Effect of Hydrogen Bonds on Crystallization Kinetics of Aqueous Solutions of Cryoprotective Agents

The temperature dependences of volume for aqueous solutions of DMSO and glycerol under various concentrations during their cooling down to –150°C and subsequent heating up to 25°C were studied in details in this paper. It was shown that within the range of 30–70% weight concentrations of cryoprotective substances these dependences differed greatly at cooling stages and during subsequent thawing. It has been also found that within the studied concentration range there was a sharp increase in volume for glycerol solutions when heated above the glass transition temperature, and vice versa, a sharp reduction in DMSO solution volume. It has been noted that the observed volume effects fit well within the concept of cluster crystallization of cryoprotective solutions, taking into account a weak HB-interaction between the components. On the basis of the findings the structure of the formed cluster particles was analyzed. It has been shown that the surface layers from the molecules of cryoprotective agent surrounding ice microcrystals can be of either crystalline or amorphous structure. The effect of these differences on protective properties of cryoprotectants was examined.

With a decrease in temperature the situation changes dramatically.In particular, even at T < -50...-70°C the value ω is reduced down to the values of about 10 s -1 and lower, i. e. the stability of AB associates increases sharply, as evidenced by the results of infrared spectroscopy [11] and diffraction of slow neutrons [18,[21][22][23].This eliminates virtually the formation of single crystals of ice and cryoprotective substances in a cooled solution below a certain temperature T c .As a result, stable AB associates transform into a solid-phase state either as an amorphous fraction [1-4, 19, 20] or hydrate phase β c [12,24,25], which is contrary to the eutectic crystallization regularities.
To explain the contradictions between theoretical and experimental data a model of cluster crystallization was proposed [12][13][14] as well as the principles of obtaining the phase diagrams, including the areas of the cluster phase β с existence [14].However, to date there is no clear experimental evidence of this model applicability in the widely applied cryoprotective solutions.This is largely due to the fact that practical cryobiology considers the survival of biological objects associated with the kinetics of crystallization of the solutions at T > T c and the majority of researches is devoted to the study of this particular temperature range.At the same time the cluster crystallization proceeding at T < T c and caused by HB-bonds between the water molecules and cryoprotective agents can have a significant impact on the quality of the crypreserved biomaterial.
In this regard, the aim of this work was to study the crystallization and melting of the solutions with a weak molecule-to-molecule relationship of the components using a specially developed method of differential volume scanning tensodilatometry.

Materials and methods
The regularities of forming the cluster β с phase during cooling-warming of aqueous solutions of cryoprotective agents were experimentally studied using a differential microvolume scanning tensodilatometer, the concept of which was previously described in details [12].The device main part consists of a differentially mounted main and reference measuring units containing the combined bellows inserts transforming the volume changes of the tested solutions into linear transitions of drawing power.
Experiments were performed in aqueous solutions of glycerol, double distilled under vacuum, and DMSO (Arterium, Ukraine).The solutions were prepared on the base of a bidistilled water with a delay for at least 20 hrs at 40°C and multiple mixing.The tested solutions were loaded with a special vacuum adjustment, providing outgassing of the fluids and units prior to the experiment.
The used weight concentrations for cryoprotective agent was within the range from 5 to 100%.The mass of the tested solution was determined with ± 10 -3 g accuracy.
Dependences of the volume of cryoprotective solutions vs. temperature within the range of 25...-150°C were investigated under the same rates of cooling and subsequent warming, i. e. 1 deg/min.Herewith, the estimation of the effect of temperature gradient in measuring units on the appearance of tensodilatograms was performed in two types of units: with V 0 = 10 cm 3 and V 0 = 1 cm 3 .Then the results were comparatively analyzed.

Results and discussion
The basic idea of applying the method of volume scanning tensodilatometry when studying the phenomenon of cluster crystallization of aqueous solutions resulting from HB-interactions of the components consists in the presence of different volume effects during crystallization of water and cryoprotective substances.It is known that during the water-ice phase transition the volume of the system is increased by 8.2%.At the same time the crystallization of most cryoprotective substances occurs with a decrease in the volume of the system within the range from 2 to 5% depending on the type of substance.In case if a cryoprotective agent does not crystallize under the experimental conditions and transits into an amorphous state, its volume reduces also by 0.1-0.3%.These facts could provide an information about the structure of the formed cluster phase particles, which essentially depends on the type of AB associates, appearing in a cooled aqueous solution due to hydrogen bonds.
Typical tensodilatograms V = V(T), reflecting the volume changes in the investigated aqueous solutions of various weight concentrations of DMSO or glycerol during their cooling and subsequent thawing within a temperature range of 20...-150°C with the rates of Представленный диапазон концентраций криопротекторных веществ C B = 30-70% является The presented concentration range of cryoprotective substances C B = 30-70% is the most interesting when studying the kinetics of crystallization and melting of the cluster phase β с [13,14].These particular concentrations are characteristic for liquid microphases forming in the solutions with typical for practical cryobiology initial concentrations of C B = 5-15% to the moment they reach the temperature interval of the cluster crystallization T c …T g [2-4, 6, 12, 19, 20, 24, 25].
The analysis of curves V = V(T) showed a significant dependence of the shape of the obtained tensodilatograms vs. the initial concentration of cryoprotective solution as well as a prominent difference of tensodilatograms obtained during cooling and subsequent warming.
Thus, in tensodilatograms obtained during cooling of the solutions with an initial concentration C B < 60% we have found only the stages of thermal contraction of the solutions within the temperature range of 20°C…T L -, as well as the stages of samples' volume increasing at the temperatures below the crystallization Рис. 1. Тензодилатограммы водных растворов с концентрацией ДМСО: A -30%; B -40%; C -55%; D -65%; охлаждение -сплошная линия, отогрев -пунктирная линия.onset point and the stage of a weak dependence of the samples' volume vs. the temperature below the vitrification point T g .Tensodilatograms of the cooled solutions with initial mass concentrations of DMSO higher than 60% and glycerol above 65% are of two-stage character: almost linear decrease in volume as the temperature decreases, characteristic of the thermal fluid compression within the temperature range of 20°C…T g and approaching the plateau below the vitrification temperature T g .
Аналогичные стадии можно выделить и на тензодилатограммах нагреваемых водных растворов глицерина, однако поведение кривой V + (T) на стадиях 2 и 3 (рис.2) принципиально отличается от ее поведения на этих стадиях в случае водных coincided with the dependence V -(T) obtained within the same temperature range during preliminary cooling; 2 -corresponded to the deviation between dependencies V + (T) and V -(T) due to uneven reduction of the system volume; 3 -characterized by a sharp increase in the system volume; 4 -characterized by a decrease in the system volume resulted from the melting of the ice crystals formed during cooling; 5 -corresponded to the almost linear increase in the system volume, characteristic of the thermal volume expansion of heated liquid and is described by the expression where ∆V is the change in volume of the studied solution during its heating by the value ∆T; V L -volume of the solution at T L + temperature, i.e. at the end of melting of ice crystals; β -coefficient of thermal volumetric expansion of the solution within the corresponding temperature range.
A slight mismatch between the dependencies V + (T) and V -(T) observed at this stage is caused by different temperature distribution along the tensodilatometer unit during cooling and heating.
Similar stages can be also found in tensodilatograms of the heated aqueous solutions of glycerol, however, the behavior of the curve V + (T) at the stages 2 and 3 (Fig. 2) is fundamentally different from its behavior during these stages for DMSO aqueous solutions (Fig. 1).In particular, a deviation between the dependencies V + (T) and V -(T) is observed at the stage 2, caused by a significant increase in the system volume.This is the reverse to the appearance of V + (T) dependence for DMSO solutions and does not correspond to the processes occurred in the tested solutions at the cooling stage as well.In turn, stage 3 is characterized by the curve V + (T) approaching to the plateau.In the heated solution this could be possible only if there are deleloping the processes, which lead to a decrease in the system volume, in such a way compensating a normal thermal expansion.
Comparing the series of tensodilatograms obtained for the solutions of DMSO (Fig. 1) and the ones of glycerol (Fig. 2) clearly showed the dependence of the shape of the dependences V + (T) within a particular stage as well as the total number of stages on the initial concentration of the solution.For example, the tensodilatogram of heated solution with a DMSO concentration C B = 65% had no stage 4 being typical for lower concentrations (see Fig. 1D).It is very prominent in the Fig. 2 tensodilatograms of the glycerol solutions under heating.The tensodilatogram of the solution containing 57% glycerol has five clearly distinguished stages (Fig. 2B).At the same time, the tensodilatograms of the heated solutions with glycerol concen- tration of 70% and above (Fig. 2D) contain only two stages corresponding to devitrification of amorphous fraction and a liquid phase thermal expansion.
Using the obtained tensodilatograms it is easy to construct a state diagram of the tested solutions.These diagrams for the water-DMSO and water-glycerol systems are shown in Fig. 3A, B. The procedure involved T L -and T с -parameters characterizing the boundaries of stages when cooling the solutions, as well as T L + and T с + parameters, reflecting these boundaries during their subsequent heating.
The discrepancy between the shape of phase diagrams, obtained when cooling and subsequent heating the solutions, requires a detailed analysis.Previously, there was a belief that such a mismatch can arise only if −  T & >> + T & where − T & and + T & were the rates of cooling and subsequent heating of the investigated solutions, respectively [24,25].The presented in Fig. 3A diagrams of states were obtained if T & , i. e. the duality of diagrams occurring within the range of C g -…C g + concentrationsis was characteristic for any ratios of rates − T & and + T & since physical states, passed during heating of the solution differed from a set of states characteristic for cooling.
Thus, according to the diagrams (Fig. 3A, B; solid lines), cooling the solution with an initial concentration CN B < C g -was accompanied with the formation of ice crystals A S at the temperature T L -, finished after reaching temperature T g and concentration C g -.Following heating of the solution with the same absolute rate of the temperature change is described with the state diagram, based on the points T L + and T c + (see Fig. 3A, B; dotted lines).Therefore, a phase trajectory corresponding to heating of the solution constructed in T -C B coordinates, will deviate from that of cooling.
According to the trajectory of warming the particles of the cluster phase β с are formed and then melt in a solution within the T g …T c + temperature range.Formation of the maximal amount of the clustered phase β с in this case corresponds to the deviation of the liquid phase concentration from the values of T L -diagram by ∆CN aS .This deviation causes a volume effect ∆VN aS , which affects the shape of the obtained tensodilatograms.In particular, in the tensodilatogram of the solution with a concentration of 57% glycerol satisfying the condition CN B < C g -(see Fig. 2, B), the stage 2 corresponds to cluster crystallization, which is accompanied by an increase in the system volume, i. e.
where ∆VN L -increase in the system volume due to thermal expansion of liquid fractions arised in the sample after devitrification.Stage 3 in Fig. 2B где ∆VN L -увеличение объема системы за счет to the melting of A S ice crystals formed during precooling.Stage 5 demonstrates thermal expansion of the solution with concentration CN B in accordance with the expression (1).
In its turn, cooling the solution with concentration CO B > C g -, as proceeds from diagrams (see.Fig. 3), will lead to a complete vitrification at the temperature of T g without any intermediate phase transitions.Further heating of the solution is described by a curve characteristic to a cluster crystallization with a maximal volume effect ∆VO aS .Melting processes of the formed β с phase particles are completed at the temperature T c + .Tensodilatograms shown in Fig. 2C correspond to the trajectories of cooling and heating.It is seen that during the solution cooling, a thermal contraction with subsequent vitrification is observed.During thawing a sharp extra increase in the solution volume occurs due to cluster crystallization (stage 2).In this case, stage 3 reflects the subsequent melting of cluster phase β с and there is no stage 4, corresponding the melting of individual ice crystals A S .
With further rise in the initial solution concentration the amount of β с phase formed during thawing and the level of corresponding volume effects diminish   [18].
Модель кластерной кристаллизации [2, 17, 18] объясняет и существенное различие между тензодилатограммами, соответствующими отогреву appearance of dependence m β (C B ) in the concentration range is easily explained on the basis of the cluster crystallization model.According to this model the index m β will enhance within the C 0 …C g concentration range with the rise in the amount of cryoprotective agent molecules and associates A n B m , capable of forming clusters.Thereafter the m β value will be reduced to zero, since there are not enough water molecules A in the C c …C g interval.Finally, the dependence m β (C B ) passes through a maximum at C B = C c [19].
Cluster crystallization model [12][13][14] explains also a significant difference between tensodilatograms corresponding to a heating of aqueous solutions of glycerol (see Fig. 2) and DMSO (see Fig. 1).In the first case, the envelope consisting of cluster particles is entirely amorphous, since glycerol does not crystallize in used in this research regimens of cooling-heating (Fig. 4).In these solutions, no phase transitions occur and there is only an usual thermal contraction or expansion of the liquid phase in accordance with the expression (2) and the reaching the plateau at T < T g , which corresponds to the solution vitrification.
The obtained results could be compared with the data of differential thermal analysis and differential scanning calorimetry, e. g.Fig. 1,B shows a thermogram obtained during heating of DMSO aqueous solution with concentration C B = 40% [19].In the thermogram an endothermic peak I corresponds to melting of cluster particles and endothermic peak II depicts the melting of ice crystals A S .Since thermal effects resulting from melting of cluster core and its crystalline envelope are summed, the thermograms obtained by means of differential thermal analysis or differential scanning calorimetry have only one peak for the melting of particles.This does not enable to draw conclusions about the structure of the clusters, which plays a decisive role in the formation of possible mechanisms of injury to biological objects in cluster crystallization.One of the major factors in this case, as well as during melting, is the structure of cluster particle envelope.If during its formation the molecules   [7].Естественно, что в этом случае вначале кластеры будут образовываться из комплексов с максимальным количеством связанной воды, а по мере понижения температуры в процесс будут включаться менее гидратированные молекулы.Это объясняет тот факт, что образование кластеров фазы β c происходит в широком диапазоне температур T c0 …T g , а не при T = T eut = const, как это требует эвтектическая кристаллизация.
Кроме того, сделанные нами предположения [2] о структуре кластерных частиц объясняют природу большинства регистрируемых объемных эффектов, сопровождающих фазовые переходы в исследуемых криопротекторных растворах.Разницу в кинетике кристаллизации и последующего плавления водных растворов ДМСО и глицерина можно объяснить с помощью представлений о тонкой структуре кластерных частиц.Они дают of cryoprotective substances transform into a crystalline state, then the accompanying this process volume effects will be negative in value and will compensate an increase in volume caused by the particle core formation from water molecules.The resulting total volume effect during cluster formation will be minimal, especially if considering a spontaneous occurrence of the latter, i. e., the core and envelope are formed almost simultaneously.In the case of amorphous structure of cluster particle envelope it is formed with a substantial increase in volume, similar to volume effects during water crystallization.This can cause drastic changes in the structure of frozen biological systems, especially at the stages of the cluster crystallization of cryoprotective solutions.
An analysis of the tensodilatograms experimentally obtained in this study supports the hypothesis of cluster crystallization of the solutions with HB-interacting components.According to this hypothesis [12][13][14] at initial C B < C g concentrations the cluster particles of β с phase are composed of ice microcrystals a S surrounded by the molecules of cryoprotective agent B, being either in amorphous b g or crystalline b S states [13,14].The possibility of microcrystals a S formation appears at quite low temperatures, when the size of the critical ice crystal nuclei are so small that they can be formed by joining the A n B m associates into clusters without breaking the hydrogen A-B bonds.Herewith the number of water molecules in a cluster formed should satisfy the conditions of a critical nucleus emergence within a particular temperature range [5].Naturally, in this case the clusters will be formed primarily from the associates with the maximum amount of bound water and the process will involve the less hydrated molecules with decrease of the temperature.This explains the fact that the formation of clusters of the β с phase occurs over a wide temperature range T c0 …T g , and not at T = T eut = const, as required by eutectic crystallization.
T ~ T g should be taken into account.At these temperatures, most liquid microphases are the inclusions, closed into solid-phase matrix.Therefore, the cluster crystallization, leading to an increase in the system volume, causes therein a pressure rise, resulting in the plastic shifts in the matrix [23] and, as a consequence, in an injury of the frozen biological objects.This fact requires a detailed study of the cluster crystallization of different cryoprotective solutions.It is entirely possible, that the proper selection of cryoprotective compositions as well as cooling and warming modes of cryopreserved biological objects requires a certain classification of cryoprotectants by the parameters of the cluster crystallization of the latter.

Conclusions
Thus, a weak interaction between water molecules and cryoprotective substances in DMSO and glycerol solutions at low temperatures leads to the formation of a cluster phase.Herewith the structure of the formed cluster particles depends on the type of cryoprotective agent and concentration of the solution tested.This is confirmed by the observed volume effects that accompany cooling of the solution and subsequent heating.These effects pass through a maximum within the concentrations range of cryoprotective agents (30-70%).Their decrease at C < 30% is related to reducing the formed by hydrogen binding associates A n B m due to small amount of cryoprotectant molecules.Meanwhile at C > 70% this was due to a reduction in the number of associates A n B m in the solution related to a lack of water molecules.
The twin diagrams of state plotted by the recorded dependencies V = V(T) for DMSO and glycerol aqueous solutions, including the region of the cluster phase existence, fully explain all the observed features of the crystallization and melting of these solutions.
The obtained diagrams of state were for the first time used to describe the solutions with weak moleculeto-molecule relationship of the components.

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http://dx.doi.org/10.15407/cryo26.03.199 проблемы криобиологии и криомедицины problems of cryobiology and cryomedicine том/volume 26, №/issue 3Initial temperature of solution to be cooled Т m Melting temperature of pure component either A or B T S Crystallization temperature of pure component either A or B T c Crystallization temperature of solution Т g Vitrification (devitrification) temperature of highly concentrated liquid fractions Т L Temperature parameters of liquidus line when cooling solution Т L Temperature parameters of liquidus line when heating frozen solution Т eut Eutectics temperature T C Temperature of cluster crystallization onset when cooling the solution Т C Temperature of ceasing the melting of clusters when heating C B Mass concentration of cryoprotective substance B C 0 , C C , Concentration parameters of diagram