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Physicochemical Response of Gelatin in a Coulombic Soup of Monovalent Salt: A Molecular Simulation and Experimental Study Pinaki Swain, Anshaj Ronghe, Utkarsh Bhutani, and Saptarshi Majumdar J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b11379 • Publication Date (Web): 14 Jan 2019 Downloaded from http://pubs.acs.org on January 14, 2019

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The Journal of Physical Chemistry

Physicochemical Response of Gelatin in a Coulombic Soup of Monovalent Salt: A Molecular Simulation and Experimental Study Pinaki Swain, Anshaj Ronghe, Utkarsh Bhutani, and Saptarshi Majumdar∗ Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Hyderabad E-mail: [email protected]

Abstract

1

The effect of salt on the static properties of aqueous solution of gelatin is studied by molecular dynamics simulation at pH=1.2, 7 and 10. At the isoelectric point(pH=7), a monotonic increase in size of the polymer is obtained with the addition of sodium chloride ions. In the positive polyelectrolyte regime(pH=1.2), collapse of gelatin is observed with increase in salt concentration. In the negative polyelectrolyte regime, we observe an interesting collapse-reexpansion behavior. This is due to the screening of repulsion between the excess charges followed by the screening of attraction of oppositely charged ions as the salt concentration is increased. This mechanism is very different from the charge inversion mechanism which causes the reexpansion in presence of multivalent ions. The location of salt concentration corresponding to the minimum size of the chain is comparable to the theoretical estimate. The shift in the peak of radial distribution function calculated between monomers and salt ions confirms this spatial reorganization. The predictions from the simulation are verified by dynamic light scattering(DLS) and small angle X-ray scattering(SAXS) experiments. The size of the hydrodynamic ‘clusters’ obtained from DLS confirms the simulation predictions. Persistence length of the gelatin is calculated from SAXS to get single chain statistics, which also agrees well with the simulation results.

The study of charged polymers is of relevance to diverse fields, such as, biophysics, material design and drug discovery. 1–3 Charged polymers can be broadly divided into two categories: polyelectrolytes containing only one kind of charged monomers and polyampholytes containing both cationic and anionic ionizable groups. RNA and DNA are the most common naturally occurring polyelectrolytes, while proteins are good examples of polyampholytes. Polystyrene sulfonate, polyacrylic acids belong to the class of synthetic polyelectrolytes while sodium alginate and gelatin are examples of charged polymers derived from natural resources. 2 The presence of electrostatic interactions make the properties of charged polymers very different from that of neutral polymers. These include lower overlap concentration (i.e. the concentration at which crossover from dilute to semi dilute regime occurs), lower concentration dependence of viscosity as given by Fuoss’ law, 4 and well defined peak in scattering function. 5 Apart from interesting fundamental properties, charged polymers have numerous practical applications as rheology-modifying agent, drug delivery vehicles, and colloidal stabilizers. 2 On the theoretical side, scaling arguments proposed by de Gennes and collaborators provided explanation for the conformation of single chain polyelectrolyte. 6,7 Dobrynin and coworkers extended the scaling ideas for the

Introduction

ACS Paragon Plus Environment

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prediction of dynamic quantities. 8 The addition of salt ions to a polyelectrolyte system screens the electrostatic interaction between monomers as the Debye length decreases. Therefore, at higher salt concentration polyelectrolytes behave like neutral polymers. 8 Compared to polyelectrolytes, polyampholytes have attracted considerably lesser attention. 9–11 The properties of a polyampholyte strongly depends on the distribution and sequence of charged monomers 12 and the pH of the environment. The presence of oppositely charged monomers in polyampholyte chains gives rise to interesting aqueous properties and makes them suitable candidates for drug delivery applications. 13 Gelatin is a naturally occurring polyampholyte which is derived from collagen. Based on the process of extraction, gelatin is divided into two types, Type A and Type B. Type A is obtained by the acidic treatment and has isoelectric point around 7-9, pK1 =5.2, pK2 =11.5 while type B is derived from alkaline process and has isoelectric point around 4.6-5.4, pK1 =3.6, pK2 =7.8. 14,15 Gelatin based hydrogels, 16 nano-fibers 17 and nanospheres 18 have been used as novel drug-delivery vehicles. The concentration dependence of static and dynamic properties of gelatin solution have investigated via light and small-angle scattering techniques. 19,20 However, these studies were conducted at a pH of 7 and at a particular value of salt concentration, 0.1M. Scattering techniques have also been employed to arrive at the scaling laws of radius of gyration and viscosity over a range of temperature. 21 From the scaling exponents, the authors concluded that water acts as a good solvent for gelatin. The swelling behaviour of gelatin has been studied in presence of salt solution at different pH. 22 In the polyampholyte regime, the authors found that the gel shows a monotonic increase in swelling, except for AlCl3 case, where ionic cross linking causes the gel to shrink at high salt concentration. However, in the negative polyelectrolyte regime a collapse-reexpansion transition is observed in presence of multivalent ions. Interestingly, this reexpansion phenomena is not observed in the positive polyelectrolyte regime

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or in presence of monovalent ions. Commonly knows as reentrant-condensation, this reexpansion behaviour of polyelectrolytes is well-known in presence of multivalent ions and has been extensively reported in literature. 23–26 Here, we would like to mention the work of Jia and collaborators, 27 who reported reexpansion behavior of polystyrene sulfonate in presence of monovalent salt(CsCl). They further commented that the mechanism behind this reexpansion has to be different than that explains the case of multivalent ions. Therefore, we revisit the problem of size and structure of gelatin molecule in aqueous media of different pH and salt concentration. Understanding the effect of ionic strength and pH on the conformation of gelatin, both at the bulk and local level, is essential for the preparation of gelatin based biomaterials with tunable physical properties. In recent years, molecular dynamics simulation has emerged as an important complementary tool to understand the properties of polymeric systems. In 1995, Stevens and Kremer, rigorously studied the concentration dependence of static properties of polyelectrolytes by performing coarse grain molecular simulations. 28 The effect of salt on polyelectrolytes and polyampholytes has also been studied at the coarse grain level. 29,30 Tanaka and coworkers studied the effect of temperature 31 and salt ions 32 on the radius of gyration of polyampholytes by computer simulations. Molecular dynamics is also used to investigate the variation of structure of polyampholyte solution with respect to temperature and valency of salt ions. 33 While coarse grain simulations are extremely useful for studying the global properties, they can not take into account the local chemical interactions. In order to understand the complicated interplay between Coulomb interactions and hydrogen bonding effects we have performed detailed atomistic simulations. Although gelatin is a biopolymer of long standing importance and has enormous potential future applications as a component of composite biomaterials, 34,35 certain fundamental questions remain unanswered. The goal of the


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present study is to combine atomistic simulations with small angle X-ray scattering(SAXS) and dynamic light scattering(DLS) techniques to probe into the static properties of gelatin in aqueous salt solutions. The pH responsiveness of gelatin is studied by considering three different pH. In particular, we are interested in the existence of collapse-reexpansion behavior of gelatin in presence of monovalent salt ions and the possible physical mechanism behind such transition.

2

all the systems. 1.0 nm is kept as the cut-off distance for both van der Walls and Coulombic interaction. All the statistics are reported after averaging over 1000 configurations, separated by 5 ps interval. Visual Molecular Dynamics(VMD) is used to generate the representative configurations. 41

Simulation method

Groningen Machine for Chemical Simulation (GROMACS, version 5.0) software package is used as the computational tool for atomistic simulations. 36 OPLS-AA is chosen as the force field for the polymer 37 and SPCE water model is used as it gives the structure and dynamics closest to the experimental values for liquid water. 38 Initial configurations are created using Avogadro software. 39 We verified that the choice of initial configuration (straight chains or folded chains) has no effect on the final statistics of the system. 1:1 ratio of carboxyl groups and amide groups are maintained in all the initial configurations. For simulating in different pH, required number of H+ or OH– ions are added to the chains within Avogadro. Five gelatin chains, each of molecular weight 4000 g/mol are simulated in presence of explicit water molecules at pH values ranging from 1.2 to 12. The box length of the system is chosen such that the concentration of the system is 4% w/v which is within the semidilute regime of the solution. For simulations at different salt concentrations, gelatin chains at pH = 1.2, 7 and 10 are considered. At each of these pH values, simulations are performed at NaCl concentration of 0.05 M, 0.1 M, 0.2 M, 0.3 M, 0.5 M, 0.7 M and 1 M. Temperature for all the systems is maintained at 310 K using V-scale thermostat. NVT equilibration is used for total time of 5 ns with time step of 2 fs. LINCS algorithm is used to constraint the bonds. 40 Finally, production runs of 10 ns, with a time step of 1 fs, are given for

Figure 1: (a) Flowchart showing the simulation protocol, (b) Initial straight chain configuration of 5 gelatin chains prepared in Avogadro software, 39 (c) Equilibrated configuration of gelatin in water at pH=1.2, and (d) Equilibrated configuration of gelatin in water in presence of 0.2M salt at pH=1.2 obtained using VMD. 41

3 3.1

Experiment method Dynamic light scattering

The size of gelatin clusters were analyzed using dynamic light scattering(Delsa Nano C, Beckman Coulter). 4% w/v gelatin solutions were prepared at pH 1.2, 7 and 10 at 40 ◦C. Once


3


a homogenous solution was formed, NaCl was added. The concentration of NaCl was varied from 0.05 M to 1 M. 2 ml of solution was collected and analyzed using DLS. The scattering angle was fixed at 165°, while the laser wavelength was 658 nm. The translational diffusion coefficient(cm2 /s) was measured and Stokes Einstein equation was used to predict the size of the gelatin clusters. D=

kB T 6πηs RH

low the isoelectric point, only the amide(NH2) groups get protonated and gelatin behaves like a positive polyelectrolyte. Above the isoelectric point, only the carboxyl(COOH) groups get ionized leading to negative polyelectrolyte behavior. At pH=7, the chain collapses due to attraction between oppositely charged groups. The increase in swelling of polyampholyte based hydrogels due to charge offset is observed experimentally. 42,43 Similar increase in hydrodynamic radius of poly-ampholyte based microgels away from the isoelectric point is also reported. 44 The flexibility of the gelatin chain is quantified by calculating the tangent-tangent correla~ · u(0)i ~ between two tangent tion function, hu(s) vectors separated by a distance s along the contour. From the slope of tangent-tangent correlation function, persistent length of the polymer is extracted and plotted in Figure 2(d). The ratio of the average square end-to-end distance and average square radius of gyration, r = R2 /Rg2 also gives a measure of shape of the polymer. For a rod-like polymer r = 12 and for a random coil r = 6. 45 Figure 2(e) shows that gelatin has a more collapsed structure at pH=7 and more open structure at other pH. Structure factor(S(q)) shown in Figure 2(f) also confirms the change in shape of the polymer with respect to the pH. Scaling theory predicts S(q) ∼ q −1/ν , ν being the Flory exponent, which is 12 for an ideal chain and 35 for a real chain. 46 At pH=7, we get the minimum value of ν, where the chain is in its most compact shape. The shape of the polymer is further investigated by analyzing the eigenvalues of radius of gyration tensor. 47–49 The relative shape anisotropic parameter(k1 ) is given by,

(1)

where ηs is the viscosity of the solvent. CONTIN algorithm was used to process the scattering data obtained during the analysis.

3.2

Small angle X-ray scattering

The gelatin-salt solutions were subjected to SAXS analysis(SAXSess, Anton Paar, Cu Xray source). The sample preparation was similar to DLS analysis. The prepared solutions were sealed in a thin walled quartz capillary of around 2 mm in diameter and 0.01 mm in thickness. The scattering intensity I(q) was recorded where q is the scattering vector desin( 2θ ) where θ is the scattering fined as q = 4π λ angle and λ is the radiation wavelength(0.1542 nm). The scattering time was set at 20 minute and the analysis was performed at the room temperature.

4 4.1

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Results and discussion In salt free condition

The isoelectric point of a polyampholyte is the pH at which there is no net charge on the molecule. Gelatin, type A, which is used in the experiment as well, has an isoelectric point around pH=7. In order to study the effect of pH on chain conformation, five chains of Gelatin, each of molecular weight 4000 g/mol, are simulated at pH = 1.2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. The average end-to-end distance(Re ) and radius of gyration(Rg ) of all the chains are plotted in Figure2(b) and 2(c) respectively. Be-

k12 = 1 − 3

λ1 λ2 + λ2 λ3 + λ3 λ1 (λ1 + λ2 + λ3 )2

(2)

and the asphericity parameter(k2 ) is defined as, 1 k2 = λ1 − (λ2 + λ3 ) 2

(3)

where λ1 ,λ2 and λ3 are the eigenvalues of radius of gyration tensor in descending order of magnitude. Both the quantities have minimum value


4

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(c)

(a) 8 Re(nm)

0.4

6

0 2 4 6 8 10 12 pH

10 Re2 8 Rg2 6 4

2.6

(g)

0 2 4 6 8 10 12 pH

(e)

Rg (nm) 2.2

1.8

0 2 4 6 8 10 12 pH

(d)

4 (b)

(f )

0.8 lp(nm) 0.6

log S(q)

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 2 4 6 8 10 12 pH

(h)

8 4 0 −4 −8 −4 −2

ν 0 log q

2

4

Figure 2: Properties of gelatin in water at different pH measured in terms of (a) end-to-end distance(Re ), (b) radius of gyration(Rg ), (c) persistence length (lp ), (d) ratio of square of end-to-end distance and square of radius of gyration, (e) structure factor(S(q)) in pH=1.2(green), 4(orange) and 7(blue). Arrow indicating the decreasing value Flory exponent as we get closer to the isoelectric point. (g − i) typical configuration of a single gelatin chain corresponding to pH=1.2, 4 and 7 respectively, obtained using VMD. 41

at the isoelectric point confirming the compact spherical shape. The results for salt free condition are summarized in Table 1. Thus our simulation methodology is able to replicate the pH responsive behavior of gelatin Type A. It is shown that at pH=7 gelatin has a compact globular shape and in the polyelectrolyte limit it exists in more extended shape. Next, we try to answer the ambiguities surrounding behavior of gelatin in presence of NaCl by performing simulations at three different pH, 1.2 ,7 and 10.

4.2

length(rD ), given by, rD =

4πlB

X

zi2 ci

!− 12 (4)

i

where zi is the valency of charged species, ci is the concentration of charged species, and 2 lB = 4πe0 kB T is the Bjerrum length. lB is the distance of separation between two unit charges where their electrostatic interaction energy is equal to the thermal energy scale kB T . For aqueous solutions at room temperature, lB ' 0.7nm and rD ' √0.3 . Here, cs is the (cs )

In presence of salt

concentration of monovalent salt in moles per liter. 1 Increase in the salt concentration leads to reduction in rD . Once rD becomes smaller than the salt-free size of the chain, further increase in cs screens the coulombic interaction between the chains. In Figure 3, size of gelatin chain in

The addition of salt introduces a new length scale in the system, known as Debye screening


5


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Table 1: Size and shape of gelatin at different pH obtained from simulation. pH 1.2 2 3 4 5 6 7 8 9 10 11 12

Re (nm) 9.28 ± 0.10 9.08 ± 0.07 8.48 ± 0.06 7.50 ± 0.05 6.22 ± 0.07 5.36 ± 0.04 4.18 ± 0.04 5.26 ± 0.08 6.06 ± 0.05 7.37 ± 0.08 8.74 ± 0.05 9.06 ± 0.05

Rg lp (nm) (nm) 2.79 ± 0.02 0.85 2.76 ± 0.01 0.83 2.67 ± 0.01 0.79 2.56 ± 0.01 0.71 2.32 ± 0.01 0.62 2.15 ± 0.01 0.56 1.91 ± 0.02 0.46 2.12 ± 0.01 0.55 2.29 ± 0.02 0.6 2.54 ± 0.01 0.68 2.71 ± 0.01 0.77 2.76 ± 0.02 0.81

R2 /Rg2

k12

k2

ν

11.08 ± 0.12 10.84 ± 0.06 10.09 ± 0.11 8.59 ± 0.08 7.19 ± 0.05 6.22 ± 0.11 4.81 ± 0.12 6.17 ± 0.04 7.01 ± 0.10 8.44 ± 0.04 10.41 ± 0.06 10.79 ± 0.12

0.25 0.24 0.23 0.22 0.20 0.17 0.14 0.16 0.18 0.21 0.23 0.24

1.95 1.89 1.72 1.57 1.21 0.99 0.84 0.96 1.14 1.49 1.78 1.87

0.74 0.70 0.64 0.56 0.50 0.46 0.36 0.47 0.48 0.54 0.65 0.69

that c∗s will depend on the pH of the medium. Higgs and Joanny, 9 showed that the minimum excluded volume(v ∗ ) for a nonneutral polyamphoyte in presence of monovalent salt, occurs at a screening length rD,0 given by,

terms of Re is given as a function of cs at three different pH values. At pH=1.2, size of the polymer decreases monotonically as the concentration of salt is increased. At the isoelectric point of pH=7, we see a increase in the size of the polymer with cs . Interestingly, at pH=10, a minimum in chain size we observed at cs = 0.2 M. In case of multivalent ions, this reexpansion is attributed to “over-charging effect”, where the ions binding to the charge monomers overcompensate the original charge and the repulsion between excess charges leads to further expansion. 50 However, the mechanism has to be different for monovalent ions, as mentioned by Jia and Jhao who observed the collapseexpansion behavior of a polyelectrolyte (sodium polystyrene sulfonate, PSS–Na+) in presence of monovalent salt (CsCl). For monovalent ions, the screening of electostatic interaction due to salt ions proposed in 9,51 may provide better insight into this phenomena. Addition of salt leads to decrease in Debye screening length. Once rD becomes smaller than the size of the chain, further addition of salt causes screening of electrostatic repulsion between excess charges. This results in a decrease in the size of the polymer. After a critical concentration (c∗s ), polymer starts to swell due to the screening of fluctuation induced attraction between oppositely charged ions. Figure 3 shows that at pH=10, cs = 0.2 is the critical concentration in our simulation. It is intuitive to suggest

rD,0

lB (f + g)2 = 8(f − g)2

(5)

where f is the fraction of positively charged monomers and g is the fraction of negatively charged monomers in the polymer. Table 2: Debye screening length corresponding to minimum excluded volume at pH=1.2,7 and 10. pH 1.2 7 10

f

g

rD,0 (nm) 0.5 0 0.09 0.5 0.5 ∞ 0.22 0.5 0.57

For rD < rD,0 , gelatin is expected to behave like a polyelectrolyte, and for rD > rD,0 it should behave like a polyampholyte. In Figure 4, we have shown the persistence length (lp ) of the polymer and ratio(r) which gives a measure of shape of the polymer. It confirms that at cs = 0.2 gelatin is in a collapsed state at pH=1.2 and pH=10 while no such minimum is observed at pH=7.


6

Page 7 of 15

11

(a)

10

rD (nm)

9 Re (nm)

8

1.5 1 0.5 0

tics at different pH is also computed. Figure 5(a) clearly shows a maximum in number of polymer-polymer hydrogen bond at pH=10 and Figure 5(b) shows a minimum in number of polymer-solvent hydrogen bond. Though electrostatic forces are the driving forces behind the global structure of the polymer, hydrogen bonding between the polymer and solvent locally stabilizes the structure.

(b)

0

c∗s 0.5 cs (M)

1

0.6

0.8

1

7 6 5 0

0.2

0.4

cs (M)

Figure 3: Size of gelatin measured in terms of end-to-end distance (Re ) in presence of salt at different pH. Symbols (green), 2 (orange), 4 (blue) denote pH=1.2, 7, 10 respectively. Inset shows the variation of Debye screening length with salt concentration as rD ' √0.3 . The (cs )

theoretical estimate of cs ∗ is obtained by its intersection with rD,0 =0.57(nm) line and is equal to 0.28M. This is very close to that observed in the simulations, c∗s =0.2M.

N umber of hydrogen bonds

4 N umber of hydrogen bonds

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


(a) 16

12

45

(b)

40 35 30 25 20

8 0 0.25 0.5 0.75 1 pH

0 0.25 0.5 0.75 1 pH

Figure 5: Hydrogen bonding information between (a) gelatin-gelatin, (b) gelatin-water. Symbols (green), 2 (orange), 4 (blue) denote pH=1.2, 7 and 10 respectively.

0.9 0.8 lp (nm) 0.7 0.6

7 0.5

Re (nm)

0.4 0

0.2

0.4

0.6

0.8

6

1

cs (M) onset of reexpansion

5

Figure 4: Flexibility of a gelatin chain in measured in terms of persistence length (lp ) in presence of salt at different pH. Symbols (green), 2 (orange), 4 (blue) denote pH=1.2, 7, 10 respectively.

0

0.2

0.4

0.6

0.8

1

cs (M)

Figure 6: Effect of adding NaCl ( ) and CaCl2 (2) on the size of gelatin at pH=10.

In order to understand the interplay between electrostatic interaction and hydrogen bonding, the average hydrogen bond statis-

The effect of valency is also studied on the reexpansion phenomenon. Figure 6 clearly shows


7


that in case of CaCl2 the onset reexpansion is around cs = 0.1M. This reduction in the critical salt concentration is because of the higher screening capacity of divalent ions.

4.3

Page 8 of 15

3 gmn (r) 2

(a)

1 0 2

Radial distribution function

(b)

gmn (r)

In order to verify the hypothesis about relative spatial arrangement of gelatin monomers and salt ions, the radial distribution function between monomers-chloride ions (gmn (r)) and monomers-sodium ions(gmp (r)) is calculated separately. Figure 7(a) clearly shows a shift in the peak of gmn (r) to lower values as the salt concentration is increased. This is in accordance with the purely polyelectrolyte behavior expected at pH=1.2, as only NH2 gets protonated. The electrostatic interaction between NH3+ and Cl– leads to collapse of the polymer as depicted in Figure 9(a). At pH=7, gelatin behaves as a pure polyampholyte, leading to expansion of the polymer with increase in salt concentration. This is confirmed by shift in the peak of gmn (r) to progressively higher values, shown in 7(b). The phenomenon of reexpansion at pH=10, is again captured by gmn (r) as shown in 7(c). As cs is increased from 0.05 M to 0.2 M, the peak of the distribution function shifts from 1.2 nm to 0.9 nm. Further increase in cs to 1 M leads to a increase the peak position to 1.05 nm. This clearly proves our picture of screening of repulsive interaction between excess charges, followed by screening of attractive interaction between opposite charges as depicted pictorially in Figure 9(b). In figure 8, gmp (r) between gelatin monomers and Na+ ions is shown. At pH=1.2, since there is only repulsive interaction between NH3+ ions and Na+ ions, gmp (r) does not give us any additional information as cs is increased. Thus, at this pH, interaction between NH3+ and Cl– is the factor playing the major role in the collapse of the polymer. However, at pH=7 and 10, both the NH2 and COOH groups get ionized. From Figure 8(b), we get the same monotonic increase in peak of gmp (r) as observed in case of chloride ions. Figure 8(c) also indicates that the minimum in peak position of gmp (r) occurs at an intermediate salt concentration of 0.5M, confirming the screen-

1 0 gmn (r) 1

(c)

0.5 0 0

1

2

r (nm)

3

4

5

Figure 7: Radial distribution function between gelatin monomers and chloride ions at (a) pH=1.2, (b) pH= 7 and (c) pH=10. Symbols (green), 2 (orange), 4 (blue) denote cs =0.05, 0.2 and 1 M respectively.

ing of interactions between both NH3+-Cl– and COO–-Na+ pairs are at play.

4.4

Dynamic light scattering

Dynamic light scattering is a powerful tool that has been extensively used to characterize the polymer solutions. 52 In order to validate the collapse-reexpansion observed in simulations, hydrodynamic radius from DLS is obtained. The normalized intensity autocorrelation function is directly obtained from the experiment, which is a measure of how particles move in the solution. It is expressed as, g2 (τ ) =

hI(t)I(t + τ )i hI(t)i2

(6)

whereas the normalized electric field autocorrelation function, which is measure of how particles move relative to each other, is given as g1 (τ ) =


8

hE(t)E(t + τ )i hE(t)i2

(7)

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gmp (r)

1

and poly dispersity index(P DI) of the solution can be obtained by methods of cummulants 54 or CONTIN algorithm. 55 We have used CONTIN in the present case and for all the samples obtained a P DI in the range 0.1-0.3, showing that the solutions are mostly mono-disperse. The normalized auto-correlation shown in Figure 10(a) shows a single mode decay. In the semidilute regime, Herning and co-authors 20 showed that, gelatin shows two decay rates and thus two diffusion rates. While the faster diffusion coefficient(10−7 −10−5 cm2 /s) is attributed to cooperative diffusion of individual chains, the slower diffusion(10−10 − 10−7 cm2 /s) is due to the movement of group of entangled coils called as ‘clusters’. Our case corresponds to the slower diffusion case as we observe a diffusion coefficient in 10−9 − 10−8 cm2 /s range. Hydrodynamic radius of such clusters is calculated using equation and plotted in 10(b). At pH=1.2, a monotonic decrease in RH is obtained which agrees qualitatively with the polymer size observed in simulation (Figure 3). At pH=7, it can be noticed that initially the size of the polymer decreases and reaches a minimum at cs = 0.05 M which is absent in simulation. This is due to the fact that in simulation, pre-ionized chains are taken as input which ensured complete charge neutrality at pH=7 in salt free condition. However, in practice this may not be true as the isoelectric point of gelatin is around 7-9 and not exactly 7. Therefore, in no salt condition, gelatin may have a net charge at pH=7. This net charge is definitely higher at pH=10, widening the polyelectrolyte regime. The onset of reexpansion is observed at cs = 0.15M which is very close to the simulation value of c∗s = 0.2M. As we go further away from the isoelectric point, c∗s will increase as more salt will be required to screen the polyelectrolyte nature. At much higher pH(>10), a purely polyelectrolyte behavior may be evident analogous to that observed at pH=1.2. Though the results from DLS exhibit a qualitative match with the simulation results, it does not give information at the single chain level. This motivated us to probe the structure of solution in more detail using SAXS.

(a)

0.5 0 3 gmp

(b)

(r) 2 1 0 1.5

(c)

gmp (r) 1 0.5 0 0

1

2

r (nm)

3

4

5

Figure 8: Radial distribution function between gelatin monomers and sodium ions at (a) pH=1.2, (b) pH= 7 and (c) pH=10. Symbols (green), 2 (orange), 4 (blue) denote cs =0.05, 0.2 and 1 M respectively.

Under the homodyene scattering approximation, Siegert showed that g1 (τ ) and g2 (τ ) are related to each other as, g2 (τ ) = B + β|g1 (τ )|2

(8)

where B is the baseline and β is a numeric constant dependent on the experimental condition. 53 For a monodisperse system g1 (τ ) decays exponentially and the rate of decay is related to the diffusion constant of the polymer. Γ = −Dq 2

(9)

sin( 2θ ) is the scattering vector. where q = 4πn λ Stokes-Einstein equation is then used to determine the hydrodynamic radius(RH ) from the diffusion coefficient. D=

kB T 6πηs RH

(10)

where ηs is the viscosity of the solvent. For hetero-disperse systems, there is a distribution ¯ G(Γ) of decay rates . The mean decay rate(Γ)


9


Page 10 of 15

Figure 9: Schematic showing the screening mechanism in (a) purely polyelectrolyte regime(pH=1.2) (b) polyampholyte regime(pH=10). The orange spheres represent ‘blobs’ carrying net charge. Each of the blob can be considered as a collection of monomers. Na+ ions are represented by magenta dots and Cl– ions are represented by blue dots. In the polyelelctolyte regime, as salt concentration is increased progressive screening of electrostatic repulsion between the blobs occurs, resulting in collapse of the polymer. In the polyampholyte regime each of the blob contains monomers of opposite charges as shown in the enlarged blob. Addition of salt initially results in collapse of the polymer as the repuslion betwen blobs gets screened first but no salt ion is present within the blobs. Above the critical concentration(c∗s ), salt ions starts penetrating within the polyampholyte blobs. This results in screening of fluctuation induced attraction causing the polymer to swell again.

4.5

Small angle X-ray scattering

In figure 11(a) we have shown the fitting procedure to obtain the intersection point of two scaling laws, q ∗ , for pH=7 and cs =0.1M. This gives us lp = 2.8 ± 0.4 nm, which compares well with the value reported in literature. 19,58 The procedure is then repeated at all other pH condition and different salt concentrations. Figure 11(b) shows lp monotonously decreases at pH=1.2 confirming the prediction from simulations. The collapse reexpansion is also present at pH=7 and 10. The onset of rerexpansion at pH=10 is at cs = 0.15M which matches very well with DLS result(Figure 10(b)). The shift of point of reexpanison as we go from pH=7 to pH=10 further confirms the screening mechanism outlined in the schematic shown in Figure 9. The agreement with simulation is only qualitative in nature as there is an order of magnitude difference between lp obtained from SAXS and those obtained from simulation(Figure 4). This may be attributed to the difference in molecular weight of the experimen-

The size of ‘clusters’ obtained from DLS is in the range of 50-150 nm while the single chain size obtained from simulation is in the order of 10 nm. Small angle X-ray scattering(SAXS) is carried out on the same sample used in DLS to get single chain statistics comparable with the simulation results. Kratky-Porod method is employed to extract persistence length(lp ) from the intensity data. 56 A power law of −5/3 is expected for the self avoiding regime and a power law of -1 for the rod-like regime, since gelatin behaves as a self avoiding polymer in water. 21 A log-log plot of I(q) versus q is made and the two power-law regimes with lines of slopes -5/3 and -1 are shown to match at a particular value of q. Persistence length of the polymer is calculated from the intersection of these two lines as, lp = πq6∗ , 56,57 q is the wave vector given by 4π sin( 2θ ), where λ is the wavelength of the scatλ tered radiation and θ is the scattering angle.


10

Page 11 of 15

0 −3

g (2) (τ ) − 1

I(q)

−9

−12

−5/3

104

(a)

−6

103

(a)

102 1

10

160 Rh (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


102 103 τ (µs)

104

105

q ∗ = 0.6 − 0.8 nm−1

−1

10−2

10−1q (nm−1 ) 100

30

101

(b) 20 lp (nm) 10

120 80

(b)

40 0 0

0.1

0.2

0.3

0.4

0.5

0

cs (M)

0.1

0.15

0.2

0.25

0.3

cs (M)

Figure 10: Dynamic light scattering:(a) Intensity autocorrelation function of 4 % gelatin solution in presence of 0.05 M salt at pH=1.2 (green solid line), 7 (orange dashed line) and 10 (blue dotted line). (b) Hydrodynamic radius of ‘clusters’ as a function of salt concentration at different pH. Symbols (green), 2 (orange), 4 (blue) denote data at pH=1.2, 7 and 10 respectively.

Figure 11: Small angle X-ray scattering:(a)Intersection point of two scaling laws for pH=7 and cs =0.1M. (b)Persistence length(lp ) obtained at all pH using the Kratky-Porod method. 56 Symbols (green), 2 (orange), 4 (blue) denote data at pH=1.2, 7 and 10 respectively.

with the theoretical estimate. This reexpansion mechanism is fundamentally different from the ‘charge inversion’ mechanism known for multivalent ions, where the repulsion between the excess charges leads to a increase in size of the polymer. These predictions from MD simulation are well supported by the size of hydrodynamic ‘clusters’ obtained from DLS. Persistence length obtained from SAXS gives further confirmation to this pH dependent collapsereexpansion behavior. It would be interesting to study the existence of this phenomenon in case of polyelectrolyte-polyampholyte complex at different pH. Finally, the molecular level insights obtained from the present study may be useful in preparing gelatin based stimuli responsive polymers for drug delivery applications. Acknowledgement The authors acknowledge

tal sample and the chain length considered in simulation. However, the nature of variation of lp with the addition of salt is the same as that observed in the simulations.

5

0.05

Conclusion

In summary, the equilibrium properties of gelatin have been investigated at different pH, both in absence and presence of monovalent salt. The addition of salt decreases the Debye screening length(rD ). As rD becomes smaller than the size of polymer in no salt condition, it starts to collapse. Further decrease in rD leads to screening of fluctuation induced attraction between oppositely charged ions. The Debye screening length corresponding to the minimum excluded volume rD,0 is found to be a function of the pH of the medium and agrees well

Mr. Kali Suresh and Dr. Chandra Shekhar Sharma for their help in SAXS experiments. We thank Indian Institute of Technology Hy-


11


derabad for providing the resources, research facilities and support. The authors thank Tithi Basu for careful reading of the manuscript and numerous discussion sessions.

Page 12 of 15

(10) Kudaibergenov, S. Polyampholytes: synthesis, characterization and application. Encycl. Polym. Sci. Technol. 2002, 214. (11) Dobrynin, A. V.; Colby, R. H.; Rubinstein, M. Polyampholytes. J. Polym Sci, Polym. Phys. 2004, 42, 3513–3538.

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