Solvent Structuring and Its Effect on the Polymer Structure and

Subscriber access provided by - Access paid by the | UC Irvine Libraries

Article

Solvent Structuring and Its Effect on the Polymer Structure and Processability: The Case of Water-Acetone Poly-#-Caprolactone Mixtures Nicodemo Di Pasquale, Daniele Luca Marchisio, Antonello A. Barresi, and Paola Carbone J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp505348t • Publication Date (Web): 27 Oct 2014 Downloaded from http://pubs.acs.org on November 2, 2014

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Solvent Structuring and its Effect on the Polymer Structure and Processability: the Case of Water-Acetone Poly-ε -Caprolactone Mixtures Nicodemo Di Pasquale,∗,†,¶ Daniele Luca Marchisio,† Antonello Alessandro Barresi,† and Paola Carbone‡ Istituto di Ingegneria Chimica, Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy, and School of Chemical Engineering and Analytical Science, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom E-mail: [email protected]

KEYWORDS: Poly-ε-Caprolactone (PCL), molecular dynamics, water-acetone mixtures, solvent clusters, Flory’s coefficient, diffusion

∗ To

whom correspondence should be addressed di Ingegneria Chimica, Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy ‡ School of Chemical Engineering and Analytical Science, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom ¶ currently at: School of Chemistry, The University of Manchester, Oxford Road, Manchester, M13 9PL, United Kingdom † Istituto

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract One of the most common processes to produce polymer nanoparticles is the solvent-displacement method, where the polymer is dissolved in a “good” solvent and the solution is then mixed with an “anti-solvent”. The polymer processability is therefore determined by its structural and transport properties in solutions of the pure solvents and at the intermediate compositions. In this work we focus on poly-ε-caprolactone (PCL) which is a biocompatible polymer that finds wide-spread application in the pharmaceutical and biomedical fields, performing full atomistic molecular dynamics simulations of one PCL chain of different molecular weight in solution of pure acetone (good solvent), pure water (anti-solvent) and their mixtures. Our simulations reveal that the nanostructuring of one of the solvent in the mixture leads to an unexpected identical polymer structure irrespectively of the concentration of the two solvents. In particular, while in the pure solvents the behaviour of the polymer is as expected very different, at intermediate compositions, the PCL chain shows properties very similar to those found in pure acetone due to the clustering of the acetone molecules in the vicinity of the polymer chain. We derive an analytical expression to predict the polymer structural properties in solution at different solvent compositions and show that the solvent clustering affects in an unpredictable way the polymer diffusion coefficient. These findings have important consequences on the optimization of the nanoparticle production process and in the implementation of continuum modelling techniques to model it.


Page 2 of 34

Page 3 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Introduction Poly-ε-caprolactone (PCL) is a saturated aliphatic polyester with hexanoate repeated units and due to a number of interesting properties is currently employed and studied in a broad range of applications. Recently it has been used also in composites of silicon-substituted carbonate apatite, which thanks to the PCL presence show increased mechanical resistance and can therefore be used as structural material. 1 PCL is also very frequently employed in the fabrication of biomedical devices and in the preparation of pharmaceutical products. The main motivation for using PCL in these latter applications lies in its bio-compatibility. 2 One of the most important use of PCL for pharmaceutical applications is the production of nanoparticles for drug delivery, a very promising application for human health. These nanoparticles contain inside the polymer matrix the drug molecules, resulting in targeted delivery, controlled release and, as a consequence, reduced side effects. 3–5 The so-called active targeted delivery is obtained by using functional groups that are often directly attached to the PCL chain, in the form of copolymers. 6 When the copolymer is constituted (as it often happens) by hydrophilic and hydrophobic parts the resulting carrier offers the additional advantage of overcoming the solubility limit of hydrophobic drugs, resulting in a hydrophobic core, where the drug is accommodated, and a hydrophilic surface. The hydrophilic surface is also interesting because it reduces the interactions with the reticuloendothelial system and it increases the residence time of the nanoparticles in the circulatory system. 7,8 Among the most used copolymers (including grafted and block copolymers) it is worth citing the PCL-based poly(ethylene glycol)co-poly(caprolactone) 9,10 and dextran-co-poly(caprolactone) 11 together with the non-PCL-based poly(methoxy polyethyleneglycol cyanoacrylate-co-hexadecyl cyanoacrylate). 10,12–15 Particularly relevant is their behaviour in solution, since it plays a crucial role in dissolution and degradation processes, as well as in the dynamics of their self-assembly into nanoparticles. This latter aspect in particular, is very important because is the key phenomenon involved in the most popular route to produce PCL-based nanoparticles, namely solvent-displacement. 16,17 In a 3 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

solvent-displacement process the polymer is dissolved in a good solvent, in most cases acetone, and the obtained solution is rapidly mixed with an anti-solvent (water in most cases). In order to efficiently control the mixing dynamics, which strongly affects the final outcome of the solventdisplacement process, different types of micro-mixers are used, as reported in the literature. 18–22 Moreover, since during solvent-displacement, PCL molecules find themselves moving from an acetone-rich environment to a water-rich environment, the investigation of their behavior in wateracetone mixtures at different compositions is particularly interesting. One of the promising way to efficiently describe these processes involving polymer systems is through the so-called multiscale modeling approach. One of the first attempts in this specific area of research was carried out by Di Pasquale et al., 23 where a description of the PCL nanoparticle formation process inside a Confined Impinging Jets Mixer (CIJM) was presented. In this initial work Molecular Dynamics (MD) was used to extract information concerning the conformation of PCL molecules and these results were used in a Population Balance Model (PBM) coupled with a Computational Fluid Dynamics (CFD) simulation to describe the self-assembly of the PCL molecules into nanoparticles. The present study focuses on the MD simulations of a single PCL chain in water-acetone mixtures and presents new simulation data, which are analysed and interpreted with standard theoretical tools from polymer physics. The MD simulation data are in particular analysed in terms of end-to-end distance, radius of gyration, radial distribution functions and diffusion coefficients; MD simulations are performed at three different PCL molecular weights and four different compositions for the water-acetone mixture, highlighting the complex influence of the solution composition on the chain configuration and conformation. The paper is organized as follows: in the first part the systems considered are presented along with the details of all the simulation performed. In the second part the results concerning the static and dynamic properties of the polymer in solution are analyzed and some general conclusions are drawn.


Page 4 of 34

Page 5 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Theoretical background In this work MD simulations will be used to estimate the radius of gyration, Rg , of PCL in wateracetone mixtures. As very well known, the dependence of the radius of gyration of a polymer upon its molecular weight, MW , can be described through the Flory’s law: 24 2ν hR2g i = kMW ,

(1)

where ν is the Flory’s coefficient, k is a scaling constant and h·i represents the ensemble average. Another important property of the polymer chain is the end-to-end distance, which for a freelyjointed chain (FJC) can be written as: 24

hR2 iFJC = Ne lk2 ,

(2)

where Ne is the equivalent number of monomers and lk is the Kuhn length. The Kuhn length can be calculated from the persistence length as lk = 2lp , while the persistence length, lp , can in turn be estimated, by evaluating the correlation of the direction of the bonds along the chain, 25,26 as follows: l hcos (θ (l))i = exp − , lp

(3)

where θ (l) is the angle between a bond li and a bond l j at distance l from li along the backbone of the chain. Another important theoretical result that will be useful in the following discussion is that according to the FJC model the end-to-end distance, R, obeys the classical Boltzmann distribution: 24

P (R) = 4πR

2

3 2πNe lk2

3 2

3R2 exp − . 2Ne lk2

(4)

MD simulations can also be used to estimate the polymer diffusion coefficient, D, in different



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 34

solvents using the Einstein relation: h(r(t) − r(0))2 i t→+∞ 6t

D = lim

(5)

where r(t) is the vector position at time t. Alternatively, the diffusion coefficient can also be calculated using the Stoke-Einstein theory which predicts the following law: 27 DSE =

kB T , 6π µRh

(6)

where T is the mixture temperature, kB is the Boltzmann constant, µ is the mixture viscosity and Rh is the hydrodynamic radius of the molecule of interest. In the case of polymers in solution this latter q quantity is very similar to the radius of gyration 28 and it can be approximated by: Rh ≈ hR2g i, whereas the viscosity of a water-acetone mixture can be evaluated by using the following equation:

µ = exp (xA ln(µA ) + (1 − xA ) ln(µW )) , where µA = 3.1 × 10−4 N s m−2 , 29 and µW = 8.0 × 10−4 N s m−2 . 30


(7)

Page 7 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Simulation Details The force field employed for the simulation of PCL and acetone is the Optimized Potentials for Liquid Simulations All Atoms (OPLS-AA) 31 . Water was simulated by making use of the popular SPC model, 32 which represents a good trade off between accuracy of the simulation and computational time. The simulations were performed by using GROMACS (version 4.6). 33 The time step of the simulation was set to 1 fs. The Berendsen thermostat 34 with coupling time constant τT = 0.1 ps was used to maintain the temperature at its reference value of 300 K, whereas the Berendsen barostat 34 with coupling constant τP = 0.5 ps was used to keep the system at the reference pressure of 1 bar. The combination rule employed to mix up the Lennard-Jones interactions are defined as follows: 1

σi j = (σii σ j j ) 2 1

εi j = (εii ε j j ) 2

(8) (9)

where σ and ε are the Lennard-Jones parameter, and i and j represent two different non-bonded atoms. Three different PCL molecular weights were considered in this work, namely 1170, 2310 and 3430 g mol−1 , corresponding to 10, 20 and 30 repeating units, showed in Figure 1 and indicated in what follows as PCL-10, PCL-20, PCL-30. For all three cases the polymer chains were terminated at both ends with methyl groups. The setup of the simulations was obtained as follows: for all the PCL molecular weights considered in this work (PCL-10, PCL-20, PCL-30) a short MD simulation (about 20 ps) in vacuum was performed. This was done in order to coil the chain up. The chain was subsequently solvated with water, acetone or combination of both in different ratios. Every operating condition is identified by the molar fraction of acetone, xA , in the water-acetone mixture. The values of xA considered are: 0, 0.50, 0.75, 1. Initially another molar fraction was considered (i.e. xA = 0.25), however, as also documented in the literature 35–38 at certain compositions unphysical de-mixing in water7 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1: Sketch of the repeating unit of the PCL acetone mixture is predicted with the most popular force fields. Therefore, after having verified that at this operating conditions de-mixing occurs this case was discarded. A 150 ns simulation of the water-acetone system (i.e. without polymer) for acetone molar fraction of xA = 0.50, and the same for xA = 0.75, were also performed to verify the absence of de-mixing at these compositions. The models were simulated for 700 ns for PCL-10 and 100 ns for PCL-20 and PCL-30. The equilibration time was chosen such that the time average of the properties of interests become invariant. The independence of the final results from the starting configuration was also checked. Four different configurations were obtained for the longest chain (PCL-30) and simulations in pure water and pure acetone were performed. In order to assess the absence of finite-size effects, simulation boxes of different size were tested for all the intermediate acetone molar fractions and for the shortest polymer chain (i.e. PCL-10). In Table 1 are summarized the number of atoms and the size of the boxes employed (labelled as SysA, SysB and SysC). The results obtained in the systems shown in Table 1 give consistent predictions between SysA, SysB and SysC. Therefore,


Page 8 of 34

Page 9 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the results from the smallest system (i.e. SysA) will be used in the next parts of the work. Table 1: Number of atoms (NA ) and length of the box (L in nm) in the systems labelled as SysA, SysB and SysC.

SysA SysB SysC

xA = 0.50 NA L 14982 5.6 47482 8.3 99482 10.6

xA = 0.75 NA L 18173 6.0 51173 8.5 94544 10.5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 34

Results and discussion Water-acetone mixture

We begin this analysis by comparing the calculated mass densities of

the four different water-acetone mixtures, corresponding to xA = 1.00 (pure acetone), 0.75, 0.50 and xA = 0.0 (pure water) with the experimentally measured ones and those calculated in other simulation works (from the literature). This comparison is reported in Table 2, for all compositions but for pure water, for which the standard prediction of SPC is obtained. As can be seen, in every simulation the calculated time-averaged densities show little deviation and are found to be in satisfactory agreement with the corresponding experimental values, 39 resulting in every case considered in an error lower than 5%. It is worth noticing that, although other force fields for acetone capable of obtaining better agreement with experimental density exist, 40 the same force field used to model the polymer chain was chosen for consistency. Table 2: Calculated time-averaged densities (in kg m−3 ) for all the different molar fractions of acetone-water mixtures considered in this work and comparison with the available corresponding experimental data and simulations taken from the literature (at 298.15 K)

xA = 1 xA = 0.75 xA = 0.50

Sim. (this work)

Exp. Data 39

Sim. 40

780 ± 3 795 ± 1 820 ± 1

785 819 858

792 851

Although the water-acetone system is well known experimentally and results from MD simulations are reported in the literature from the early 90’s, 41 a valid atomistic model for water-acetone mixtures is still far to be obtained. In this respect two different aspects should be considered. An interesting feature of water-acetone mixtures, already observed in the literature, both experimentally 42 and by using MD simulations, 40 is the appearance of acetone molecular clusters, resulting in an appreciable segregation of the two solvents. In particular, the maximum of the segregation between water and acetone molecules is observed at xA = 0.50. 42 This feature is detected also in our simulations, that show the presence of clusters for xA = 0.50 and 0.75, as reported in Figure 2. These clusters wander across the simulation box, through Brownian motion, and are continuously enriched and depleted, by solvents molecules coming from and going back to the bulk of the so10 ACS Paragon Plus Environment

Page 11 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


lution. They are however resulting from instantaneous fluctuations, which cancel out, if averaged over long enough time intervals, for most, but not all compositions.

Figure 2: Snapshots extracted from the simulation without the polymer for an acetone molar fraction of xA = 0.5 at different points of the trajectory (namely after 15 ns (on the left) and after 30 ns (on the right)). Water molecules are represented as red spheres whereas the yellow points represent the space of the box occupied by the acetone. In fact, unfortunately, the force fields commonly employed to simulate the water-acetone mixture are not capable of describing the complete miscibility of the two solvents for all compositions (i.e. 0 < xA < 1). 35,37 In particular, as already mentioned unphysical de-mixing is typically detected for xA = 0.3 when OPLS-AA together with SPC are used. 35 Even when employing newer force fields, specifically designed to overcome this issue, 35 a correct description of the wateracetone mixture seems not to be possible yet, 36–38 as definitive conclusions on this issue have not been drawn. Therefore in this work the values of xA corresponding to intermediate water-acetone mixtures are chosen in the region where the unphysical de-mixing is not observed (i.e. 0.30 < xA < 1.00). The remaining cases considered (i.e. xA = 0.50 and 0.75) consistently evidenced the presence of acetone clustering, without resulting in de-mixing.

Static properties of PCL

The formation of this structures observed for the binary mixtures (see

Figure 2) greatly affects the behaviour of the PCL molecules in solutions. In fact, the PCL chain tends to reside in the acetone clusters which are energetically favourable. It is important to stress again that simulations carried out without the PCL chain, only with the solvents molecules, also 11 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

highlighted the presence of these acetone clusters, causing instantaneous density fluctuations, that however cancel out if averaged over time, resulting in flat time-averaged density profiles across the simulation box. As a consequence of these clusters and strong interactions between solvents molecules, the overall structure of the polymer chain does not appreciably change with the wateracetone concentration of the mixture. On the contrary very little differences in the chain structure can be observed when moving from a pure solvent solution to every other water-acetone mixtures and remarkable differences can be observed only in pure water. The sequestration of the PCL molecule in the acetone cluster can be qualitatively assessed by looking at the radial distribution functions calculated between the atoms belonging to the PCL chain, and those of the water and acetone molecules, as reported in Figure 3. In this figure the radial distribution functions for the two different intermediate compositions of the water-acetone mixture investigated (i.e. xA = 0.50 and 0.75) and for PCL-10 are reported. Simulations carried out for PCL-20 and PCL-30 resulted in very similar trends and for the sake of brevity the corresponding radial distribution functions are omitted. The absolute value of these radial distribution functions is of no interest for a comparison, since different systems have different numbers of solvent molecules, but the position of the peaks gives a clear insight about the structure of the solvent around the PCL chain. As it can be seen from Figure 3, the shortest distance from the polymer at which the solvent atoms can be found is about 0.2 nm. At this length-scales very different behaviours between mixture of different concentrations are observed. Very few water molecules are located in a shell at about 0.2 nm, where a small peak in the radial distribution function is found, followed by a minimum. The number of water molecules then increases very slowly and more rapidly for small xA values. The radial distribution function for PCL-10 and acetone molecules is quite different. Starting from the same distance from the polymer atoms (i.e. 0.2 nm) it can be seen that the number of solvent molecules increases very rapidly until a peak is reached at about 0.6 nm. A solvent shell around the polymer molecule can be defined by considering the position of the first peak of the PCL-acetone radial distribution function. This position defines the maximum distance, rs , at which a solvent molecule can be considered inside the shell. From Figure 3, the


Page 12 of 34

Page 13 of 34

1

g(r)

1

g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.5

0.5

0 0

0.5

1

1.5

2

2.5

r (nm) 0 0

0.5

1

1.5

r (nm)

2

2.5

Figure 3: Radial distribution function between all the atoms belonging to PCL-10 and all the atoms belonging to acetone for xA = 0.50 (red dashed line) and for xA = 0.75 (green continuous line). In the inset, radial distribution function between all the atoms belonging to PCL-10 and all the atoms belonging to water for xA = 0.50 (red dashed line) and for xA = 0.75 (green continuous line).



value of rs is chosen to be 0.6 nm. Using this definition, the time evolution of the number of solvent molecules inside the solvent shell can be calculated and is reported in Figure 4. From the figure 450

xA=0.75

xA=0

300

acetone

150

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 34

water

450

xA=1

xA=0.5

300

acetone

150 water

0

25

50

75

100 0

25

50

75

100

Time (ns) Figure 4: Time evolution for the number of acetone (black line) and water (red line) molecules (identified by their centre of mass), within a shell of radius equal to the first peak of the radial distribution function around the PCL-30, for every acetone molar fraction considered. the remarkable difference (almost of an order of magnitude) in the number of the molecules of the two solvents, identified by their centre of mass, surrounding the polymer chain can be clearly appreciated. It is very interesting to further notice that by moving from pure water (xA = 0) to an intermediate mixture the number of water molecules inside the shell dramatically drops down, and further increases in xA do not result in major changes, until the PCL chain is in pure acetone (xA = 1). Moreover, simulations conducted with boxes of increasing size, showed that these are actual features of the investigated systems and not artifacts due to finite-size effects. The structuring of the solvent around the polymer chain is qualitatively showed in Figure 5, where the PCL-30 chain and all the solvent atoms found at a distance shorter than 0.6 nm from it are depicted. The structuring of the solvent molecules has a great impact on the overall shape of the PCL 14 ACS Paragon Plus Environment

Page 15 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5: Single molecule of PCL-30 in a water-acetone mixture with xA = 0.5 and the shell around it, represented by all the acetone (purple) and water (blue) molecules at distance shorter than 0.6 nm from any atom of the PCL-30 chain.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 34

chain as it can be inferred from the chain radius of gyration (Rg ). In Table 3 the time-averaged values of the squared radius of gyration, hR2g i, as obtained for PCL-10 in different water-acetone mixtures are reported along with their projections on the principal axes of inertia of the polymer, hR2g,x i, hR2g,y i and hR2g,z i. Similar trends and behaviors are observed for PCL-20 and PCL-30 and these results are reported only in the Supporting Information Table S1 and Supporting Information Table S2). Table 3: Time-averaged squared radius of gyration, hR2g i, and its projections along the principal axes of inertia, hR2g,x i, hR2g,y i and hR2g,z i (in nm2 ), for all the different molar fractions of acetone in the water-acetone mixtures considered in this work and for PCL-10.

xA = 1 xA = 0.75 xA = 0.50 xA = 0

hR2g i 1.56 ± 0.60 1.52 ± 0.60 1.41 ± 0.50 0.41 ± 0.07

hR2g,x i 1.24 ± 0.60 1.21 ± 0.60 1.10 ± 0.50 0.23 ± 0.08

hR2g,y i 0.24 ± 0.10 0.24 ± 0.10 0.23 ± 0.10 0.12 ± 0.02

hR2g,z i 0.07 ± 0.03 0.07 ± 0.03 0.07 ± 0.03 0.07 ± 0.01

Comparison of results obtained for PCL-10, PCL-20 and PCL-30 confirms that, as one can expect, the value of the radius of gyration increases with the polymer molecular weight. In pure water, the PCL molecule is very compact and moving from PCL-10 to PCL-30 the squared radius of gyration varies from 0.41 to 0.78 nm2 . The projections of hR2g i along the principal axes of inertia show very similar values, meaning that the shape of the PCL molecule is very close to a sphere. Being acetone a good solvent of the polymer, in this solvent (i.e. xA = 1) the variation of the squared radius of gyration with the molecular weight is considerably higher compared with those observed in water. hR2g i varies from 1.50 to 3.42 and to 5.90 nm2 when moving from PCL-10, PCL-20 and PCL-30. But the most interesting results are obtained for intermediate compositions (i.e. xA = 0.50 and 0.75) where, rather than a gradual change of behaviour from pure water to pure acetone, an abrupt variation is detected as soon as some acetone is introduced in the mixture. This is explained by the anisotropic solvent structuring around the polymer chain already discussed in the previous section. Irrespectively to the acetone content, as soon as some acetone molecules are introduced in the solution, these tend to surround the PCL molecule resulting in the observed behaviour. 16 ACS Paragon Plus Environment

Page 17 of 34

This effect is even more evident when the simulation data are compared with each other (for all conditions investigated) as in Figure 6. The figure reports the time-averaged squared radius of gyration versus the polymer molecular weight for different compositions of the water-acetone mixture. As can be seen the observed trend in pure water (xA = 0) is very different from those shown for xA > 0, which tend instead to be very similar for all the compositions.

10

2

2

(nm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

1000

2000

-1

4000

MW (g mol ) Figure 6: Time-averaged squared radius of gyration for PCL, hR2g i, for all the molecular weights investigated (PCL-10 corresponding to MW = 1170 g mol−1 , PCL-20 corresponding to MW = 2310 g mol−1 , PCL-30 corresponding to MW = 3430 g mol−1 ) and for xA = 0 (• blue), xA = 0.50 ( red), xA = 0.75 (N green) and xA = 1.0 (H purple). Symbols: simulations; dashed lines: interpolation through Eq. (1). By fitting these values with the Flory’s law reported in Eq. (1) the scaling constant, k, and the Flory exponent, ν, can be identified as a function of the solution composition. The result of this fit-



ting is reported in Figure 7 together with the following polynomial and exponential interpolations:

2 ν(xA ) = 0.30 + 0.45xA − 0.15xA ,

(10)

k(xA ) = 0.0064 exp (−3.15xA ).

(11)

As can be seen the identified Flory’s coefficients for pure water (ν ≈ 0.30) and pure acetone (ν ≈ 0.60) are in good agreement with the theoretical values for poor (1/3) and good (3/5) solvents. 24

0.6

0.008 k (mol nm g )

0.4 -2ν

0.006

2

ν

0.004

2ν

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 34

0.2

0.002 0

0

0.2

0.4

0.6

0.8

1

XA

0 0

0.2

0.4

XA

0.6

0.8

1

Figure 7: Calculated from MD simulations (symbols) and interpolated (red lines) coefficients of the Flory’s law (ν), reported in Eq. (1), as a function of the acetone molar fraction, xA , for all the water-acetone mixtures investigated in this work. In the inset, calculated from MD simulations (symbols) and interpolated (red lines) values of k as a function of the acetone molar fraction. The identification of the interpolating equations, Eqs. (10) and (11), allows to empirically extend Eq. (1) to every water-acetone mixture, as a function of the acetone molar fraction, xA . This procedure results in the following working equation for the calculation of hR2g i for PCL chains


Page 19 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


characterized by different molecular weights in different water-acetone solutions: (0.60+0.90xA −0.30xA2 ) hR2g i = [0.0064 exp (−3.15xA )] MW ,

(12)

where hR2g i is in nm2 and MW is in g mol−1 . Let us now discuss the results concerning the persistence and Kuhn lengths, as well as the end-to-end distance. Since lp is a quantity defined in the limit of infinite long chain 25 only the PCL-30 is considered in the calculation. The persistence length obtained from the simulations, irrespectively to the concentration of the two solvents, is lp = 0.3 nm (the error is less than 0.5% and is not reported) from which it follows a Kuhn length equal to lk = 0.6 nm. This value of Kuhn length is in satisfactory agreement with the experimental value of 0.7 nm reported by Herrera et al. 43 and Huang et al. 44 The inhomogeneity of the solvent mixture at the molecular scale has an important effect also on the polymer end-to-end distance, R. The time-averaged end-to-end distances, hRi, for all the compositions and for all the PCL molecular weights investigated are reported in Table 4. By looking at these values it again can be noticed that the polymer structure is very similar in each investigated water-acetone mixture (including pure acetone) and drastically changes only in pure water. Table 4: Time-averaged end-to-end distance, hRi (in nm), for all the different molar fractions of acetone in the water-acetone mixtures considered in this work for PCL-10, PCL-20 and PCL-30.

xA = 1 xA = 0.75 xA = 0.50 xA = 0

PCL-10

PCL-20

PCL-30

3.21 ± 1.13 3.21 ± 1.10 3.01 ± 1.10 1.34 ± 0.48

4.72 ± 2.7 4.15 ± 1.4 4.07 ± 1.7 1.47 ± 0.5

6.22 ± 2.0 5.50 ± 1.9 4.82 ± 1.8 1.69 ± 0.6

These values are also compared with those obtained from the FJC model, which is the theoretical model normally used to predict the behaviour of the polymer in dilute solutions. 24 In the FJC model, the polymer is represented by Ne equivalent freely-jointed monomers, each of which has dimension equal to the Kuhn length lk . Using the Kuhn length, lk , obtained from the simulations, 19 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

the calculated (from MD) end-to-end distance distribution is fitted using Eq. (4). The result of this fitting procedure is reported for PCL-10 in Table 5 and in Figure 8. In Figure 8 the distribution of R, as obtained from the MD simulations, and the theoretical distribution of Eq. (4), are compared for PCL-10. Results for PCL-20 and PCL-30 are reported in the supporting information in Supporting Information Figures S1-S2 and in Supporting Information Table S3-S4 and showed a similar behaviour even though a longer sampling may be needed for longer chains. Table 5: Comparison between end-to-end distance predicted by the FJC model hRiFJC (calculated through Eq. (2) and end-to-end distance obtained from simulations (in nm2 ), for PCL-10 and all the different molar fractions of acetone considered in this work (the error on Ne is not shown because it is less than unity in all the cases considered).

xA = 1 xA = 0.75 xA = 0.50 xA = 0

Ne

hR2 i

hR2 iFJC

31 31 27 5

10.3 10.3 7.8 1.8

11.2 11.2 9.1 1.8

Again, the predicted values of hR2 i and the distributions in the presence of acetone (notwithstanding the amount of acetone present) are quite similar, whereas a clearly distinct behaviour is observed for pure water only. Moreover, the results show that in pure solvents the polymer behaves like a FJC. In fact, the agreement between the values of hR2 i and hR2 iFJC , reported in Table 5, and between the distributions evaluated via MD and predicted by the FJC model, reported in Figure 8, is good only for xA equal to one and zero (i.e. difference smaller than 5 %). At intermediate solvent molar fractions, instead the fitting is not that satisfactory, as evident by observing the results of Table 5 and Figure 8 for 0 < xA < 1 (i.e. difference of about 20 %). The propensity of the polymer chain to reside at the interface between to immiscible solvent 45,46 could help explaining the peculiar behaviour of PCL in the range of solvent concentrations analysed. In pure water due to unfavourable energetic interactions between the polymer and the solvent the configuration of polymer chain is folded; in pure acetone, on the contrary, because of the favourable interactions between the chain and the solvent, the chain extends, experiencing a broad range of configurations. At the intermediate compositions, the chain is surrounded preferen20 ACS Paragon Plus Environment

Page 20 of 34

Page 21 of 34

0.8

a

0.4 d c

0.3

P(R)

0.6

P(R)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

0.2 0.1

b

0 0

0.2 0 0

2

4

6

8

10

R (nm) 2

4

6

8

10

R (nm) Figure 8: Comparison between the end-to-end distance distributions for PCL-10 (dashed line) and the distribution obtained from the FJC model (continuous line), for xA = 0 (a, blue line), xA = 0.50 (c, red line), xA = 0.75 (d, green line) and xA = 1.0 (b, purple line).



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

tially by acetone molecules, that form an interface with the water. The polymer chain extends (as it is in pure acetone) until it encounters water molecules when it regains the coiled-up configuration. The resulting end-to-end distributions in intermediate water-acetone mixtures are therefore similar to that of pure acetone, but are not well fitted by the FJC model.

Dynamic properties One question that can arise is whether the PCL chain moves inside the acetone cluster or instead the chain moves together with the cluster as a single “entity”. To further investigate this issue the distribution of the lifetime of the contacts between PCL, water and acetone molecules has been calculated. A contact is established if one atom of the solvent (water or acetone) stays at a distance shorter than 0.6 nm from the center of mass of the PCL chain and each solvent molecule is counted only once (i.e. if multiple atoms of the same solvent molecule are within the distance only one contact is considered). The results extracted from our MD simulations are reported in Figure 9 for PCL-30 and for three intermediate compositions of the water-acetone mixture (i.e. xA = 0.50 and 0.75). As can be seen and as stated before, the PCL chain sees the same “environment”, no matter which composition the solution has, since very little difference between the three curves is detected. Closer observation of Figure 9 reveals that the time in which the contact between solvent and PCL molecules is lost is around 200 ps, which may suggest that the shell moves together with the PCL chain as one single entity. This of course will affect the behaviour of the dynamic properties of PCL chains in solution, as for example the mean squared displacement (MSD) and the resulting diffusion coefficient. At last some transport properties of PCL molecules in the water-acetone mixture are determined by looking at the time evolution of the MSD of the PCL chain reported in Figure 10. As shown in Figure 10, the PCL molecule in acetone solutions needs more time to reach the free diffusion regime with respect the pure water system. Also, at intermediate water-acetone mixtures this time is even longer. This behaviour is the sum of different effects whose relative importance is difficult to predict. In pure water the spherical shape of the PCL molecule helps in reducing the


Page 22 of 34

Page 23 of 34

4

Number of contacts

6

Number of contacts

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

0.5

2

0 0

100

200

Time (ps)

0 0

100

200

Time (ps)

300

Figure 9: Distribution for the lifetime of the contacts between PCL-30 and acetone (main plot) and PCL-30 and water (inset) for xA = 0.50 (red dashed curve), xA = 0.75 (green continuous curve). time to reach the free diffusion regime. However, in water-acetone mixture another effect takes place that slows the dynamic of the PCL molecule, other that of the molecule shape. The PCL molecule at intermediate mixture seems to move together with the solvent cluster surrounding it, resulting in a sensible slowing down of the dynamics with respect of the same molecule in pure acetone. From the mean-square displacement, through Eq. (5), the diffusion coefficient for PCL is obtained. Results are summarized in Figure 11 for the four compositions (xA ) investigated and for the lower molecular weight (i.e. PCL-10). The analysis is limited to PCL-10 because only for this molecular weight the collected results contained enough data to reliably estimate the diffusion coefficient. As one may expect, the diffusion coefficient in pure water is always larger than that in pure acetone, as in water the hydrodynamic radius of the PCL chain is sensibly smaller than in acetone. At intermediate compositions (xA = 0.50 and 0.75) the diffusion coefficient slightly varies between 1.00 and 2.00 × 10−10 m2 s−1 . It is interesting to compare the estimation of the diffusion coefficient obtained via MD simulations with the predictions of the Stokes-Einstein theory, calcu-


Page 24 of 34

2

1.5

1

-2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

msd/(6t) · 10 (nm /ps)


a

0.5 b c

d

8e-06

0.0004 -1

-1

0.02

t (ps ) Figure 10: Mean-square displacement of PCL-10 normalized by 6t, for xA = 0 (a, blue line), xA = 0.50 (c, red line), xA = 0.75 (d, green line) and xA = 1.0 (b, purple line).


Page 25 of 34

4

-10

2 -1

(m s )

6

D · 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2

0

0

0.2

0.4

xA

0.6

0.8

1

Figure 11: Diffusion coefficients for PCL-10 versus the composition of the water-acetone mixture (xA ) as simulated with MD ( •) and as predicted with the Stokes-Einstein theory (◦) of Eq. (6). Lines are provided only as guide to the eyes.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

lated with Eq. (6) and with the hydrodynamic radius estimated through Eq. (12). The comparison is reported for the four compositions (xA ) investigated and the lower molecular weight (i.e. PCL10) in Figure 11. As it can been seen the theory predicts a minimum for the diffusion coefficient as the molar fraction of acetone increases from zero to one. This is due to the fact that an increase in xA causes an increase in the hydrodynamic radius but at the same time a strong decrease in the viscosity of the mixture, resulting in a minimum at about xA ≈ 0.5. Although a shallow minimum is highlighted also by MD simulation data it is clear that the entity of the minimum is sensibly different. Eventually, it is interesting to highlight that the agreement between MD predictions and the Stokes-Einstein theory is acceptable in pure water, where the PCL molecule is coiled-up and is probably characterized by a behaviour closer to that of a sphere. The agreement worsen as xA increases and is poor in pure acetone, where the PCL molecule is, on average, more stretched, but undergoes more frequent transitions from extended to un-extended random coil configurations, resulting in an additional effect, very difficult to predict a-priori.

Conclusions Molecular Dynamics simulations have been used to investigate the structural and dynamical properties of solution of poly-ε-caprolactone in water, acetone and their mixtures. Three molecular weights for PCL were considered for four different solution compositions (ranging from pure water to pure acetone). Being acetone a good solvent and water a poor solvent for the polymer the simulations have shown that, as expected, the polymer chain behaves very differently in the solution of the pure solvents and structural properties such as radius of gyration and end-to-end distance follow the theoretical predictions. More interestingly however, we showed that due to the clustering of acetone molecules around the polymer chain, at intermediate compositions rather than a gradual change in the PCL behaviour an abrupt change of trend is observed. Indeed even the addition of a small amount of acetone in the water solution leads to the formation of a nanostructured aggregate


Page 26 of 34

Page 27 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


around the polymer, favouring its extended configuration. Little changes in this trend are observed when more acetone is added to the solution. The clustering of the acetone molecule has important consequence in predicting the polymer structural and diffusion properties in the mixture. For example, while when dissolved in pure solvents the polymer end-to-end distance distributions can be fitted with the freely jointed chain model, at intermediate solvents concentrations the theoretical predictions cannot be fitted with the FJC model, regardless of the water-acetone ratio. The solvent structuring also greatly affects the dynamic of the polymer chain in solution. The calculation of the transport properties has highlighted a trend in the PCL diffusion coefficient that is consistent with the Stokes-Einstein theory only at intermediate concentrations and whose absolute values would have been difficult to predict a-priori. This effect on the diffusion of polymer chains in solution can eventually have an impact on macro-scale description of polymer chains, as well as applications in which properties like polymers diffusion coefficient are needed. The reported results, notably the law formulated in Eq. (12) and the diffusion coefficients reported in Figure 11, can be used to model at the meso- and macro-scale the self-assembly of PCL molecules into nanoparticles.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Supporting Information Available Time-averaged squared radius of gyration and its projections along the principal axes of inertia for all the different molar fractions of acetone in the water-acetone mixtures considered in this work and for PCL-20 (Tab. S1) and PCL-30 (Tab. S2). Comparison between end-to-end distance predicted by the FJC model and end-to-end distance obtained from simulations for all the different molar fractions of acetone considered in this work and for PCL-20 (Tab. S3) and PCL-30 (Tab. S4). Comparison between the end-to-end distance distributions and the distribution obtained from the FJC model for all the different molar fractions of acetone considered in this work and for PCL-20 (Fig. S1) and PCL-30 (Fig. S2). This material is available free of charge via the Internet at http://pubs.acs.org.


Page 28 of 34

Page 29 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


References (1) Bang, L. T.; Kawachi, G.; Nakagawa, M.; Munar, M.; Ishikawa, K.; Othman, R. The Use of Poly (e-caprolactone) to Enhance the Mechanical Strength of Porous Si-Substituted Carbonate Apatite. J. Appl. Polym. Sci. 2013, 130, 426–433. (2) Wu, C.; Jim, T.; Gan, Z.; Zhao, Y.; Wang, S. A Heterogeneous Catalytic Kinetics for Enzymatic Biodegradation of Poly(ε-Caprolactone) Nanoparticles in Aqueous Solution. Polymer 2000, 41, 3593–3597. (3) Jabr-Milane, L. S.; van Vlerken, L. E.; Yadav, S.; Amiji, M. M. Multi-Functional Nanocarriers to Overcome Tumor Drug Resistance. Cancer Treat. Rev. 2008, 34, 592–602. (4) Dash, T. K.; Konkimalla, B. Polymeric Modification and Its Implication in Drug Delivery: Poly-ε-caprolactone (PCL) as a Model Polymer. Mol. Pharmaceutics 2012, 9, 2365–2379. (5) Maeda, H.; Bharate, G. Y.; Daruwalla, J. Polymeric Drugs for Efficient Tumor-Targeted Drug Delivery Based on EPR-Effect. Eur. J. Pharm. Biopharm. 2009, 71, 409–419. (6) Pirollo, K. F.; Chang, E. Does a Targeting Ligand Influence Nanoparticle Tumor Localization or Uptake? Trends Biotechnol. 2008, 26, 552–558. (7) Kataoka, K.; Hurada, A.; Nakagasaki, Y. Block Copolymer Micelles for Drug Delivery: Design, Characterization and Biological Significance. Adv. Drug Deliv. Rev 2001, 47, 113–131. (8) Adams, M. L.; Lavasanifar, A.; Kwon, G. S. Amphiphilic Block Copolymers for Drug Delivery. J. Pharm. Sci. 2003, 92, 1343–1355. (9) Diao, Y.; Li, H.; Fu, Y.; Han, M.; Hu, Y.; Jiang, H.; Tsutsumi, Y.; Wei, Q.; Chen, D.; Gao, J. Doxorubicin-Loaded PEG-PCL Copolymer Micelles Enhance Cytotoxicity and Intracellular Accumulation of Doxorubicin in Adriamycin-Resistant Tumor Cells. Int. J. Nanomedicine 2011, 6, 1955–1962.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(10) Kao, H.; Chan, C.; Chang, Y.; Hsu, Y.; Lu, M.; Wang, J. S.; Lin, Y.; Wang, S.; Wang, H. A Pharmacokinetics Study of Radiolabeled Micelles of a Poly(ethylene glycol)-blockpoly(caprolactone) Copolymer in a Colon Carcinoma-Bearing Mouse Model. Appl. Radiat. Isot. 2013, 80, 88–94. (11) Li, B.; Wang, Q.; Wang, X.; Wang, C.; Jiang, X. Preparation, Drug Release and Cellular Uptake of Doxorubicin-Loaded Dextran-b-poly(ε-caprolactone) Nanoparticles. Carbohyd. Polym. 2013, 93, 430–437. (12) Valente, I.; Stella, B.; Marchisio, D. L.; Dosio, F.; Barresi, A. A. Production of PEGylated Nanocapsules Through Solvent-Displacement in Confined Impinging Jets Mixers. J. Pharm. Sci. 2012, 101, 2490–2501. (13) Lince, F.; Bolognesi, S.; Marchisio, D. L.; Stella, B.; Dosio, F.; Barresi, A. A.; Cattel, L. Preparation of Poly(MePEGCA-co-HDCA) Nanoparticles with Confined Impinging Jets Reactor: Experimental and Modelling Study. J. Pharm. Sci. 2011, 100, 2391–2405. (14) Lince, F.; Bolognesi, S.; Stella, B.; Marchisio, D. L. Preparation of Polymer Nanoparticles Loaded with Doxorubicin for Controlled Drug Delivery. Chem. Eng. Res. Des. 2011, 89, 2410–2419. (15) Valente, I.; Celasco, E.; Marchisio, D. L.; Barresi, A. A. Nanoprecipitation in Confined Impinging Jets Mixers: Production, Characterization and Scale Up of Pegylated Nanospheres and Nanocapsules for Pharmaceutical Use. Chem. Eng. Sci. 2012, 77, 217–227. (16) Lince, F.; Marchisio, D. L.; Barresi, A. A. Strategies to Control the Particle Size Distribution of Poly-ε-Caprolactone Nanoparticles for Pharmaceutical Applications. J. Colloid Interface Sci. 2008, 322, 505–515. (17) Zelenkova, T.; Fissore, D.; Marchisio, D. L.; Barresi, A. A. Size Control in Production and Freeze-Drying of Poly-ε-Caprolactone Nanoparticles. J. Pharm. Sci. 2014.


Page 30 of 34

Page 31 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(18) Marchisio, D. L.; Omegna, F.; Barresi, A. A. Production of TiO2 Nanoparticles with Controlled Characteristics by Means of a vortex Reactor. Chem. Eng. J. 2009, 146, 456–465. (19) Liu, Y.; Cheng, C.; Prud’homme, R. K.; Fox, R. O. Mixing in a Multi-Inlet Vortex Mixer (MIVM) for Flash Nano-Precipitation. Chem. Eng. Sci. 2008, 63, 2829–2842. (20) Gradl, J.; Schwarzer, H. C.; Schwertfirm, F.; Manhart, M.; Peukert, W. Precipitation of Nanoparticles in a T-Mixer: Coupling the Particle Population Dynamics with Hydrodynamics Through Direct Numerical Simulation. Chem. Eng. Process 2006, 45, 908–916. (21) Choi, Y. J.; Chung, S. T.; Oh, M.; Kim, H. S. Investigation of Cristallization in a Jet YMixer by a Hybrid Computational Fluid Dynamics and Process Simulation Approach. Cryst. Growth Des. 2005, 5, 959–968. (22) Johnson, B. K.; Prud’homme, R. K. Chemical Processing and Micromixing in Confined Impinging Jets. AIChE Journal 2003, 49, 2264–2282. (23) Di Pasquale, N.; Marchisio, D. L.; Carbone, P.; Barresi, A. A. Identification of Nucleation Rate Parameters with MD and validation of the CFD Model for Polymer Particle Precipitation. Chem. Eng. Res. Des. 2013, 91, 2275–2290. (24) Rubinstein, M.; Colby, R. H. Polymer Physics; Oxford University Press: New York, 2003. (25) Flory, P. J. Statistical Mechanics of Chain Molecules; Hanser Publisher: New York, 1988. (26) Frontali, C.; Dore, E.; Ferrauto, A.; Gratton, E. An Absolute Method for the Determination of the Persistence Length of Native DNA from Electron Micrographs. Biopolymers 1979, 18, 1353–1373. (27) Bird, R.; Stewart, W.; Lightfoot, E. Transport Phenomena; John Wiley & Sons, Inc.: New York, 2002. (28) Kok, C. M.; Rudin, A. Relationship Between the Hydrodynamic Radius and the Radius of Gyration of a Polymer in Solution. Macromol. Rapid Commun. 1981, 2, 655–659. 31 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(29) Kinart, C. M.; Kinart, J. W.; Cwiklinska, A. Density and Viscosity at Various Temperatures for 2-Methoxyethanol + Acetone Mixtures. Journal Chemical Engineering Data 2002, 47, 76–78. (30) Kestin, J.; Sokolov, M.; Wakeham, W. A. viscosity of Liquid Water in the Range −8◦ C To 150◦ C. J. Phys. Chem. Ref. Data 1978, 7, 941–948. (31) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225–11236. (32) Berendsen, H. J. C.; Postma, J. P. M.; van Gusteren, W. F.; Hermans, J. Intermolecular Forces; Reidel: Dordrecht, 1981. (33) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindhal, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435–447. (34) Berendsen, H.; Postma, J. P. M.; Gunsteren, W. F. V.; Di Nola, A.; Haak, J. R. Molecular Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684. (35) Perera, A.; Sokolic, F. Modeling Nonionic Aqueous Solutions: the Acetone-Water Mixture. J. Chem. Phys. 2004, 121, 11272. (36) Kang, M.; Perera, M.; Smith, P. E. Comment on “Can Existing Models Quantitatively Describe the Mixing Behavior of Acetone with Water” [J. Chem. Phys. 130, 124516 (2009)]. J. Chem. Phys. 2009, 131, 157101. (37) Jedlovszky, P.; Idrissi, A.; Jancsó, G. Can Existing Models Qualitatively Describe the Mixing Behavior of Acetone with Water? J. Chem. Phys. 2009, 130, 124516.


Page 32 of 34

Page 33 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(38) Jedlovszky, P.; Idrissi, A.; Jancsó, G. Response to “Comment on ‘Can Existing Models Qualitatively Describe the Mixing Behavior of Acetone-Water Mixtures?’ ”. J. Chem. Phys. 2009, 131, 157102. (39) Estrada-Baltazar, A.; De Leon-Rodriguez, A.; Hall, K. R.; Ramos-Estrada, M.; IglesiasSilva, G. A. Experimental Densities and Excess Volumes for Binary Mixtures Containing Propionic Acid, Acetone, and Water from 283.15 K to 323.15 K at Atmospheric Pressure . J. Chem. Eng. Data 2003, 48, 1425–1431. (40) Weerasinghe, S.; Smith, P. E. Kirkwood–Buff Derived Force Field for Mixtures of Acetone and Water. J. Chem. Phys. 2003, 118, 10663–10670. (41) Ferrario, M.; Haughney, M.; McDonald, I. R.; Klein, M. L. Molecular Dynamics Simulation of Acqueous Mixtures: Methanol, Acetone, and Ammonia. J. Chem. Phys. 1990, 93, 5156. (42) Matteoli, E.; Lepori, L. Solute–Solute Interactions in Water. II. An Analysis Through the Kirkwood–Buff Integrals for 14 Organic Solutes. J. Chem. Phys. 1984, 80, 2856–2863. (43) Herrera, D.; Zamora, J.; Bello, A.; Grimau, M.; Laredo, E.; Muller, A. J.; Lodge, T. P. Miscibility and Crystallization in Polycarbonate/Poly(epsilon-Caprolactone) Blends: Application of the Self-Concentration Model. Macromolecules 2008, 38, 5109–5117. (44) Huang, Y.; Xu, Z.; Huang, Y.; Ma, D.; Yang, J.; Mays, J. W. Characterization of Poly(epsilonCaprolactone) Via Size Exclusion Chromatography with Online Right-Angle Laser-Light Scattering and Viscometric Detectors. Int. J. Polym. Anal. Charact. 2003, 8, 383–394. (45) Halperin, A.; Pincus, P. Polymers at Liquid-Liquid Interface. Macromolecules 1986, 19, 79– 84. (46) Taddese, T.; Carbone, P.; Cheung, D. Thermodynamics of Linear and Star Polymers at Fluid Interfaces. Soft Matter 2014, DOI: 10.1039/C4SM02102A.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Graphical TOC Entry


Page 34 of 34

Solvent Structuring and Its Effect on the Polymer Structure and

Recommend Documents