spatial scale) of the experimental observations for PIPOZ systems. Though relatively short, the simulation time is enough in order to show up the LCST effect. In order to get further clear picture at the molecular level, we illustrate with snapshots from the simulation trajectories the computed molecular structures in the final stages of the simulations for the two extreme temperature points (Figure3). Both the NIPAM and the IPOZ oligomer chains show extended, though not strictly “coiled” conformations at the low Entropy 2020, 22, x FOR PEER REVIEW 7 of 19 Entropy 2020, 22, x FOR PEER REVIEW 7 of 19 with snapshots from the simulation trajectories the computed molecular structures in the final stageswith snapshots of the simulations from the for simulation the two extremetrajectories temperature the computed points molecular(Figure 3). structuresBoth the NIPAMin the finaland Entropy 2020 22 thestages IPOZ of the,oligomer, 1187simulations chains for show the twoextended, extreme though temperature not strictly points “coiled” (Figure conformations 3). Both the NIPAM at the7 oflowand 18 temperaturethe IPOZ oligomer regime andchains even show simple extended, visual inspectithough onnot at strictlythe higher “coiled” temperature conformations gives evidence at the lowfor temperatureadoptingtemperature globular regimeregime form. andand Obviously, eveneven simplesimple the visualvisual globular inspectioninspecti conformationson atat thethe higherhigher suggest temperaturetemperature dehydration givesgives of evidencetheevidence polymer forfor adoptingmoleculesadopting globularglobular due to diminishing form.form. Obviously, of their thethe contact globularglobular surface conformationsconformations with the surrounding suggestsuggest dehydrationdehydration solvent molecules. ofof thethe polymerpolymer moleculesmolecules duedue toto diminishingdiminishing ofof theirtheir contactcontact surfacesurface withwith thethe surroundingsurrounding solventsolvent molecules.molecules.

(a) (b) (a) (b)

(c) (d) (c) (d) Figure 2. Variation with the simulation time of the end-to-end distance and the radius of gyration FigureforFigure the 2.30-mer2. VariationVariation NIPAM with with and the the simulationIPOZ simulation molecules, time time of startingof the the end-to-end en fromd-to-end an distance initially distance and extended and the the radius conformationradius of gyration of gyration in for a thecubicfor 30-merthe box 30-mer with NIPAM 300NIPAM andÅ side: IPOZ and (a molecules,)IPOZ Simulation molecules, starting of NIPAM starting from at an from263.0 initially anK; extendedinitially(b) simulation extended conformation of NIPAM conformation in aat cubic 333.0 boxin K; a with(cubicc) simulation 300 box Å with side: of 300 (IPOZa) SimulationÅ side: at 263.0 (a) ofSimulationK; NIPAM(d) simulation at of 263.0 NIPAM of K; IPOZ (b at) simulation 263.0 at 333.0 K; ( K.b of) simulation NIPAM at 333.0of NIPAM K; (c) simulationat 333.0 K; of(c) IPOZ simulation at 263.0 of K;IPOZ (d) simulationat 263.0 K; of(d) IPOZ simulation at 333.0 of K. IPOZ at 333.0 K.

(a) (b) (a) (b) Figure 3. Cont. Entropy 2020, 22, 1187 8 of 18 EntropyEntropy 2020 2020, 22,, 22x FOR, x FOR PEER PEER REVIEW REVIEW 8 of8 19 of 19

FigureFigureFigure 3. Variation3. Variation ofof oligomeroligomerof oligomer morphology morphology morphology with with with the the simulation the simulation simulation time time fortime for the forthe 30-mer the 30-mer 30-mer NIPAM NIPAM NIPAM (a,b )(a and, b(a) ,b) andIPOZand IPOZ ( cIPOZ,d) ( molecules.c, d(c) ,dmolecules.) molecules. The simulation The The simulation simulation time is time 10.0 time ns.is 10.0is The 10.0 ns. ﬁnal ns.The snapshots The final final snapshot extracted snapshots extracted froms extracted the molecularfrom from the the moleculardynamicsmolecular trajectoriesdynamics dynamics trajec are trajec presented:toriestories are are (presented:a) NIPAMpresented: at(a 263.0) (NIPAMa) NIPAM K; (b )at NIPAM 263.0at 263.0 K; at K; 333.0(b ) (bNIPAM) K; NIPAM (c) IPOZ at 333.0at at333.0 263.0 K; K;(c K;) (c) IPOZ(d)IPOZ IPOZ at 263.0at at 263.0 333.0 K; (K;d K.) (IPOZd) IPOZ at 333.0at 333.0 K. K.

TheTheThe next next set set of ofNIPAM/IPOZ NIPAM NIPAM/IPOZ/IPOZ 30-mer 30-mer simulations simulations uses uses smaller smaller cubic cubic box box with with side side 100.0 100.0 Å but Å but thethethe time time time scale scale scale was was was extended extended up up up to 30.0to 30.0 ns. ns. A A cave caveatA caveat at with with using using small small simulation simulation box box box is theis the problem problem withwith thethe the application application application of periodicof ofperiodic periodic boundary boundary boundary conditions. conditions. conditions. In the caseIn Inthe of the acase small case of box ofa sizesmalla small the box NIPAM box size /sizeIPOZ the the NIPAM/IPOZoligomerNIPAM/IPOZ molecules oligomer oligomer might molecules molecules interact might with might theinteract interact chain with image with the inthe chain the chain adjacent image image in periodic inthe the adjacent adjacent cell. Thisperiodic periodic artificial cell. cell. ThisinteractionThis artificial artificial might interaction interaction produce might nonphysical might produce produce e ffnonphysicalects—periodic nonphysical effects—periodic effects—periodic images are identical images images physical are are identical identical objects physical and physical the objectsproducedobjects and and eff theect the isproduced actuallyproduced self-interaction.effect effect is isactually actually We self-i tookself-interaction. carenteraction. to check We We fortook took artificial care care to interactions tocheck check for for betweenartificial artificial interactionsneighboringinteractions between periodic between imagesneighboring neighboring in order periodic toperiodic avoid images nonphysicalimages in inorder order eff ectsto toavoid in avoid the simulationnonphysical nonphysical results. effects effects Figure in inthe 4the simulationillustratessimulation theresults. results. time Figure dependence Figure 4 illustrates 4 illustrates of the largethe the time scale time de structural pendencedependence changes of ofthe the large for large the scale NIPAMscale structural structural and IPOZ changes changes 30-mer for for theoligomersthe NIPAM NIPAM occurring and and IPOZ IPOZ at 30-mer the 30-mer two oligomers extreme oligomers temperatures.occu occurringrring at theat the two two extreme extreme temperatures. temperatures.

(a)( a) (b)( b)

Figure 4. Cont.

Figure 3. Variation of oligomer morphology with the simulation time for the 30-mer NIPAM (a,b) and IPOZ (c,d) molecules. The simulation time is 10.0 ns. The final snapshots extracted from the molecular dynamics trajectories are presented: (a) NIPAM at 263.0 K; (b) NIPAM at 333.0 K; (c) IPOZ at 263.0 K; (d) IPOZ at 333.0 K.

The next set of NIPAM/IPOZ 30-mer simulations uses smaller cubic box with side 100.0 Å but the time scale was extended up to 30.0 ns. A caveat with using small simulation box is the problem with the application of periodic boundary conditions. In the case of a small box size the NIPAM/IPOZ oligomer molecules might interact with the chain image in the adjacent periodic cell. This artificial interaction might produce nonphysical effects—periodic images are identical physical objects and the produced effect is actually self-interaction. We took care to check for artificial interactions between neighboring periodic images in order to avoid nonphysical effects in the simulation results. Figure 4 illustrates the time dependence of the large scale structural changes for the NIPAM and IPOZ 30-mer oligomers occurring at the two extreme temperatures.

Entropy 2020, 22, 1187 9 of 18 (a) (b)

Figure 4. Variation with the simulation time of the end-to-end distance and the radius of gyration for the 30-mer NIPAM and IPOZ molecules, starting from an initially extended conformation in a cubic box with 100 Å side: (a) Simulation of NIPAM at 263.0 K; (b) simulation of NIPAM at 333.0 K; (c) simulation of IPOZ at 263.0 K; (d) simulation of IPOZ at 333.0 K.

Special care had to be taken in order to ascertain that no direct interactions between the oligomer molecules and their periodic images could take place. For this purpose we regularly checked the minimal distance between periodic images by using the mindist routine of the GROMACS suite. However, the indirect effects from the interactions of the periodic images are quite difficult to monitor and list out. These hard to follow interactions are indirect in the sense of being mediated through the structure of the surrounding solvent molecules, namely the ordering of water molecules at the nanometer range. Beyond these considerations the results are unequivocally clear that at high temperatures the 30-mer IPOZ chain experiences collapse as monitored by the abrupt change in the radius of gyration/end-to-end distance, which is in support for the PIPOZ thermoresponsive behavior. Data displayed in Figure S1 (in Supporting Information) supports the above conclusions for the 24-mer NIPAM and IPOZ cases. We used alternative initial setups for the 12-mer case corresponding to extended and optimized conformations of the oligomer molecules. In addition, the simulation box contains five oligomers, thus we attempted to reproduce the effect of agglomeration (concomitant with the chain collapse). Figure S2 (Supporting Information) presents data for NIPAM and IPOZ starting from an initially extended conformation. A tendency is evident for polymers to collapse at high temperatures as the molecule strives to adopt a globular state (Figure S2b). Although slight, the shrinking of the structure is clearly present above LCST. The same data series for the IPOZ oligomers (Figure S2d) at the high temperature point also indicates a slight tendency for getting smaller average extent of the molecule as a consequence of the adoption of a globular structure. At the low temperature point (Figure S2a,c) the MD trajectories end with structures which preserve some of the spatial extent of the oligomer molecule which is a sign that temperatures below LCST favor the coil hydrated state. Thus, the simulations for the 12-mer IPAM and IPOZ molecules also provide evidences for thermoresponsive type behavior. Besides the process of polymer chain collapse at the single molecule level, an additional phenomenon manifests itself in the molecular dynamics’ simulations of multiple chains, namely agglomeration of the collapsed chains. The collapse of the polymer chain is a prerequisite for the aggregation and the precipitation of the solution thus the two processes can be considered concomitant. At phenomenological level it can be observed as shrinkage of the polymer microgel. Our multiple chain simulations are illustrative in this respect and reproduce faithfully the experimentally observed agglomeration. Figure5 contains snapshots extracted from the simulation trajectory of NIPAM oligomers using an extended starting conformation, leading finally to chain collapse at 333.0 K. The visual inspection in a molecular viewer (VMD) supports the phenomenon of low critical solution point phase transition. A comparison of the first snapshot (dispersed chains in Entropy 2020, 22, 1187 10 of 18 solution) and the last snapshot of the trajectory (i.e., at 0.0 ns and 12.0 ns, respectively) witnesses the collapse of the oligomer chains and their consequent aggregation which experimentally is registered as insolubility—formation of aggregates above the transition temperature point. Analogous results (computational reproduction of agglomeration) were reported for yet another N-substituted acrylamide-based polymer—poly(N-n-propylacrylamide) (PnnPAm) which is a structural isomer of theEntropy poly( 2020N,-isopropylacrylamide) 22, x FOR PEER REVIEW [46]. 10 of 19

(a) (b)

FigureFigure 5.5. VisualizationVisualization of the 12-mer12-mer NIPAMNIPAM morphologymorphology inin solution.solution. The simulation time is 12.0 ns. SnapshotsSnapshots ofof thethe ﬁrstfirst andand thethe lastlast framesframes areare shown:shown: ((aa)) TheThe ﬁvefive NIPAMNIPAM 12-mers12-mers withwith extendedextended initialinitial conformations;conformations; ( (bb)) a a snapshot snapshot at at the the end end of of the the simulation simulation carried carried out out at high at high temperature temperature point. point.

TheThe dependencedependence ofof thethe resultsresults onon thethe startingstarting conformationsconformations waswas alsoalso examined.examined. FigureFigure S3S3 displaysdisplays thethe resultsresults forfor thethe 12-mer12-mer NIPAMNIPAM andand IPOZIPOZ molecules,molecules, startingstarting fromfrom anan initiallyinitially optimizedoptimized conformationconformation [41[41].]. There There is slightis slight tendency tendency for both for oligomersboth oligomers to unfold to at unfold low temperature at low temperature conditions. Thisconditions. result isThis an interestingresult is an computationalinteresting computat evidenceional for evidence the thermoresponsive for the thermoresponsive effect in the effect reverse in direction—thethe reverse direction—the case with initial case with pre-collapsed initial pre-collapsed chain conformation chain conformation which strives which to adoptstrives extended to adopt stateextended when state subjected when subjected to low temperature. to low temperature. Previous Previous attempts attempts to demonstrate to demonstrate the effect the for effect initially for collapsedinitially collapsed NIPAM oligomerNIPAM oligomer chain failed chain to observefailed to such observe behavior, sucheven behavior, at very even long at duration very long of theduration simulation—1.0 of the simulation—1.0µs [47]. A μ possibles [47]. A reason possible could reason be could hidden be behind hidden theirbehind MD their setup MD with setup a singlewith a chainsingle NIPAM chain NIPAM oligomer oligomer [47] against [47] against the multiple the multiple chains’ chains’ simulations simulations in our in case. our case. The lowThe temperaturelow temperature simulation simulation of the IPOZof the oligomer IPOZ oligomer (with optimized (with optimized starting conformation) starting conformation) also shows signs also forshows computational signs for computational reproduction of reproduction the thermoresponsive of the thermoresponsive effect: As expected effect: the simulationsAs expected at thethe lowsimulations temperature at the regime low temperature lead to increase regime of the lead end-to-end to increase distance of the end-to-end (Figure S3d). distance However, (Figure obtaining S3d). extendedHowever, final obtaining coil state extended in a hydrated final coil (a swollenstate in coil)a hydrated conformation (a swollen is beyond coil) conformation reach in our simulation is beyond setupreach sincein our the simulation effect could setup be fully since revealed the effect in computationscould be fully with revealed much in longer computations time scales. with much longerNext, time we scales. looked for details about the solvent structure around the hydrophobic and the hydrophilic moietiesNext, of thewe oligomers.looked for More details specifically, about the in ordersolven tot elicitstructure the factors around at molecularthe hydrophobic level that and govern the thehydrophilic thermoresponsive moieties of behavior the oligomers. we examined More thespecifically, modes of in solvent–polymer order to elicit the interactions factors at in molecular terms of hydrogen-bondinglevel that govern the and thermoresponsive overall polar contacts. behavior Supposedly we examined the major the rolemodes in the of processsolvent–polymer has to be ascribedinteractions to the in so-calledterms of hydrogen-bonding “bound water”. One and can overall differentiate polar contacts. two types Supposedly of bound waterthe major molecules: role in Hydrogenthe process bonded has to waterbe ascribed molecules to the with so-called the –C “bound=O or –N–H water”. groups One can of the differentiate polymer molecule two types and of interactionsbound water that molecules: can take Hydrogen place with bonded the participation water mo oflecules the hydrophobic with the –C=O groups—methyl or –N–H groups groups of the or thepolymer main-chain molecule skeleton. and interactions As far as hydrophobic that can take ordering place is with concerned, the participation we tackle the of issuethe hydrophobic of solvation patternsgroups—methyl and reorganizations groups or the around main-chain hydrophobic skeleton. moieties As far in as terms hydrophobic of entropy ordering contribution. is concerned, Actually, thewe organizationtackle the issue of theof solvation proximal patterns solvent moleculesand reorganizations is reflected around in the entropy hydrophobic calculations moieties (vide in infra).terms Theof entropy detailed contribution. local structure Actually, of the water the organization clathrates around of the theproximal polymer solvent molecule molecules is beyond is reflected the scope in ofthe our entropy examination. calculations (vide infra). The detailed local structure of the water clathrates around the polymerWe considermolecule atoms is beyond X–H the... scopeY (X, of Y–N our or examination. O) to constitute a hydrogen bond if they fulfill the followingWe consider requirements: atoms The X–H donor–acceptor … Y (X, Y–N distanceor O) to X cons... Ytitute is less a thanhydrogen 3.6 Å, bond the hydrogen–acceptor if they fulfill the following requirements: The donor–acceptor distance X … Y is less than 3.6 Å, the hydrogen– acceptor distance is less than 2.45 Å, and the angle between the donor–hydrogen vector and the donor–acceptor vector is less than 30.0°. The water–polymer hydrogen bonds are of two types: The polymer molecule provides the donor group and the water oxygen atoms are acceptors in hydrogen bonding, or the polymer molecule participates with acceptor groups and the water molecules are the donors in the hydrogen bond pair. We estimated also the number of pairs of oligomer–solvent polar atom contacts. Entropy 2020, 22, 1187 11 of 18 distance is less than 2.45 Å, and the angle between the donor–hydrogen vector and the donor–acceptor vector is less than 30.0◦. The water–polymer hydrogen bonds are of two types: The polymer molecule provides the donor group and the water oxygen atoms are acceptors in hydrogen bonding, or the polymer molecule participates with acceptor groups and the water molecules are the donors in the Entropy 2020, 22, x FOR PEER REVIEW 11 of 19 hydrogen bond pair. We estimated also the number of pairs of oligomer–solvent polar atom contacts. The results for the variation with the simulation time of the hydrogen bond number and the The results for the variation with the simulation time of the hydrogen bond number and the polar contacts for the 30-mer, 24-mer, and 12-mer NIPAM/IPOZ oligomer molecules are presented in polar contacts for the 30-mer, 24-mer, and 12-mer NIPAM/IPOZ oligomer molecules are presented Figures6 and7 (and in Figures S4 and S5). The data is consistent with the thermoresponsive e ffect. in Figures 6 and 7 (and in Figures S4 and S5). The data is consistent with the thermoresponsive The number of hydrogen bonds remains constant at the low temperature (263.0 K) (Figure6a,c and effect. The number of hydrogen bonds remains constant at the low temperature (263.0 K) (Figures Figure7a,c and Figures S4a,c and S5a,c), whereas it diminishes sharply with the simulation time at 6a,c and 7a,c, and Figures 4Sa,c and 5Sa,c), whereas it diminishes sharply with the simulation time high temperature (333.0 K) reflecting the folding process of the oligomer chains with concomitant at high temperature (333.0 K) reflecting the folding process of the oligomer chains with concomitant breaking of water-oligomer hydrogen bonds (Figure6b,d and Figure7b,d and Figures S4b,d and breaking of water-oligomer hydrogen bonds (Figures 6b,d and 7b,d, and Figures 4Sb,d and 5Sb,d). S5b,d). The time dependence of the polar contacts follows closely the hydrogen bond number curve in The time dependence of the polar contacts follows closely the hydrogen bond number curve in all all cases. cases.

(a) (b)

Figure 6. VariationVariation with with the simulation time time of the number of hydrogen bo bondsnds and the contacts between polarpolar atomsatoms ofof the the 30-mer 30-mer NIPAM NIPAM/IPOZ/IPOZ molecules molecules and and the solventthe solvent molecules, molecules, starting starting from frominitially initially extended extended conformations conformations in a cubic in a boxcubic with box 300 with Å side:300 Å (a side:) Simulation (a) Simulation of NIPAM of NIPAM at 263.0 K;at (263.0b) simulation K; (b) simulation of NIPAM of at NIPAM 333.0 K; (atc) simulation333.0 K; (c of) simulation IPOZ at 263.0 of K;IPOZ (d) simulationat 263.0 K; of(d IPOZ) simulation at 333.0 K.of IPOZ at 333.0 K. Entropy 2020, 22, 1187 12 of 18 Entropy 2020, 22, x FOR PEER REVIEW 12 of 19

(a) (b)

Figure 7. VariationVariation with with the the simulation time time of the number of hydrogen bo bondsnds and the contacts between polarpolar atomsatoms ofof the the 30-mer 30-mer NIPAM NIPAM/IPOZ/IPOZ molecules molecules and and the solventthe solvent molecules, molecules, starting starting from frominitially initially extended extended conformations conformations in a cubic in a boxcubic with box 100 with Å side:100 Å (a side:) Simulation (a) Simulation of NIPAM of NIPAM at 263.0 K;at 263.0(b) simulation K; (b) simulation of NIPAM of at NIPAM 333.0 K; (atc) simulation333.0 K; (c of) simulation IPOZ at 263.0 of IPOZ K; (d) simulationat 263.0 K; of(d IPOZ) simulation at 333.0 K.of IPOZ at 333.0 K. With the next set of time series (Figure8) we seek to find di fferences in the time dependent hydrogenWith bondingthe next patternsset of time for theseries NIPAM (Figure and 8) the we IPOZ seek oligomers to find differences when the startingin the time conformation dependent of hydrogenthe oligomer bonding molecule patterns is optimized for the NIPAM from conformational and the IPOZ oligomers search [41 ].when At high the starting temperature conformation (333.0 K) ofthe the number oligomer of both molecule PNIPAM-water is optimized (Figure from8b) conformational and PIPOZ-water search (Figure [41].8d) At hydrogen high temperature bonds remains (333.0 K)constant the number (very low)of both with PNIPAM-water the simulation time,(Figure as 8b) expected and PIPOZ-water for the folded (Figure state of 8d) a thermoresponsive hydrogen bonds remainspolymer constant at high temperature. (very low) with The rapidthe simulation increase of time, the oligomer–water as expected for hydrogen the folded bonds state number of a thermoresponsiveat low temperature polymer in the first at few high nanoseconds temperature. reflects The the rapid process increase of unfolding of the for oligomer–water both PNIPAM hydrogen(Figure8a) bonds and PIPOZ number (Figure at low8c). temperature Evidently, the in ethffeects first are few even nanoseconds more strongly reflects pronounced the process when of unfoldingusing initially for both optimized PNIPAM geometries. (Figure 8a) and PIPOZ (Figure 8c). Evidently, the effects are even more strongly pronounced when using initially optimized geometries. Entropy 2020, 22, 1187 13 of 18 Entropy 2020, 22, x FOR PEER REVIEW 13 of 19

(a) (b)

Figure 8. VariationVariation with with the the simulation time time of the number of hydrogen bo bondsnds and the contacts between polarpolar atomsatoms ofof the the 12-mer 12-mer NIPAM NIPAM/IPOZ/IPOZ molecules molecules and and the solventthe solvent molecules, molecules, starting starting from frominitially initially optimized optimized conformations conformation in a cubics in a boxcubic with box 100 with Å side:100 Å (a side:) Simulation (a) Simulation of NIPAM of NIPAM at 263.0 at K; 263.0(b) simulation K; (b) simulation of NIPAM of at NIPAM 333.0 K; (atc) simulation333.0 K; (c of) simulation IPOZ at 263.0 of IPOZ K; (d) simulationat 263.0 K; of(d IPOZ) simulation at 333.0 K.of IPOZ at 333.0 K. For the sake of delving deeper into the thermodynamic factors governing the phase transition, we focusedFor the onsake estimating of delving the deeper entropy into componentthe thermodynamic of the free factors energy governing as a possible the phase reason transition, for the wethermoresponsive focused on estimating behavior. the Such entropy a scenario component consistently of the explains free energy the reverse as a temperaturepossible reason effect: for If the thermoresponsivechange of entropy isbehavior. positive (increaseSuch a scenario of entropy), consiste thenntly with explains increasing the the reverse temperature temperature the free effect: energy If theof the change system of willentropy change is positive favorably (increase (diminishes of entr dueopy), to thethen term with–T increasing∆S). Moreover, the temperature one can decompose the free energythe entropy of the e ffsystemect into will separate change contributions favorably (diminishes that provides due meansto the term to gain –TΔ furtherS). Moreover, insight intoone can the decomposemechanism ofthe the entropy thermoresponsive effect into phaseseparate transition. contributions The entropy that provides change can means be decomposed to gain further either insightin terms into of thethe separatemechanism system of the components thermoresponsive (e.g., solute phase vs. transition. solvent) or The estimated entropy as change contributions can be decomposedcorresponding either to the in classification terms of ofthe the separate degrees syst of freedomem components of the system (e.g., as translational,solute vs. solvent) rotational or estimatedand vibrational. as contributions What we attempted corresponding was to determineto the classification the entropy diofff theerences degrees of the of oligomer freedom chains of the at systemtwo temperatures, as translational, one of themrotational below and thevibrat otherional. above What the LCST,we attempted and to compare was itto with determine the entropy the entropychange relateddifferences to the of water the oligomer solvent shell. chains Our at estimates two temperatures, are based onone the of approach them below of Schlitter and the [ 43other,44]. aboveThe covariance the LCST, matrix and to of compare the positional it with fluctuations the entrop ofy thechange atoms related (the g_covar to the routinewater solvent of the GROMACS shell. Our estimatessuite was used)are based was determinedon the approach for the of purpose, Schlitter i.e., [43,44]. the configurational The covariance entropy matrix was of extractedthe positional from fluctuationsthe fluctuations of the of theatoms 3N-6 (the internal g_covar degrees routine of freedomof the GROMACS of the oligomer. suite was The used) elements was of determined the covariance for thematrix purpose, are time i.e., averages the configurational over the configurations entropy wa alongs extracted the molecular from dynamics’the fluctuations trajectory. of the Then 3N-6 the internalSchlitter’s degrees formula of was freedom applied of by the using oligomer. the eigenvalues The elements/eigenvectors of the ofcovariance the covariance matrix matrix are time [44]. averagesThe estimation over the of the configurations entropy changes along of the solventmolecular also dynamics’ poses specific trajectory problems,. Then originating the Schlitter’s from formula was applied by using the eigenvalues/eigenvectors of the covariance matrix [44]. The estimation of the entropy changes of the solvent also poses specific problems, originating from the Entropy 2020,, 22,, 1187x FOR PEER REVIEW 14 of 19 18 diffusive motion of the water molecules which leads to enlargement of the configurational space theavailable diffusive to the motion solvent. of the Here water again molecules we evalua whichted the leads Cartesian-coordinate to enlargement of thecovariance configurational matrix. space availableFigure to the9 displays solvent. the Here computed again we total evaluated entropy the changes Cartesian-coordinate (including both, covariance the oligomer matrix. and the solventFigure contributions)9 displays theat 263.0 computed K and total333.0 entropy K. For all changes 30-mer (including cases the calculated both, the oligomerentropy change and the is solventnegative contributions) at the low temperature at 263.0 K and and 333.0 it is K. positi For allve 30-merfor the casessimulations the calculated at the entropyhigh temperature change is negativeregime. The at the data low unequivocally temperature supports and it ispositive the “entro forpy the driven” simulations hypothesis at the for high the temperature thermoresponsive regime. Theeffect. data On unequivocally the other hand, supports the case the of “entropy 24-mers driven” and 12-mers hypothesis is characterized for the thermoresponsive with positive etotalffect. Onentropy the other changes hand, at the high case and of 24-mers at low and temperatures. 12-mers is characterized However, the with entropy positive change total entropy at 263.0 changes K is atsmaller high andin comparison at low temperatures. to the 333.0 However, K and thus the entropyentropy changeis still atfavorable 263.0 K for is smaller the folding in comparison events at tohigh the temperatures 333.0 K and thusin this entropy case. isThis still difference favorable is for even the foldingmore pronounced events at high in terms temperatures of the entropy in this case.contribution This diff toerence the isfree even energy more pronouncedchange, since in termsthe entropy of the entropy term is contribution given higher to the weight free energy with change,heightening since of the the entropy temperature term is given(due higherto the weight–TΔS term). withheightening Thus, evenof close the temperaturevalues of the (due entropy to the –Tvariation∆S term). may Thus, lead even to significant close values differences of the entropy in the variationfree energy may change lead to of significant the process. diff Therefore,erences in the freesets energyof 24-mer change and of12-mer the process. data is Therefore,also in support the sets for of the 24-mer decisive and role 12-mer of the data entropy is also inchange support as the for thekey decisivethermodynamic role of the factor entropy responsible change asfor the the key co thermodynamicllapse of the polymer factor responsibleat high temperatures. for the collapse It is ofhonest the polymerto mention at high that temperatures. this data set Itcontai is honestns a topeculiar mention point—NIPAM12_OPT that this data set contains large a peculiarentropy point—NIPAM12_OPTchange which cannot be large logically entropy explained. change which cannot be logically explained.

Figure 9. The overall entropy changes for the 30-mer, 24-mer and 12-mer NIPAM and IPOZ systems (NIPAM30_L andand IPOZ30_LIPOZ30_L refer refer to to simulations simulations with with large large box box size size (300 (300 Å side); Å side); NIPAM12_OPT NIPAM12_OPT and IPOZ12_OPTand IPOZ12_OPT refer torefer simulations to simulations with initially with optimizedinitially optimized forms). The forms). ﬁgure The displays figure the displays results from the simulationsresults from atsimulations two extreme at temperaturetwo extreme points—at temperature 263.0 points—at K (blue bars) 263.0 and K (blue at 333.0 bars) K (redand bars).at 333.0 K (red bars). We have to keep in mind the approximations underlying the quasiharmonic approach, namely not accountingWe have for to anharmonicities keep in mind the of theapproximations vibrations and underlying the correlations the quasiharmonic of the probability approach, distributions. namely Anot necessary accounting condition for anharmonicities for convergence toof realistic the vibrations entropy valuesand the is the correlations adequate phase of the space probability sampling whichdistributions. could beA controllednecessary butcondition may require for convergenc long simulatione to realistic times. entropy Besides, va adequatelues is the sampling adequate is problematicphase space forsampling rugged which and frustrated could be energycontrolled surfaces—it but may is require tricky tolong visit simulation all relevant times. energy Besides, wells andadequate estimate sampling their relative is problematic populations. for rugged Therefore, and anfrus importanttrated energy limiting surfaces—it factor appears is tricky to be to a visit system all speciﬁcrelevant property—the energy wells properties and estimate of the their energy relative surface. populations. It is supposed Therefore, to be approximated an important by quadratic limiting functionfactor appears of the to internal be a system coordinates. specific This property—the condition is properties severely critical of the for energy the solvent surface. dynamics. It is supposed If the waterto be molecules’approximated dynamics by quadratic do not deviate function from of harmonicthe internal approximation coordinates. (which This condition validates theis severely analysis ofcritical the covariance for the solvent matrix) dynamics. we can giveIf the credit water to mo thelecules’ reported dynamics computational do not resultsdeviate andfrom consequent harmonic conclusions.approximation Unfortunately, (which validates the literature the analysis is scant of forthe datacovariance on the numericalmatrix) we accuracy can give of thecredit approach. to the Onereported possible computational avenue for futureresults improvements and consequent of the conc accuracylusions. of Unfortunately, the results is the the inclusion literature of the is cubicscant for data on the numerical accuracy of the approach. One possible avenue for future improvements Entropy 2020, 22, x FOR PEER REVIEW 15 of 19

Entropy 2020, 22, 1187 15 of 18 of the accuracy of the results is the inclusion of the cubic anharmonic terms [48]. Assuming that our systems meet these conditions, we can proceed with this method to dissect further the entropy anharmoniccontributions. terms [48]. Assuming that our systems meet these conditions, we can proceed with this methodNext, to dissectwe estimated further thethe entropy variation contributions. of the entropy in a decomposed mode, namely for the oligomerNext, component we estimated (Figure the variation 10a) versus of the the entropy solvent in component a decomposed (Figure mode, 10b) namely for the for two theoligomer extreme componenttemperature (Figure points—263.0 10a) versus K vs. the 33 solvent3.0 K. componentBoth the NIPAM (Figure and 10b) the for IPOZ the two oligomers extreme show temperature loss of points—263.0configurational K entropy vs. 333.0 of K. the Both backbone the NIPAM chain and upon the its IPOZ collapse oligomers at high show temperature loss of configurational for all cases, entropyexcept for of thethe backbone12-mer IPOZ chain with upon optimized its collapse initia at highl conformation. temperature However, for all cases, the except concurrent for the entropy 12-mer IPOZchange with of the optimized solvent increases initial conformation. in all cases (Figur However,e 10b) the and concurrent compensates entropy for the change entropy of the loss solvent of the increasesoligomer—in in all total cases the (Figure entropy 10 changeb) and is compensates positive as shown for the in entropy Figure 9. loss The of backbone the oligomer—in chain entropy total thechanges entropy at low change temperature is positive are as negative shown infor Figure most9 cases.. The A backbone notable chainexception entropy is the changes 12-mer at IPAM low temperatureoligomer with are optimized negative for initial most conformation. cases. A notable However, exception this is theis not 12-mer surprising, IPAM oligomer because with the optimizedthermoresponsive initial conformation. oligomer is However,supposed this to isstrive not surprising, to unfoldbecause at low thetemperature thermoresponsive and increase oligomer its isabsolute supposed entropy to strive thus to unfoldmaking at the low entropy temperature change and for increase the process its absolute positive. entropy The thussolvent making entropy the entropychange for change the low for thetemperature process positive. series is The markedly solvent convenient entropy change for explaining for the low the temperature thermoresponsive series is markedlyeffect in convenientthe 30-mer for case, explaining i.e., the the negative thermoresponsive entropy echangeffect in thecontribution 30-mer case, which i.e.,the overcomes negative entropyconsiderably change the contributionpositive entropy which change overcomes of the considerably oligomers, makes the positive temperature entropy induced change folding of the oligomers,unfavorable. makes The temperaturecase of the solvent induced entropy folding valu unfavorable.es for the 24-mers The case and of the 12 solvent-mers at entropy low temperature values for thecan 24-mersbe discussed and 12-mers in comparison at low temperature with the canhigh be temperature discussed in comparisonpoint results with and the explained high temperature as done pointabove results for the and total explained entropy as donechanges above in for order the total to entropyapply the changes entropy in order calculations to apply theresults entropy for calculationsexplanation resultsof the thermoresponsive for explanation of effect. the thermoresponsive effect.

(a) (b)

Figure 10.10. DecompositionDecomposition of of the the overall overall entropy entropy change change into (intoa) oligomer (a) oligomer contribution contribution and (b )and solvent (b) contribution.solvent contribution. The figure The displays figure displays the results the from resu simulationslts from simulations at two extreme at two temperature extreme temperature points—at 263.0points—at K (blue 263.0 bars) K and (blue at 333.0bars) Kand (red at bars).333.0 EntropyK (red bars calculations). Entropy were calculations carried out were for thecarried 30-mer, out 24-merfor the and30-mer, 12-mer 24-mer NIPAM and and 12-mer IPOZ systemsNIPAM (NIPAM30_L and IPOZ andsystems IPOZ30_L (NIPAM30_L refer to simulations and IPOZ30_L with largerefer box to sizesimulations (300 Å side); with NIPAM12_OPT large box size (300 and IPOZ12_OPTÅ side); NIPAM12_OPT refer to simulations and IPOZ12_OPT with initially refer optimized to simulations forms). with initially optimized forms). On the other hand, a possible explanation at the molecular level might be given in terms of the solvent-solventOn the other hand, interactions a possible in theexplanation presence at of the exposed molecular functional level might groups be ofgiven the polymerin terms inof thethe extendedsolvent-solvent conformation, interactions and compared in the presence with the of inaccessibility exposed functional of these functionalgroups of groups the polymer by the solventin the inextended the collapsed conformation, globular and state. compared For the extendedwith the inac formcessibility of the polymer, of these at functional temperatures groups below by the LCST,solvent the in solventthe collapsed molecules globular organize state. themselves For the inextended ordered form structures of the of polymer, water clusters at temperatures around the exposedbelow the polymer LCST, the functional solvent groupsmolecules linked organize via hydrogen-bonded themselves in ordered networks structures with the of polymer. water clusters It had beenaround shown the exposed that the solventpolymer molecules functional of groups the first linked solvation via shellhydrogen-bonded are involvedin networks a hydrogen with bond the networkpolymer. characterized It had been shown by hydrogen that the bonding solvent bridges molecu betweenles of the neighboring first solvation isopropylamide shell are involved groups in in a ahydrogen way that favorsbond annetwork extended characterized conformation by of thehydrogen PNIPAM bonding molecule bridges below LCST between [49]. Suchneighboring ordered structuresisopropylamide contribute groups for thein a lowering way that of favors the overall an extended entropy ofconformation the system by of restricting the PNIPAM the degrees molecule of freedombelow LCST of the [49]. system. Such Thisordered arrangement structures of contribute water molecules for the islowering no longer of stablethe overall above entropy the transition of the temperaturesystem by restricting point. The the additional degrees of degreesfreedom of of freedom the system. upon This release arrangement of solvent of molecules water molecules raise the is Entropy 2020, 22, 1187 16 of 18 entropy significantly. With increasing the temperature, increases the weight of the entropy contribution to the overall free energy of mixing, whereas when the free energy change is positive then the observed effect is phase separation. According to our results, the entropy of the solvent is the decisive factor for the thermoresponsive behavior of the PNIPAM/water and the PIPOZ/water binary solutions.

4. Conclusions We attempted to elucidate the mechanism of the heat-induced phase separation in two thermoresponsive polymers containing amide groups, PNIPAM and PIPOZ, and we succeeded in reproducing the existence of transition temperature point. We found out that the entropy has an important contribution to the thermodynamics of the phase separation transition. Moreover, we revealed that the entropy of the solvent has the decisive share for the lowering of the free energy of the system when increasing the temperature above the LCST. The water molecules structured around the functional groups of the polymer that are exposed to contact with the solvent in the extended conformation lower the enthalpy of the system, but at certain temperature the extended conformation of the polymer collapses as a result of dominating entropy gain from “released” water molecules. In addition to further longer simulations, one could expect that upon increasing the number of polymer chains in the simulation box and the size of the oligomer molecules the eﬀect of the temperature change on the polymer conformation and consequent aggregation of the solute molecules will be more clearly pronounced.

Supplementary Materials: The following are available online at http://www.mdpi.com/1099-4300/22/10/1187/s1, Figures presenting the variation with the simulation time of the end-to-end distance, the radius of gyration and the polymer–water hydrogen bonds. A section describing AMBER03 force field with explicit functional form. Author Contributions: Conceptualization, P.M.I.; Investigation, A.K. and P.M.I.; Methodology, A.K. and P.M.I.; Writing—original draft, A.K.; Writing—review & editing, P.M.I. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported also by the European Regional Development Fund within the Operational Program “Science and Education for Smart Growth 2014-2020” under the Project CoE “National center of mechatronics and clean technologies” BG05M2OP001-1.001-0008-C01. Acknowledgments: Financial support from the National Science Fund, Bulgaria (Contract grant number NSF-TK01/0167) is acknowledged. Conflicts of Interest: The authors declare no conflict of interest.

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