Antifreeze Effect of Carboxylated ε-Poly-l-lysine on the Growth Kinetics

Aug 11, 2014 - Cryopreservation of a Two-Dimensional Monolayer Using a Slow Vitrification Method with Polyampholyte to Inhibit Ice Crystal Formation...
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Antifreeze Effect of Carboxylated ε‑Poly‑L‑lysine on the Growth Kinetics of Ice Crystals Dmitry A. Vorontsov,*,†,‡ Gen Sazaki,‡ Suong-Hyu Hyon,§ Kazuaki Matsumura,∥ and Yoshinori Furukawa‡ †

Lobachevsky State University of Nizhny Novgorod, Gagarin Avenue, 23, Nizhny Novgorod, 603950 Russia Institute of Low Temperature Science, Hokkaido University, Kita-19, Nishi-8, Kita-ku, Sapporo, 060-0819 Japan § Center for Fiber and Textile Science, Kyoto Institute of Technology, 105 Jibucho, Kyoto Fushimi-ku, Kyoto, 612-8374 Japan ∥ Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi-shi, Ishikawa, 923-1292 Japan ‡

ABSTRACT: Some biological substances control the nucleation and growth of inorganic crystals. Antifreeze proteins, which prohibit ice crystal growth in living organisms, promise are also important as biological antifreezes for medical applications and in the frozen food industries. In this work, we investigated the crystallization of ice in the presence of a new cryoprotector, carboxylated ε-poly-L-lysine (COOH-PLL). In order to reveal the characteristics and the mechanism of its antifreeze effect, free-growth experiments of ice crystals were carried out in solutions with various COOH-PLL concentrations and degrees of supercooling, and the depression of the freezing point and growth rates of the tips of ice dendrites were obtained using optical microscopy. Hysteresis of growth rates and depression of the freezing point was revealed in the presence of COOH-PLL. The growth-inhibition effect of COOH-PLL molecules could be explained on the basis of the Gibbs−Thomson law and the use of Langmuir’s adsorption isotherm. Theoretical kinetic curves for hysteresis calculated on the basis of Punin−Artamonova’s model were in good agreement with experimental data. We conclude that adsorption of large biological molecules in the case of ice crystallization has a non-steady-state character and occurs more slowly than the process of embedding of crystal growth units.

1. INTRODUCTION Antifreeze proteins are examples of biological substances that make it possible to control the formation processes of ice crystals in their supercooled solution. These substances can be classified into two groups: natural biological antifreezes produced by living organisms in animate nature and artificially created compounds. The properties of these substances have been intensively studied to understand the biological processes that occur and with the aim of finding applications in the frozen food industry and for medical treatments like cryosurgery, organ transplants, and so on. As typical examples of the former, antifreeze proteins (AFPs) or antifreeze glycoproteins (AFGPs) produced by some living organisms (polar fish, insects, plants) for survival in a subfreezing environment are perhaps the most well-known.1−4 AF(G)Ps exhibit important properties such as depression of the freezing point5 and inhibition of ice recrystallization. Some artificially created agents are used for preservation and transplantation of living cells and tissues.6 In spite of their prospective applications, the widespread use of AF(G)Ps is essentially restrained due to their high cost and low efficiency of production. The search for synthetic compounds with properties similar to natural AFPs is actually an urgent issue at the present time and has spurred research. For example, it has been found that poly(vinyl alcohol) can exhibit a small thermal hysteresis of 0.18 K during ice crystallization.7 Zirconium © 2014 American Chemical Society

acetate and zirconium acetate hydroxide reduce the growth rate of ice and show thermal hysteresis.8 Glycine peptoid oligomers also inhibit ice crystal growth.9 Recently, it has been shown that carboxylated ε-poly-L-lysine (COOH-PLL) can be a highly efficient novel cryoprotective agent with lower cytotoxicity,10 and is useful as an alternative to dimethyl sulfoxide.11 Cryoprotective properties for mammalian cells, such as mesenchymal stem cells, were imparted to PLL by carboxylation.10 However, the characteristics of the effect of COOHPLL on the crystallization of ice remain unknown. The role of macromolecules during biological crystal growth processes, such as the formation of bones, tissues, or mollusc shells, is also being intensively studied in the field of biomineralization.12−14 Since COOH-PLL is a macromolecule with a molecular weight of about 4000 Da, elucidation of the functional mechanism of COOH-PLL on the growth of ice is of great importance not only for clarifying the freezing prohibition kinetics but also for a general understanding of biomineralization processes in nature. In this study, we observed in situ the free growth of ice crystals in a supercooled solution of COOH-PLL, and measured the growth rates as functions of concentrations and supercooling temperatures. Analyzing the experimental results, Received: July 31, 2014 Published: August 11, 2014 10240

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where supercooling was less. When measuring growth rates, we kept the supercooling inside the growth chamber constant during the whole experiment until the moment of mass crystallization. Dew condensation on the windows of the cell was prevented by a flow of nitrogen gas. The experiment was stopped when ice reached the inside walls of the chamber and started to cover them. This moment was clearly detected due to a sharp rise in temperature in the cell because of the release of latent heat. Then, the temperature in the cell was increased above 0° to melt all of the formed ice. After that, it was possible to set up the desired supercooling again and perform the next experiment. The growing ice crystal was observed through the glass window using a transmission microscope illuminated by a laser diode (580 nm wavelength and 5 mW). After exiting the capillary, an ice crystal began to grow toward the center of the chamber and in the opposite direction along the outer surface of the capillary. The growth of ice crystals was recorded as a sequence of images captured at fixed time intervals. Images were analyzed by a time-space analysis method, and then, growth velocities could be calculated. COOH-PLL containing 65 mol % COOH groups was synthesized by mixing 25% w/w ε-poly-L-lysine aqueous solution (10 mL; JNC Corp., Tokyo, Japan) and succinic anhydride (1.3 g of SA; Wako Pure Chem. Ind. Ltd., Osaka Japan) and reacting them at 323 K for 1 h to convert 65% amino groups to carboxyl groups. The molecular weight of COOH-PLL was about 4000 g/mol. The structural formula of a COOH-PLL molecule is shown below.7

we clarify the capabilities of COOH-PLL on the morphology and growth kinetics of ice crystals, and discuss the mechanism of the retardation of ice growth by COOH-PLL molecules and the adsorption characteristics of COOH-PLL molecules at the ice−water interfaces.

2. EXPERIMENTAL METHODS Ice crystals were freely grown in a supercooled bulk solution with a specified amount of COOH-PLL. Since the design and principles of the growth cell have been described in detail elsewhere,15 we show only a general concept of the growth cell in Figure 1. A cylindrical 1.5 cm in diameter growth chamber

Figure 1. Schematic of the growth cell: 1, growth chamber with water or COOH-PLL solution; 2, triple glass window; 3, Peltier elements; 4, heat reservoir with circulating water; 5, capillary holder; 6, tube with water or COOH-PLL solution; 7, inlet for cold spray; 8, seed crystal; 9, capillary; 10, thermistor.

with a volume of about 3 cm3 was formed as a hole inside the copper block and ended by the triple glass windows on two sides. A thin glass capillary, which was used for ice nucleation, was inserted into the center of the growth chamber. The outer diameter of the capillary tip was 312 μm, and the diameter of the inner channel of the tip was ∼100 μm. Peltier elements were attached to the upper and lower parts of the copper block and used to control the solution temperature inside. A thermistor in a hole in the copper wall of the chamber was used for temperature measurement of the solution. The temperature of the solution sample was controlled with an accuracy of ±0.02 K by a PID thermo-controller (Melcor MTCA Series). The growth of ice crystals was performed by the following procedure. Prior to the beginning of the experiment, the whole growth cell and supply tubes were cleaned with 0.1 mol/L nitric acid to remove traces of any organic compounds. Then, the growth chamber and glass capillary were filled with COOHPLL solution. The solution in the growth chamber was cooled down to an appropriate temperature, and a steady-state temperature distribution inside the solution was established. Then, ice crystals were nucleated inside a glass capillary by injection of cold spray through inlet 7. The amount of injected spray was carefully controlled manually to prevent excess cooling of liquid in the growth chamber. Ice particles that nucleated in the capillary continued to grow inside it, and finally, only one ice particle could survive when the ice crystal reached the opposite end of the capillary. At that time, a platelike ice single crystal of hexagonal modification (space group P63/mmc) appeared at the tip of the capillary and free growth of the ice crystal was observed in the chamber. Supercooling of the solution near the outlet for spray injection was much greater than that inside the chamber, and growth occurred from the area with more supercooling toward the growth chamber

The sample solutions used for ice crystal growth were prepared by dissolving dry COOH-PLL powder in ultrapure water with a specific resistance of 18 MΩ·cm. The solution was agitated until total dissolution of COOH-PLL. The prepared solution was kept in a refrigerator at about 277 K.

3. EXPERIMENTAL RESULTS 3.1. Morphology of Ice Crystals. Parts a and b of Figure 2 show a side-view image and a plan-view image of an ice single crystal growing in pure water without any additive under the supercoiling condition of 0.1 K. Both the upper and lower faces of the circular disk crystal are basal faces {0001} perpendicular to the crystallographic c-axis. The growth rate of the basal faces was 1 or 2 orders of magnitude smaller than that along the aaxis. The smaller the supercooling of solution and the higher the concentration of COOH-PLL, the longer the delay in the appearance of ice at the tip of the capillary. Typically, the delay varied in our experiments from 10 s to 40 min. Sometimes at small supercoolings (ΔT = 0.03−0.2 K), the ice crystal exited the capillary after several hours or almost stopped in the capillary. This observation is explained by different orientations of the crystallographic axes of formed seed crystals relative to the capillary. When the orientation of the preferential growth 10241

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and growth kinetics of ice were the same as in pure water. At CCP ≥ 20 mg/mL, chains of small inclusions of solution appeared in crystals (for example, see the image for ΔT = 0.2 K and CCP = 20 mg/mL in Figure 3). In the presence of COOHPLL, morphological instability from a circular disk to a dendrite occurred at smaller supercoolings than in pure water. Figure 3 also shows that the size of dendrites at a fixed supercooling condition became smaller with an increase in concentration of COOH-PLL. When supercooling was more than 0.8 K and the concentration of COOH-PLL was higher than 40 mg/mL, elementary branches of dendrites looked very similar to those at ΔT = 0.8 K and CCP = 40 mg/mL but secondary branches became smaller and less distinguishable (to enhance the visibility of the micrographs, we did not show them in Figure 3). Branches of dendrites laid down in one plane, and formation of three-dimensional dendrites was not observed. Interference fringes in Figure 2c and Figure 3 were obtained by Mach−Zehnder interferometry for the measurements of the growth rate of basal faces. Although in this paper we focus on the growth in the crystallographic a-direction, we will report the growth rates of basal faces in the future. 3.2. Growth Rates of Ice Crystals in the Presence of COOH-PLL. Just after the appearance of a single ice crystal from the capillary, we first intentionally rotated the capillary so that the plane of the ice disk or dendrite was oriented perpendicular to a screen, and then, we took a side-view image of the crystal. Using this picture, we measured the angle between the crystal plane and the capillary longitudinal axis located parallel to the image plane. This angle was used for further correction of the growth rates measured from the plan view images of the crystals. After that, we rotated the capillary by 90° and recorded the subsequent growth process. From these data, we accurately determined the growth rate in the adirection. Growth rates of dendrites were determined by position changes of dendrite tips in time. In the case of a disklike crystal, the growth rate was determined along the perpendicular to the lateral interface of the disk. The growth rate of the ice crystal after its appearance from the capillary inside the chamber was not constant, even though the supercooling was fixed. The dependence of length L(t) along the direction of the a-axis from the top of capillary until the tip of a dendrite and, consequently, the growth rate R(t) of the crystal on experimental time had three characteristic parts (Figure 4). In region 1, R rapidly dropped. This reduction may occur as a consequence of the initial development of a thermal diffusion field around the growing crystal, because the dissipation of the latent heat is extremely efficient at the beginning of crystal growth. The slow decrease of R(t) in region 2 was due to the release of latent heat by the growing crystal. The beginning of region 3 corresponded to the moment when ice spread along the outer surface of the capillary reached the walls of the chamber and then began to form on them. After that, mass crystallization occurred, leading to the release of more latent heat and, finally, a total cessation of the growth rate of the main crystal on the capillary. Therefore, the growth rate was calculated as the average value of the dependence R(t) in region 2, and then, a correction for the angle between the crystal plane and the longitudinal axis of the capillary was taken into account. We obtained the growth rate R in the direction of the a-axis as a function of supercooling ΔT over a range of COOH-PLL concentrations of 20−150 mg/mL. Experimental points shown in Figure 5 represent growth rates averaged from the

Figure 2. Morphology of a disk-like ice crystal growing on the tip of the capillary in water: (a, b) the direction of preferential growth was parallel to the longitudinal axis of the capillary; in contrast to image a, in image b, the capillary with an ice crystal was rotated 90° around the longitudinal axis (supercooling ΔT = 0.1 K); (c) the crystallographic a direction was oriented at a slant with respect to the longitudinal axis of the capillary.

direction (along the a-axis) was close to the longitudinal axis of the capillary (Figure 2a), an ice crystal appeared at the tip of the capillary considerably faster than that in the case of an inclined or, very rarely, a transversal location of the a-axis relative to the capillary (Figure 2c). Typically, the angle between the direction of the a-axis and the longitudinal axis of the capillary usually varied from 0 to 30°. Figure 3 shows the morphology of ice crystals grown at different degrees of supercooling ΔT and concentrations of

Figure 3. Morphology of ice crystals at different supercoolings ΔT and concentrations of COOH-PLL CCP. The outer diameter of the capillary tip is 312 μm.

COOH-PLL CCP. At small ΔT (up to 0.2−0.3 K), the ice crystal had a disk-like shape. Crystallization in pure water and COOH-PLL solutions was not accompanied by the formation of {101̅0} and {112̅0} faces of a hexagonal prism. With further increase in supercooling, the lateral surface of the disk lost stability and the formation of dendrites with branches parallel to the basal faces was observed. When the COOH-PLL concentration was smaller than 20 mg/mL, the morphology 10242

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increase in supercooling up to 1.0−1.6 K. We determined the width of the dead zone for every CCP during both gradual decrease (ΔTd1) and increase (ΔTd2) of supercooling (Figure 6). In the first case, we used the lowest supercooling to ensure

Figure 4. Typical time dependence for (a) length L(t) and (b) growth rate R(t) of the ice crystal in the growth cell. The growth rate R(t) was derived by differentiation of the experimental L(t) data.

Figure 6. Critical supercooling (dead zone) as a function of the concentration of COOH-PLL: ΔTd1, reduction of supercooling from high values to ΔTd1 (the dotted line for ΔTd1 is drawn in handwriting); ΔTd2, increase of supercooling from ΔT < ΔTd1 until high values; ● and ○, experimental points; ×, calculated values.

reproducible growth of the crystal. Then, we gradually decreased the supercooling until the growth of the crystal completely stopped. This supercooling corresponds to the dead zone ΔTd1 (points in Figures 5 and 6). In the second case, to determine critical supercooling ΔTd2 (Figure 6), we first stopped the growth of the crystal located inside the capillary by increasing the temperature, and then after a certain time, we began to lower the temperature until the ice crystal started to grow. When we determined ΔTd2, we decreased the temperature in 0.015 K steps and waited about 20−25 s after every step to take into account the temperature delay of the growth chamber. Recovery from the dead zone occurred slowly with a subsequent sharp burst of growth. Thus, the change of supercooling from high values to the melting point made it possible to grow ice at a smaller ΔT than that in the second case when supercooling was changed in the opposite direction. The appearance of hysteresis is evidence of slow adsorption of COOH-PLL on ice crystal faces; that is, the exposure time of a surface at high growth rates is less than the characteristic time of adsorption of COOH-PLL molecules, and the surface concentration of adsorbate therefore does not reach an equilibrium value. We found that the higher the concentration of COOH-PLL in water, the larger the hysteresis of the dead zone. Because of the much larger molecular weight of COOHPLL (4000 g/mol) than those of inorganic salts, we could ignore the molar depression of the melting point in our experimental conditions. 3.3. Effect of the Density and Viscosity of COOH-PLL Solutions. The density of the COOH-PLL solutions was determined with the use of an A&D GR-202 analytical balance and Nichiryo mechanical pipet. We experimentally obtained the following dependence of the density of aqueous COOH-PLL solutions in a concentration range of 20−150 mg/mL at a temperature of 277 ± 2 K

Figure 5. Growth rate of ice crystals as a function of supercooling ΔT at various concentrations of COOH-PLL. Solid lines denote R0i(ΔT) curves plotted according to eq 7 (the curve R0i(ΔT) for CCP = 20 mg/ mL is not shown for simplicity), and dotted lines correspond to the values calculated from eqs 8 and 9.

independent values obtained in three to seven experiments. The effect of COOH-PLL on the growth kinetics of ice became noticeable when CCP ≥ 20 mg/mL. In the presence of COOHPLL, a characteristic region of supercoolings ΔT < ΔTd1, a socalled dead zone, appeared where ice did not grow. When supercooling decreased until it reached a certain critical value ΔTd1, the growth rate very quickly fell to zero. At CCP = 20 mg/ mL, a narrow dead zone existed, but at higher supercoolings, the crystal grew at the same velocity as that in pure water. With an increase in CCP, the growth rate of ice passed through a maximum at CCP = 40 mg/mL at a fixed amount of supercooling, and then quickly decreased with increases in the concentration of cryoprotector. The growth of ice was unstable at supercoolings close to the dead zone. Sometimes ice stopped growing even inside the capillary, and it was possible to resume growth only after an

ρCP (CCP) = 4.375 × 10−4CCP + 0.993 [g/cm 3] 10243

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where Cis and C0 are surface densities (in number/cm2) of adsorption sites occupied by COOH-PLL and total number of adsorption sites, respectively. Taking into account eqs 2 and 3 and li = (1/Cis)1/2, we obtain

where the concentration CCP is taken in mg/mL. The density of a 150 mg/mL COOH-PLL solution exceeds the density of water by approximately 6%. We measured the viscosity of COOH-PLL solutions by dynamic light scattering using a DelsaNano HC microanalyzer. We used calibrated polystyrene nanoparticles of 162 nm in diameter (manufactured by Duke Scientific Corp.) as lightscattering particles in solutions. Then, we obtained the following empirical function for viscosity of a solution with a COOH-PLL concentration of 20−150 mg/mL and temperature near 273 K. μ(CCP) =

0.904μ0 1 − 0.005CCP

ΔTd =

[Pa·s]

θ=

Cvi =

0.001CCPρsol MCP(CCP + ρH O )

≈

0.001CCP MCP

1/2 ⎛ CCP ⎞ ΔTd(CCP) = ⎜a12 ⎟ ⎝ a 2 + CCP ⎠

3

(6)

(2ωαT0/h0)C1/2 0

where a1 = and a2 = kLMCP/0.001. The best fit of experimental data for ΔTd2(CCP) by function 6 (Figure 6) gives the following values for the parameters: a1 = 5 K and a2 = 1780 g/cm3. From a1, we could estimate the density of adsorption sites on the surface C0 = 1.2 × 1012 cm−2. The average distance between adsorption sites is L0av = C0−0.5 = 0.009 μm. From parameter a2, we find Langmuir’s adsorption constant kL = 4.45 × 10−4 mol/cm3, and then using eqs 5 and 3, we finally obtain the average distance between adsorbates on the surface li = (1/C0θ)1/2 as a function of the COOH-PLL concentration in the bulk solution shown in Figure 7.

is the specific latent heat of fusion in [J per 1 water molecule], where H0 = 333.6 J/g is the latent heat of fusion of ice, Mice = 18.015 g/mol is the molar weight of ice, and NA = 6.022 × 1023 mol−1 is the Avogadro number. Let us introduce the following criterion for stopping growth of the surface: the critical size dcr is equal to the average distance l i between adsorbates, that is, dcr ≈ l i (for simplification, consider COOH-PLL molecules as points). Then, from eq 1, we obtain the following expression for critical supercooling (dead zone): 2ωαT0 h 0 li

(5)

where MCP = 4000 g/mol is the molar weight of COOH-PLL, CCP is the concentration of COOH-PLL in [mg/mL of solution], ρsol(CCP) is the density of COOH-PLL solution at 277 K with concentration CCP, and ρH2O is the density of water. Combining eqs 4 and 5, we derive a function for the dependence of the critical supercooling on the concentration of COOH-PLL in the case of steady-state adsorption:

H0M ice NA

ΔTd =

⎛ E ⎞ kds exp⎜ − d ⎟ kad ⎝ k bT ⎠

2

where ω = 3.2 × 10 cm is the volume of a water molecule in a crystal lattice, α = 2.8 × 10−6 J/cm2 17 is the free surface energy of the ice−water interface (other values for the ice− water interface reported in the literature are 3.3 × 10−6 J/cm2 (Ketcham18) and 3.2 × 10−6 J/cm2 (Hollomon19)), T0 = 273.15 K is the melting point, and ΔT is the supercooling.

h0 =

kL =

in [mol of COOH‐PLL/cm 3 solution]

(1) −23

Cvi , kL + Cvi

where Cvi is the COOH-PLL concentration in a bulk solution in [mol/cm3 solution], kL is Langmuir’s adsorption constant, kds and kad are desorption and adsorption coefficients of COOHPLL molecules, respectively, and Ed is the energy of desorption. Further, let us denote

4. MODEL OF THE DEAD ZONE AND HYSTERESIS OF GROWTH RATES 4.1. Concentration Dependence of Dead Zone Width. During the crystallization of ice, COOH-PLL molecules adsorb on the surface and prevent growth of the crystal. We assume that molecules of the cryoprotector are distributed on the surface in the form of a two-dimensional net of growth inhibitors. Considering the local equilibrium of the interfacial melting temperature based on the thermodynamics, it can be expected that a surface covered by impurity particles will be able to grow when the interparticle distance exceeds the critical value dcr given by the Gibbs−Thomson equation:16 2ωαT0 h0ΔT

(4)

Now consider monolayer adsorption of COOH-PLL molecules. Assume that there are no mutual lateral interactions in an adlayer, and take Langmuir’s adsorption isotherm to describe the process of COOH-PLL adsorption on the surface. Then, the degree of coverage16 will be equal to

Here, μ0 = 0.041 Pa·s is the viscosity of a 20 mg/mL COOHPLL solution. The data obtained show that the viscosity of COOH-PLL solutions is significantly larger that of water (μH2O = 1.797 × 10−3 Pa·s, T = 273.15 K).

dcr =

2ωαT0 2ωαT0 1/2 2ωαT0 1/2 1/2 = Cis = C0 θ h 0 li h0 h0

(2)

The degree of surface coverage by the inhibitors is given as θ=

Cis C0

Figure 7. Calculated average distance between COOH-PLL molecules on the ice surface for different concentrations of cryoprotector.

(3) 10244

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4.2. Supercooling Dependence of Growth Rates. It is known that the supercooling dependence20,21 of the tip growth rate for the ice dendrites in pure water in crystallographic direction a can be expressed as

R(ΔT ) = β ΔT n where β is the kinetic coefficient of the face. The model of dendritic growth17 and experimental data from various studies20,21 give n ∼ 1.7−2.37. Our experimental result shown in Figure 5 gave the following relation between the growth rate in pure water and supercooling:

Figure 8. Kinetic coefficient of a face as a function of COOH-PLL concentration. The growth of ice occurs along the a-axis.

R 0(ΔT ) = 88·ΔT1.79 [μm/s]

Since the morphologies of ice crystals grown in pure water and COOH-PLL solutions were similar, we assumed that the growth rates in the presence of cryoprotector also could be expressed by a power function of the supercooling. In order to determine the kinetic coefficient βi in COOH-PLL solutions, we approximated the experimental data in the supercooling range ΔT ≥ ΔTd1 by functions (solid curves in Figure 5): R 0i(ΔT ) = βi ·ΔT1.79 ,

ΔT ≥ ΔTd1

cryoprotector concentration may cause some modifications of the configuration of COOH-PLL molecules in solution, resulting in an interaction with the solvent. However, as far as we know, there are still no experimental data that reveal a concrete dependence of the activation energy of water molecules on COOH-PLL concentration and information about the configuration of COOH-PLL molecules in an aqueous solution. The noticeable decrease in the kinetic coefficient when the COOH-PLL concentration is higher than 40 mg/mL can be explained by an increase in the viscosity of the solution. 4.3. Hysteresis of Growth Rates. By studying the crystallization of ice in the presence of COOH-PLL, we found a hysteresis of the growth rate and the value of critical supercooling. At the same supercooling, two values of growth rate exist in the temperature range ΔTd1 < ΔT < ΔTd2. When ΔT > ΔTd1, one value is close to the growth rate R0 in a pure system, and such a growth rate can be observed during the reduction of supercooling (curve 1, Figure 9). In contrast,

(7)

where βi is the fitting parameter. If supercooling is above a critical value, the face will break through the retardant layer, and the growth rate is expected to rise until it reaches the same velocity as that in a pure system. However, the kinetic curves R(ΔT) (Figure 5) obtained at COOH-PLL concentrations higher than 70 mg/mL show that the growth rate after recovery from the dead zone remains noticeably lower than R0 (in pure water), and, consequently, the kinetic coefficient of the surface decreases with an increase in the COOH-PLL concentration. This fact can be explained by the increase in viscosity of solutions and, therefore, the deceleration of transport rate of growth units (water molecules) from the solution to kinks on the surface. A similar phenomenon was observed in an earlier study on ice crystallization from saccharose solutions.22 The velocity of the movement of water molecules through the boundary layer from the bulk solution to a growing surface depends on the diffusion coefficient, which is inversely proportional to the viscosity of the solution as D ∼ 1/μ. For example, the viscosity of an aqueous solution containing 20 mg/mL of COOH-PLL is approximately 1 order of magnitude higher than the viscosity of water (see paragraph 3.3) and 3.6 times lower than the viscosity of a solution with CCP = 150 mg/mL. The kinetic coefficient of a rough face can be written as

Figure 9. Scheme of R(ΔT) kinetic curves in the case of hysteresis; R0 and Ri are growth rates in pure and additive doped systems (arrows show the direction of change in supercooling).

βi = A1D(CCP) exp( −E /k bT ) = A 2 (1/μ(CCP)) exp(−E /k bT )

during an increase in supercooling, the second value remains zero until ΔT = ΔTd2 and then sharply increases until the rate is close to R0 (curve 2, Figure 9). Growth rates R0i obtained from experimental data according to function 7 were used as an approximation to take into account the influence of viscosity of the solution on the kinetic coefficient of faces. Several studies describing the hysteresis phenomenon can be found in the literature.23−27 The model of Kubota23 offers only a qualitative level hysteresis of growth rates. Ferreira et al.,24 studying the growth of lysozyme crystals, developed a model which takes into account the density of kinks on growth steps. Miura and Tsukamoto25 also revealed hysteresis of step growth velocity in the presence of an impurity.

where A 1 and A 2 are constants independent of the concentration of COOH-PLL, μ(CCP) is the viscosity of the solution with COOH-PLL concentration CCP, and E is the activation energy associated with the barrier for incorporation of water molecules onto kinks. Figure 8 shows that the kinetic coefficient passes through a maximum at C CP = 40 mg/mL while increasing the concentration of cryoprotector. It seems that this behavior is connected to a change in the activation energy of water molecules at different COOH-PLL concentrations. We propose the following explanation for the data in Figure 8, though we still do not have any experimental evidence. An increase in the 10245

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degree of non-steady-state coverage of a face θneq can be calculated as

We have applied the model of Punin and Artamonova,27 which gives the relationship between growth rate and supercooling, to describe the hysteresis. Assume that COOHPLL molecules are located on an ice face in knots of a square net and that the surface percolates through the adsorbate layers during growth. The growth rate of a face in the presence of COOH-PLL molecules can be represented as (by analogy with the expression derived by Cabrera and Vermilyea28)

θneq = θ0·(θ /θ0) = θ0·y

where the ratio θ/θ0 = y was obtained from eqs 8 and 9 and θ0 was obtained from the approximation for ΔTd2 (steady-state adsorption of COOH-PLL). The average distance between COOH-PLL molecules adsorbed on a surface at ΔT = ΔTd1 is equal to Li = (C0θneq)−1/2, where C0 = 1.2 × 1012 cm−2. Then, we put ΔT = ΔTd1 and find from the Gibbs−Thomson relationship the calculated values for critical supercooling ΔTd1. Figure 6 shows that experimental and calculated values of ΔTd1 (non-steadystate adsorption) are close. From eqs 8 and 9 and experimental curves R(ΔT) at different COOH-PLL concentrations (20−150 mg/mL), we found the parameter B and estimated the characteristic time of adsorption of COOH-PLL molecules τ = hel/(B·R0i(ΔTd1)) (Figure 10), which varied from ∼0.04 s (CCP = 20 mg/mL) to ∼5 × 10−4 s (CCP = 150 mg/mL).

R i = R 0i(1 − dcrθ1/2)1/2

where dcr is the critical size given by the Gibbs−Thomson relationship. The degree of non-steady-state coverage of a face by inhibitors is ⎛ ⎛ ⎛ hel ⎞⎞ ⎛ t ⎞⎞ θ = θ0⎜1 − exp⎜ − ex ⎟⎟ = θ0⎜⎜1 − exp⎜ − ⎟⎟⎟ ⎝ τ ⎠⎠ ⎝ ⎝ R i(ΔT )τ ⎠⎠ ⎝

where θ0 is the degree of steady-state coverage at a given concentration of COOH-PLL in a solution, tex is the exposure time of a surface or, in other words, the time during which a surface is available for adsorption, τ is the characteristic time of adsorption of COOH-PLL molecules, hel = 4.5 × 10−8 cm is the height of the elementary layer of ice, and Ri(ΔT) is the normal growth rate of the face. Finally, we obtain the following set of equations: 1/2 ⎞1/2 ⎛ ΔTd2 ⎛ θ ⎞ ⎟ Ri ⎜ = ⎜1 − x= ⎜ ⎟ ΔT ⎝ θ0 ⎠ ⎟⎠ R 0i ⎝

y=

⎛ B⎞ θ = 1 − exp⎜ − ⎟ ⎝ x⎠ θ0

(8)

(9)

Figure 10. Characteristic time of adsorption τ (in seconds on a logarithmic scale) of COOH-PLL molecules as a function of their concentration in solution.

where ΔTd2 is the critical supercooling in the case of steadystate adsorption, B = hel/(R0iτ). Solutions of these equations were studied in detail in previous work.27 Two stable solutions for the growth rate exist within the ΔTd1 ≤ ΔT ≤ ΔTd2 interval of supercooling, with one solution being equal to zero. The parameter ΔTd2/ΔT = 1 corresponds to the critical supercooling ΔTd2 during the steady-state adsorption of adsorbates. Here, only one solution x = 0 exists, and it corresponds to zero growth rate when the value of the parameter B is large (i.e., rapid adsorption of inhibitors). When B is smaller than a certain critical value, the second solution of x being close to unity appears. Thus, hysteresis appears as a critical phenomenon when the time of adsorption increases above a threshold value. By solving numerically eqs 8 and 9, we calculated kinetic curves for various COOH-PLL concentrations. It can be seen that the theoretical curves drawn by dotted lines in Figure 5 are in agreement with the experimental data. 4.4. Critical Supercooling for Non-Steady-State Adsorption of COOH-PLL Molecules. Non-steady-state adsorption of crystal growth inhibitors takes place when the time of their adsorption is longer than, or comparable to, the exposure time of a part of the surface. This phenomenon is clearly observed in the case of ice crystallization in the presence of COOH-PLL. During the decrease of supercooling, the dead zone width became smaller than ΔTd2 because at higher growth rates the surface concentration of COOH-PLL molecules did not have enough time to reach the equilibrium value. The

5. THE MECHANISM OF ICE GROWTH INHIBITION BY COOH-PLL In contrast to antifreeze proteins, which cause the appearance of the faces of a hexagonal prism or bipyramid, the addition of COOH-PLL did not lead to a change in ice crystal habitus. We only observed a decrease in the size of dendrite branches in comparison with the growth in pure water at the same supercooling. The absence of growth in a certain interval of small supercoolings is an apparent indication of the influence of COOH-PLL on ice crystallization. The inhibitory effect of COOH-PLL is much weaker than that of AFPs. In the presence of AFPs or antifreeze glicoproteins (AFGPs), depression of the freezing point appears at very small concentrations of about 0.05 mg/mL.29 In contrast, in the presence of COOH-PLL, depression of the freezing point occurred only when CCP was 20 mg/mL or higher. Although some AFGPs exhibit a low thermal hysteresis activity of ∼0.2 K at a concentration of 20 mg/mL,30 other AFGPs and type I AFPs have a higher efficiency at smaller concentrations than COOH-PLL. For example, for AFGPs, thermal hysteresis values equal to 0.8 K at 20 mg/mL were found30 and for AFPs ∼0.6 K at 7.5 mg/mL,31 whereas for COOH-PLL, we obtained a value of 0.3 K at 20 mg/mL. 10246

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According to past studies,32−37 biological macromolecules attach to the ice surface by formation of hydrogen bonds and by van der Waals interactions.31,36 How well the fragments of a macromolecule geometrically match the relief of the ice surface plays a crucial role. For example, AFPs extracted from the winter flounder bind well to the faces of a hexagonal bipyramid and suppress ice growth in this direction.35,38 AFGP molecules having helical structures with a size close to the periodic structure of the ice surface bond tightly onto prism faces by means of hydrogen bond formation.33,39 Thus, the weak influence of COOH-PLL compared to that of AFPs on ice crystallization can be explained by peculiarities of the structure of COOH-PLL molecules and their interaction with the ice surface. It is difficult to choose fragments in COOH-PLL molecules that match the relief of the ice surface well. A COOH-PLL molecule can bind to ice by hydrogen bonds on a hydroxyl group on the residue tails or by van der Waals interactions. Intact PLL molecules without COOH groups (i.e., before carboxylation) do not exhibit any cryoprotective properties. The small molecular weight of COOH-PLL in comparison with AFPs also possibly favors weak COOH-PLL adsorption. The smaller the weight of the adsorbed molecule, the greater the probability of it breaking away from the crystal surface because of thermal fluctuations. Various authors have proposed different models to explain the depression of the freezing point of ice in the presence of AFPs. One proposed mechanism is that an adsorbing AFP increases the step energy (line tension) and, therefore, the energy barrier for the creation of 2D nuclei.40 It should be noted that the representations mentioned above are applicable to basal faces growing by a layer-by-layer mechanism.38 However, in the direction perpendicular to the c-axis, the ice surface is atomically rough in the temperature range used, and the existence of steps is not needed for growth. According to Raymond et al.,5 molecules of an AFP adsorb on the surface like a net and impede step advancement. Parts of the steps percolating through the net increase the curvature. As a result, according to the Gibbs−Thomson effect, a lower temperature for freezing is necessary. Sander and Tkachenko41 solved a three-dimensional problem when biological antifreezes acting like “stones on pillow” pin the growing surface penetrating through the retarding net. However, in that model, irreversible adsorption of AFP molecules and their following capture by the growing crystal is assumed, whereas later experimental studies have shown that the character of adsorption depends on the type of AFP. For example, AFP type III adsorbs irreversibly,42 but AFGP is expected to stop ice growth at reversible adsorption.43 Adsorption of COOH-PLL molecules is relatively weak, and it most probably occurs in a reversible manner, as is indicated by the absence of a change in the ice crystal habitus and its poor ability to reduce the freezing point (a large concentration of COOH-PLL being necessary to stop growth). The results presented in paragraph 4.1 (Figure 7) show that the average distance between adsorbed COOH-PLL molecules was longer than the estimated average distance between adsorption sites on the surface. It seems therefore that the surface is not completely covered by COOH-PLL, and some free sites for adsorption of COOH-PLL molecules still remain. However, the concentration of adsorbates is sufficient to block the movement of the surface. Therefore, at a mesoscale level, growth of the surface with adsorbed inhibitors is controlled by the Gibbs−Thomson effect. Although our model can explain the experimental results well, at present, we do not have direct

evidence for adsorbed COOH-PLL molecules on the ice crystal surface. In the future, we plan to perform observations with COOH-PLL molecules labeled with a fluorescent dye to study in detail their adsorption. The ice growth rate at a constant supercooling nonmonotonically changed with increasing concentration of COOH-PLL, as shown in Figure 5. Possible reasons for this unexpected result may be a reduction of the activation energy for incorporation of molecules into kinks or better heat liberation from dendrite tips, since the dendrite branches are slightly thinner than those in pure water. The further decrease in the growth rate when the COOH-PLL concentration was larger than 40 mg/mL can be explained by the increase in solution viscosity and an accompanying reduction of the diffusion coefficient of water molecules from the solution to the ice surface. The hysteresis observed for the dependence between growth rate and supercooling indicates that the adsorption process of COOH-PLL molecules on the ice surface is fairly slow. While the crystal face grew sufficiently fast, the actual number of COOH-PLL molecules on an ice surface was less than the threshold value that was necessary to stop growth. However, when the growth rate decreased below a certain critical level, the number of adsorbates on the surface reached an equilibrium value. When the average distance between adsorbed inhibitors was less than a critical size given by the Gibbs−Thomson relationship, the growth rate dropped to zero. A considerably large supercooling was required to resume the face growth, so that penetration of the surface through the adsorbate net occurred. The characteristic time of adsorption τ of COOHPLL molecules depends on their concentration in the bulk solution. It follows from Fick’s law of diffusion that the average velocity of diffusing molecules is directly proportional to the gradient of its concentration and diffusion coefficient. This can be seen from the estimated value obtained for time τ during consideration of hysteresis for growth rates. The higher the concentration of COOH-PLL molecules in solution, the more rapid their adsorption. However, the viscosity of the solution increases with an increase in the COOH-PLL concentration, and the diffusion coefficient of cryoprotector molecules to the surface becomes smaller. As a result, time τ actually does not decrease when the COOH-PLL concentration is 70 mg/mL or higher (Figure 10). The upper value of the exposure time of a part of growing surface tex (i.e., the time when a part of the surface is available for adsorption) can be estimated as tex = hel/ Rd ≈ 4.5 × 10−5 s, where hel = 4.5 × 10−4 μm is the height of the elementary layer in a growth direction and Rd ∼10 μm/s is the velocity at supercooling below which the growth rate falls to zero (Figure 5). Time τ is about 10 times longer than tex at CCP = 150 mg/mL. Thus, the actual surface concentration of adsorbed COOH-PLL molecules during ice growth is smaller than their equilibrium value.

6. CONCLUSIONS We studied the morphology and growth kinetics in the direction of the a-axis of ice crystals in water containing COOH-PLL. An ice crystal has a disk-like shape at small supercoolings (up to 0.2−0.3 K) with the top and bottom planes being basal {0001} faces. Further increase in supercooling leads to the formation of dendrites with branches parallel to the {0001} faces. The change to dendritic growth in the presence of COOH-PLL occurs at a lower degree of supercooling than it does in pure water. The increase in 10247

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(7) Budke, C.; Koop, T. Ice Recrystallization Inhibition and Molecular Recognition of Ice Faces by Poly(vinyl alcohol). ChemPhysChem 2006, 7, 2601−2606. (8) Mizrahy, O.; Bar-Dolev, M.; Guy, S.; Braslavsky, I. Inhibition of Ice Growth and Recrystallization by Zirconium Acetate and Zirconium Acetate Hydroxide. PLoS One 2013, 8, e59540. (9) Huang, M. L.; Ehre, D.; Jiang, Q.; Hu, C.; Kirshenbaum, K.; Ward, M. D. Biomimetic Peptoid Oligomers as Dual-action Antifreeze Agents. Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 19922−19927. (10) Matsumura, K.; Hyon, S. H. Polyampholytes as Low Toxic Efficient Cryoprotective Agents with Antifreeze Protein Properties. Biomaterials 2009, 30, 4842−4849. (11) Matsumura, K.; Hayashi, F.; Nagashima, T.; Hyon, S. H. Longterm Cryopreservation of Human Mesenchymal Stem Cells Using Carboxylated Poly-L-lysine without the Addition of Proteins or Dimethyl Sulfoxide. J. Biomater. Sci., Polym. Ed. 2013, 24, 1484−1497. (12) Fu, G.; Qiu, S. R.; Orme, C. A.; Morse, D. E.; De Yoreo, J. J. Acceleration of Calcite Kinetics by Abalone Nacre Proteins. Adv. Mater. 2005, 17, 2678−2683. (13) De Yoreo, J. J.; Dove, P. M. Shaping Crystals with Biomolecules. Science 2004, 306, 1301−1302. (14) Elhadj, S.; Salter, A.; Wierzbicki, A.; De Yoreo, J. J.; Han, N.; Dove, P. M. Polyaspartate Chain Length as a Stereochemical Switch for Control of Calcite Growth and Morphology. Cryst. Growth Des. 2006, 6, 197−201. (15) Zepeda, S.; Nakatsubo, S.; Furukawa, Y. Apparatus for Single Ice Crystal Growth from the Melt. Rev. Sci. Instrum. 2009, 80, 115102-1− 115102-4. (16) Chernov, A. A.; Givargizov, E. J.; Bagdasarov, K. S.; Kuznetsov, V. A.; Demianets, L. N.; Lobachev, A. N. Modern Crystallography III: Crystal Growth; Springer-Verlag: Berlin, 1984; p 517. (17) Langer, J. S.; Sekerka, R. F.; Fujioka, T. Evidence for a Universal Law of Dendritic Growth Rates. J. Cryst. Growth 1978, 44, 414−418. (18) Ketcham, W. M.; Hobbs, P. V. An Experimental Determination of the Surface Energies of Ice. Philos. Mag. 1969, 19, 1161−1173. (19) Hollomon, J. H.; Turnbull, D. Nucleation. Prog. Met. Phys. 1953, 4, 333−388. (20) Fletcher, N. H. The Chemical Physics of Ice; Cambridge University Press: Cambridge, U.K., 1970; p 272. (21) Tirmizi, S. H.; Gill, W. N. Effect of Natural Convection on Growth Velocity and Morphology of Dendritic Ice Crystals. J. Cryst. Growth 1987, 85, 488−502. (22) Gonda, T.; Sei, T. The Inhibitory Growth Mechanism of Saccharides on the Growth of Ice Crystals from Aqueous Solutions. Prog. Cryst. Growth Charact. Mater. 2005, 51, 70−80. (23) Kubota, N.; Yokota, M.; Doki, N.; Guzman, L. A.; Sasaki, S.; Mullin, J. W. A Mathematical Model for Crystal Growth Rate Hysteresis Induced by Impurity. Cryst. Growth Des. 2003, 3, 397−402. (24) Ferreira, C.; Rocha, F. A.; Damas, A. M.; Martins, P. M. On Growth Rate Hysteresis and Catastrophic Crystal Growth. J. Cryst. Growth 2013, 368, 47−55. (25) Miura, H.; Tsukamoto, K. Role of Impurity on Growth Hysteresis and Oscillatory Growth of Crystals. Cryst. Growth Des. 2013, 13, 3588−3595. (26) Vorontsov, D. A.; Kim, E. L.; Portnov, V. N.; Chuprunov, E. V. Growth of Filamentary KDP Crystals from Solution with the Addition of Al(NO3)3·9H2O. Crystallogr. Rep. 2003, 48, 335−338. (27) Punin, Yu. O.; Artamonova, O. I. Hysteresis of the Growth Rates of KH2PO4 Crystals. Kristallographiya 1989, 34, 1262−1266. (28) Cabrera, N.; Vermilyea, D. A. The Growth of Crystals from Solution. Growth and Perfection of Crystals; Wiley: New York, 1958; pp 393−410. (29) Knight, C. A.; DeVries, A. L. Ice Growth in Supercooled Solutions of a Biological “Antifreeze”, AFGP 1−5: an Explanation in Terms of Adsorption Rate for the Concentration Dependence of the Freezing Point. Phys. Chem. Chem. Phys. 2009, 11 (27), 5749−5761. (30) Wu, Y.; Banoub, J.; Goddard, S. V.; Kao, M. H.; Fletcher, G. L. Antifreeze Glycoproteins: Relationship Between Molecular Weight, Thermal Hysteresis and the Inhibition of Leakage from Liposomes

COOH-PLL concentration inhibits growth of the faces of ice crystals at a fixed supercooling. An interval of critical supercooling (dead zone), in which ice growth is blocked, exists when the concentration of COOH-PLL is 20 mg/mL or higher. The growth rate sharply increases when supercooling reaches a critical value. Depression of the melting point of ice has not been revealed in water with COOH-PLL additives. The width of the dead zone increases nonlinearly when the COOHPLL concentration becomes higher. The blocking effect of COOH-PLL molecules is explained on the basis of the Gibbs− Thomson law and under the assumption of Langmuir’s dynamics of COOH-PLL adsorption. Calculated values of critical supercooling for different concentrations of cryoprotector are in agreement with obtained experimental data. The viscosity of solutions becomes considerably higher with an increasing concentration of COOH-PLL. This fact makes it necessary to take into account reduction of the diffusion coefficient of water molecules to kinks. Hysteresis of the dead zone width and in growth rates of ice crystals was revealed. It has been shown that hysteresis appears due to slow adsorption of COOH-PLL molecules. On the basis of the model proposed by Punin and Artamonova describing hysteresis of growth rates, we obtained theoretical growth rates for different COOH-PLL concentrations, which correspond to measured curves, and estimated the characteristic time of adsorption of COOH-PLL molecules. Adsorption of COOH-PLL molecules during ice crystallization has a non-steady-state character and occurs more slowly than the process of embedding of crystal growth units. Thus, our study of the activity of COOH-PLL on formation of ice shows that this compound exhibits antifreeze properties and can be suggested as an alternative to natural AFPs.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +79101316701. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support by Japan Society for the Promotion of Science and Japan Russia Youth Exchange Center is gratefully acknowledged. The work presented here was supported in part as a Collaborative Research Project organized by the Interuniversity Bio-Backup Project (IBBP).

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REFERENCES

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