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NASA NTRS1992

Control of solvent evaporation in hen egg white lysozyme crystallization

An investigation of the role of solvent evaporation in tetragonal lysozyme crystallization was preformed with a device that employs N2(g) to control the evaporation of solvent from a micro-volume crystallization hanging drop. The number of crystals was found to vary with the rate at which the final supersaturation level was achieved. It was found that the more rapid the approach to supersaturation the larger the number of crystals. Accordingly, the crystals reached a smaller terminal size. Elongation of the (110) face parallel to the four-fold axis was observed with the slower evaporation rates.

Wilson, L. J.↗
NASA NTRS1992

Crystal growth in a microgravity environment

Gravitational phenomena, including convection, sedimentation, and interactions of materials with their containers all affect the crystal growth process. If they are not taken into consideration they can have adverse effects on the quantity and quality of crystals produced. As a practical matter, convection, and sedimentation can be completely eliminated only under conditions of low gravity attained during orbital flight. There is, then, an advantage to effecting crystallization in space. In the absence of convection in a microgravity environment cooling proceeds by thermal diffusion from the walls to the center of the solution chamber. This renders control of nucleation difficult. Accordingly, there is a need for a new improved nucleation process in space. Crystals are nucleated by creating a small localized region of high relative supersaturation in a host solution at a lower degree of supersaturation.

Kroes, Roger L.↗
NASA NTRS1991

Ground based experiments on the growth and characterization of L-Arginine Phosphate (LAP) crystals

L-Arginine Phosphate (LAP) is a new nonlinear optical material with higher efficiency for harmonic generation compared to KDP. Crystals of LAP were grown in the laboratory from supersaturated solutions by temperature lowering technique. Investigations revealed the presence of large dislocation densities inside the crystals which are observed to produce refractive index changes causing damage at high laser powers. This is a result of the convection during crystal growth from supersaturated solutions. It is proposed to grow these crystals in a diffusion controlled growth condition under microgravity environment and compare the crystals grown in space with those grown on ground. Physical properties of the solutions needed for modelling of crystal growth are also presented.

Rao, S. M.↗
NASA NTRS1994

The effects of temperature and NaCl concentration on tetragonal lysozyme face growth rates

Measurements were made of the (110) and (101) face growth rates of the tetragonal form of hen egg white lysozyme at 0.1M sodium acetate buffer, pH 4.0, from 4 to 22 C and with 3.0%, 5.0%, and 7.0% NaCl used as the precipitating salt. The data were collected at supersaturation ratios ranging from approximately 4 to approximately 63. Both decreasing temperature and increasing salt concentrations shifted plots of the growth rate versus C/C(sat) to the right, i.e. higher supersaturations were required for comparable growth rates. The observed trends in the growth data are counter to those expected from the solubility data. If tetragonal lysozyme crystal growth is by addition of ordered aggregates from the solution, then the observed growth data could be explained as a result of the effects of lowered temperature and increased salt concentration on the kinetics and equilibrium processes governing protein-protein interactions in solution. The data indicate that temperature would be a more tractable means of controlling the growth rate for tetragonal lysozyme crystals contrary to the usual practice in, e.g., vapor diffusion protein crystal growth, where both the precipitant and protein concentrations are simultaneously increased. However, the available range for control is dependent upon the protein concentration, with the greatest growth rate control being at the lower concentration.

Forsythe, Elizabeth↗
NASA NTRS1996

Diffusion, Viscosity and Crystal Growth in Microgravity

The diffusivity of TriGlycine Sulfate (TGS), Potassium Dihydrogen Phosphate (KDP), Ammonium Dihydrogen Phosphate (ADF) and other compounds of interest to microgravity crystal growth, in supersaturated solutions as a function of solution concentration, 'age' and 'history was studied experimentally. The factors that affect the growth of crystals from water solutions in microgravity have been examined. Three non-linear optical materials have been studied, potassium dihydrogen phosphate (KDP), ammonium dihydrogen phosphate (ADP) and triglycine sulfate (TGC). The diffusion coefficient and viscosity of supersaturated water solutions were measured. Also theoretical model of diffusivity and viscosity in a metastable state, model of crystal growth from solution including non-linear time dependent diffusivity and viscosity effect and computer simulation of the crystal growth process which allows simulation of the microgravity crystal growth were developed.

Myerson, Allan S.↗
NASA NTRS1996

Renal-Stone Risk Assessment During Space Shuttle Flights

The metabolic and environmental factors influencing renal stone formation before, during, and after Space Shuttle flights were assessed. We established the contributing roles of dietary factors in relationship to the urinary risk factors associated with renal stone formation. 24-hr urine samples were collected prior to, during space flight, and following landing. Urinary factors associated with renal stone formation were analyzed and the relative urinary supersaturation ratios of calcium oxalate, calcium phosphate (brushite), sodium urate, struvite and uric acid were calculated. Food and fluid consumption was recorded for a 48-hr period ending with the urine collection. Urinary composition changed during flight to favor the crystallization of stone-forming salts. Factors that contributed to increased potential for stone formation during space flight were significant reductions in urinary pH and increases in urinary calcium. Urinary output and citrate, a potent inhibitor of calcium-containing stones, were slightly reduced during space flight. Dietary intakes were significantly reduced for a number of variables, including fluid, energy, protein, potassium, phosphorus and magnesium. This is the first in-flight characterization of the renal stone forming potential in astronauts. With the examination of urinary components and nutritional factors, it was possible to determine the factors that contributed to increased risk or protected from risk. In spite of the protective components, the negative contributions to renal stone risk predominated and resulted in a urinary environment that favored the supersaturation of stone-forming salts. The importance of the hypercalciuria was noted since renal excretion was high relative to the intake.

Whitson, Peggy A.↗
NASA NTRS1996

Thermal Optimization of Growth and Quality in Protein Crystals

Experimental evidence suggests that larger and higher quality crystals can be attained in the microgravity of space; however, the effect of growth rate on protein crystal quality is not well documented. This research is the first step towards providing strategies to grow crystals under constant rates of growth. Controlling growth rates at a constant value allows for direct one-to-one comparison of results obtained in microgravity and on earth. The overall goal of the project was to control supersaturation at a constant value during protein crystal growth by varying temperature in a predetermined manner. Applying appropriate theory requires knowledge of specific physicochemical properties of the protein solution including the effect of supersaturation on growth rates and the effect of temperature on protein solubility. Such measurements typically require gram quantities of protein and many months of data acquisition. A second goal of the project applied microcalorimetry for the rapid determination of these physicochemical properties using a minimum amount of protein. These two goals were successfully implemented on hen egg-white lysozyme. Results of these studies are described in the attached reprints.

Wiencek, John M.↗
NASA NTRS1998

Ground Based Program for the Physical Analysis of Macromolecular Crystal Growth

During the past year we have focused on application of in situ Atomic Force Microscopy (AFM) for studies of the growth mechanisms and kinetics of crystallization for different macromolecular systems. Mechanisms of macrostep formation and their decay, which are important in understanding of defect formation, were studied on the surfaces of thaumatin, catalase, canavalin and lysozyme crystals. Experiments revealed that step bunching on crystalline surfaces occurred either due to two- or three-dimensional nucleation on the terraces of vicinal slopes or as a result of uneven step generation by complex dislocation sources. No step bunching arising from interaction of individual steps in the course of the experiment was observed. The molecular structure of the growth steps for thaumatin and lipase crystals were deduced. It was further shown that growth step advance occurs by incorporation of single protein molecules. In singular directions growth steps move by one-dimensional nucleation on step edges followed by lateral growth. One-dimensional nuclei have different sizes, less then a single unit cell, varying for different directions of step movement. There is no roughness due to thermal fluctuations, and each protein molecule which incorporated into the step remained. Growth kinetics for catalase crystals was investigated over wide supersaturation ranges. Strong directional kinetic anisotropy in the tangential step growth rates in different directions was seen. The influence of impurities on growth kinetics and cessation of macromolecular crystals was studied. Thus, for catalase, in addition to pronounced impurity effects on the kinetics of crystallization, we were also able to directly observe adsorption of some impurities. At low supersaturation we repeatedly observed filaments which formed from impurity molecules sedimenting on the surfaces. Similar filaments were observed on the surfaces of thaumatin, canavalin and STMV crystals as well, but the frequency was low compared with catalase crystallization. Cessation of growth of xylanase and lysozyme crystals was also observed and appeared to be a consequence of the formation of dense impurity adsorption layers. Attachment: "An in situ AFM investigation of catalase crystallization", "Atomic force microscopy studies of living cells: visualization of motility, division, aggregation, transformation, and apoptosis", AFM studies on mechanisms of nucleation and growth of macromolecular crystals", and "In situ atomic force microscopy studies of surface morphology, growth kinetics, defect structure and dissolution in macromolecular crystallization".

Malkin, Alexander J.↗
NASA NTRS1996

Repartitioning of NaCl and Protein Impurities in Lysozyme Crystallization

Nonuniform precipitant and impurity incorporation in protein crystals can cause lattice strain and, thus, possibly decrease the X-ray diffraction resolution. To address this issue, a series of crystallization experiments were carried out, in which initial supersaturation, NaCl concentration, protein purity level and crystallized fraction were varied. Lysozyme and protein impurities, as well as sodium and chloride were independently determined in the initial solution, supernatant and crystals. The segregation coefficients for Na(+) and Cl(-) were found to be independent of supersaturation and NaCl concentration, and decreased with crystallized fraction/crystal size. Numerical evaluation of the extensive body of data, based on a nucleation-growth- repartitioning model, suggests a core of approx. 40 microns in which salt is incorporated in much greater concentrations than during later growth. Small crystals containing higher amounts of incorporated NaCl also had higher protein impurity contents. This suggests that the excess salt is associated with the protein impurities in the core. X-ray topography revealed strain fields in the center of the crystals comparable in size to the inferred core. The growth rates of crystals smaller than 30-40 pm in size were consistently 1.5-2 times lower than those of larger crystals, presumably due to higher chemical potentials in the core.

Vekilov, Peter G.↗
NASA NTRS1998

The Effect of Solution Parameters on Lysozyme Nucleation Rates and Crystal Quality

In the pursuit of strongly diffracting high quality macromolecule crystals of suitable volume, this study investigates how the formation of macromolecules in solution and their growth characteristics effect crystal volume and diffracting quality. We systematically investigated the effect of solution conditions on lysozyme nucleation rates and the volume of crystals produced. Batch crystallization plates were used in combination with a video microscope system to measure nucleation rates and crystal volume. As expected from classical nucleation theory, crystal numbers were found to increase with increases in temperature and supersaturation. Small changes in solution pH, at constant supersaturation values were found, however, to dramatically effect the number of crystals nucleated in the wells varying from 1000s to 10s in the pH range 4.0 to 5.2. Having optimized the conditions required to produce an appropriate number of crystals of a suitable volume for X-ray analysis, a large number of uniform crystals were produced under exactly the same conditions. In the X-ray analysis of more than 50 such crystals there was found a wide variation in crystal lattice parameters and data quality. The variation in X-ray quality crystal samples is thought to be related to the growth rate variation caused by growth rate dispersion seen in lysozyme crystal growth experiments.

Judge, R. A.↗
NASA NTRS1998

The Effect of Temperature and Solution pH on Tetragonal Lysozyme Nucleation Kinetics

Part of the challenge of macromolecular crystal growth for structure determination is obtaining an appropriate number of crystals with a crystal volume suitable for x-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of supersaturation, temperature and pH on the nucleation rate of tetragonal lysozyme crystals. Batch crystallization plates were prepared at given solution concentrations and incubated at set temperatures over one week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions, Duplicate experiments indicate the reproducibility of the technique, Crystal numbers were found to increase with increasing supersaturation and temperature. The most significant variable however, was pH, where crystal numbers changed by two orders of magnitude over the pH range 4.0 to 5.2. Crystal size varied also with solution conditions, with the largest crystals being obtained at pH 5.2. Having optimized the crystallization conditions, a batch of crystals were prepared under exactly the same conditions and fifty of these crystals were analyzed by x-ray techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.

Judge, Russell A.↗
NASA NTRS1999

The Effect of Temperature and Solution pH on the Nucleation of Tetragonal Lysozyme Crystals

Part of the challenge of macromolecular crystal growth for structure determination is obtaining crystals with a volume suitable for x-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of supersaturation, temperature, and pH on the nucleation rate of tetragonal lysozyme crystals. Batch crystallization plates were prepared at given solution concentrations and incubated at set temperatures over 1 week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions. Crystal numbers were found to increase with increasing supersaturation and temperature. The most significant variable, however, was pH; crystal numbers changed by two orders of magnitude over the pH range 4.0-5.2. Crystal size also varied with solution conditions, with the largest crystals obtained at pH 5.2. Having optimized the crystallization conditions, we prepared a batch of crystals under the same initial conditions, and 50 of these crystals were analyzed by x-ray diffraction techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.

Judge, Russell A.↗
NASA NTRS2000

Vapor Transport Within the Thermal Diffusion Cloud Chamber

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Ferguson, Frank T.↗
NASA NTRS2000

A Novel Approach to Solving the Problem of Needle Microcrystals (A Case Study of Ribosome Crystals)

Different morphology crystals (needle, rod-tetragonal and wedge-shaped) were grown from the same solution of ribosome; furthermore, in the same drop using 10- 15% 2-methyl-2,4pentanediol as a precipitant. The crystals appeared in 5-48 hours. Observations of the kinetics of crystals appearance lead to the conclusion that higher supersaturation of ribosome solution produces needle-shaped crystals, while the tetragonal-rod and the wedge-shaped crystals grow at lower supersaturation. The ribosome packing in the crystals was characterized by electron microscopy (EM). An analysis of EM ultrathin sections indicates that the unit cells, with a high degree of probability, are the same in the crystals of different morphology. The data obtained suggests how to shift the process of crystal formation from the needles to the crystals with comparative size in all three dimensions.

Karpova, Elizaveta A.↗
NASA NTRS1999

A Study of Direct and Cloud-Mediated Radiative Forcing of Climate Due to Aerosols

The Intergovernmental Panel on Climate Change (IPCC) has reported that in the southeastern US and eastern China, the general greenhouse warming due to anthropogenic gaseous emissions is dominated by the cooling effect of anthropogenic aerosols. To verify this model prediction in eastern China and southeastern US, we analyzed regional patterns of climate changes at 72 stations in eastern China during 1951- 94 (44 years), and at 52 stations in the southeastern US during 1949-94 (46 years) to detect the fingerprint of aerosol radiative forcing. It was found that the mean rates of change of annual mean daily, maximum, minimum temperatures and diurnal temperature range (DTR) in eastern China were 0.8, -0.2, 1.8, and -2.0 C/100 years respectively, while the mean rates of change of annual mean daily, maximum, minimum temperatures and DTR in the southeastern US were -0.2, -0.6, 0.2, and -0.8 C/100 years, respectively. This indicates that the high rate of increase in annual mean minimum temperature in eastern China results in a slightly warming trend of daily temperature, while the high rate of decrease in annual mean maximum temperature and low rate of increase in annual mean minimum temperature lead to the cooling trend of daily temperature in the southeastern US. We found that the warming from the longwave forcing due to both greenhouse gases and aerosols was completely counteracted by the shortwave aerosol forcing in the southeastern US in the past 46 years. A slightly overall warming trend in eastern China is evident; winters have become milder. This finding is explained by hypothesizing that increasing energy usage during the past 44 years has resulted in more coal and biomass burning, thus increasing the emission of absorbing soot and organic aerosols in eastern China. Such emissions, in addition to well-known Asia dust and greenhouse gases, may be responsible for the winter warming trend in eastern China that we have reported here. The sensitivity of aerosol radiative properties to aerosol composition, size distribution, relative humidity (RH) is examined for the following aerosol systems: inorganic and organic ions (Cl-, Br-, NO3 -, SO4 2-, Na+, NH4 +, K+, Ca2+, Mg2+, HCOO-, CH3COO-, CH3CH2COO-, CH3COCOO-, OOCCOO2-, MSA-1); water-insoluble inorganic and organic compounds (elemental carbon, n-alkanes, SiO2, Al2O3, Fe2O3 and other organic compounds). The partial molar refraction method was used to calculate the real part of the refractive index. It was found that the asymmetry factor increased by approximately 48% with the real part varying from 1.40 to 1.65, and the single scattering albedo decreased by 24% with the imaginary part varying from -0.005 to -0.1. The asymmetry factor increased by 5.4 times with the geometric standard deviation varying from 1.2 to 3.0. The radiation transmission is very sensitive to the change in size distribution; other factors are not as significant. To determine the aerosol direct radiative forcing (ADRF), the aerosol optical depth (AOD) values at the three operational wavelengths (415, 500 and 673 nm) were determined at a regionally representative site, namely, Mt. Gibbs (35.78 deg N, 82.29 deg W, elevation 2006 m) in Mt. Mitchell State Park, NC, and a site located in an adjacent valley (Black Mountain, 35.66 deg N, 82.38 deg W, elevation 951 m) in the southeastern US. The two sites are separated horizontally by 10 km and vertically by 1 km. It was found that the representative total AOD values at 500 nm at the valley site for highly polluted (HP), marine (M) and continental (C) air masses were 0.68 +/- 0.33, 0.29 +/- 0.19 and 0.10 +/- 0.04, respectively. A search-graph method was used to retrieve the columnar size distribution (number concentration N, effective radius reff and geometric standard deviation=?g) from the optical depth observations at three operational wavelengths. The ground albedo, single scattering albedo and imaginary part of the refractive index were calculated using a mathematically unique procedure involving a Mie code and a radiative transfer code in conjunction with the retrieved aerosol size distribution, AOD, and diffuse-direct irradiance ratio. It was found that N, r(eff) and sigma(g) were in the ranges of 10 to 1.7 x 10(exp 4)/cubic cm, 0.09 to 0.68 micrometers and 1.12 to 2.95, respectively. The asymmetry factor and single scattering albedo were in the ranges of 0.63 to 0.75 and 0.74 to 0.97 respectively. The ground albedo for the forested terrain and imaginary part of refractive index were found to be in the ranges of 0.06 to 0.29 and 0.005 to 0.051 respectively. On the basis of these aerosol radiative properties obtained at the research sites and computations using the Column Radiation Model (CRM) of National Center of Atmospheric Research (NCAR) Community Climate Model (CCM3), it was found that the average cloud-free 24-hour ADRF values were -13 +/- 8, -8 +/- 3, -33 +/- 16 W/square m for marine, continental, and polluted air masses, respectively. On the assumption that the fractional coverage of clouds is 0.61, it was estimated that the annual mean ADRF was 7 +/- 2 W/square m in the southeastern US. The review with respect to the current knowledge of organic acids shows that aerosol formate and acetate concentrations range from 0.02 to 5.3 nmol/cubic m and from 0.03 to 12.4 nmol/cubic m respectively, and that between 34% to 77% of formate and between 21% to 66% of acetate are present in the fine fraction of aerosols. It was found that although most (98-99%) of these volatile organic acids were present in the gas phase, their concentrations in the aerosol particles were sufficient to make them a good candidate for cloud condensation nuclei (CCN). It is hypothesized that organic acids are at least one of the primary sources of CCN in the atmosphere due to their ubiquitous presence in the troposphere, especially over the continental forested areas. The results of our measurements at Palmer Station, Antarctica show that the daily average CCN concentrations at 0.3% and 1% supersaturations ranged from 0.3 to 160/cubic cm and from 4 to 168/cubic cm, respectively, during the period from 17 January to 26 February, 1994. New evidence for substantial and definitive CCN enhancement near and within cloud has been observed at Mt. Mitchell, North Carolina. The results show that the average monthly CCN concentrations were 460 +/- 217, 386 +/- 286, 429 +/- 228 and 238 +/- 134/cubic cm for in-cloud, overcast, clear and rainy conditions, respectively. The typical CCN spectra show that there were a lot of small CCN produced and the ion concentrations (especially H+ and SO4 2-) were very high during the CCN enhancement period. The significantly positive correlation between black carbon (BC) and CCN at 1% supersaturation indicates that a percentage of the BC measured at the site may be in the form of an internal mixture and participated in the formation of CCN.

Yu, Shao-Cai↗
NASA NTRS1997

Ice Nucleation Processes in Upper Tropospheric Wave-Clouds Observed During SUCCESS

We have compared in situ measurements near the leading-edges of wave-clouds observed during the SUCCESS experiment with numerical modeling of ice nucleation. Observations of high supersaturations with respect to ice (\geq 150\%) near the leading edge of a very cold wave cloud (T < --60^\circC) are consistent with recent theoretical and laboratory studies suggesting that large supersaturations are required to homogeneously freeze sulfate aerosols. Also, the peak ice crystal number densities observed in this cloud (about 4cm -3/sup>) are consistent with the number densities calculated in our model. The consistency between model results (using homogeneous freezing and the observations indicates that the number density of effective heterogeneous ice nuclei must be no more than about 2 cm -3 . In the warmer wave-cloud (T (approx.)eq --37^\circC) relatively large ice number densities were observed (20--40 cm -3 . Our model calculations suggest that these large number densities are only possible if liquid droplets were activated at the cloud leading-edge, followed by subsequent homogeneous freezing. If sulfate aerosols had frozen before liquid droplets could be activated, then the peak ice crystal number density should have been less than 10 cm -3 .

Jensen, E. J.↗
NASA NTRS2003

Gibbs-Thomson Law for Singular Step Segments: Thermodynamics Versus Kinetics

Classical Burton-Cabrera-Frank theory presumes that thermal fluctuations are so fast that at any time density of kinks on a step is comparable with the reciprocal intermolecular distance, so that the step rate is about isotropic within the crystal plane. Such azimuthal isotropy is, however, often not the case: Kink density may be much lower. In particular, it was recently found on the (010) face of orthorhombic lysozyme that interkink distance may exceed 500-600 intermolecular distances. Under such conditions, Gibbs-Thomson law (GTL) may not be applicable: On a straight step segment between two corners, communication between the comers occurs exclusively by kink exchange. Annihilation between kinks of opposite sign generated at the comers results in the grain in step energy entering GTL. If the step segment length l much greater than D/v, where D and v are the kink diffusivity and propagation rate, respectively, the opposite kinks have practically no chance to annihilate and GTL is not applicable. The opposite condition of the GTL applicability, l much less than D/v, is equivalent to the requirement that relative supersaturation Delta(sub mu)/kT much less than alpha/l, where alpha is molecular size. Thus, GTL may be applied to a segment of 10(exp 3)alpha approx. 3 x 10(exp -5)cm approx 0.3 micron only if supersaturation is less than 0.1%, while practically used driving forces for crystallization are much larger. Relationships alternative to the GTL for different, but low, kink density have been discussed. They confirm experimental evidences that the Burton-Cabrera-Frank theory of spiral growth is growth rates twice as low as compared to the observed figures. Also, application of GTL results in unrealistic step energy while suggested kinetic law give reasonable figures.

Chernov, A. A.↗
NASA NTRS2003

Kinetic Roughening and Energetics of Tetragonal Lysozyme Crystal Growth

Lysozyme crystal growth rates over 5 orders of magnitude in range can be described using a layer-by-layer model where growth occurs by 2D nucleation on the crystal surface. Based upon the 2D nucleation model of layer growth, the effective barrier for growth was determined to be gamma = 1.3 plus or minus 0.3 x 10(exp -13) erg/molecule, corresponding to a barrier of 3.2 plus or minus 0.7 k(sub B)T, at 22 C. For solution supersaturation, In c/c(sub eq) greater than or equal to 1.9 plus or minus 0.2, the nucleation model would not predict or consistently estimate the highest observable crystal growth rates. As such, a kinetic roughening hypothesis where crystal growth occurs by a continuous mode was implemented for all growth rate data obtained above In c(sub r)/c(sub eq) greater than or equal to 2. That is, independent of the solution conditions that vary with either buffer pH, temperature or precipitant concentration, crystal growth occurs by the continuous addition of molecules anywhere on the crystal surface, above a roughening solution supersaturation. The energy barrier, E(sub c), for the continuous growth process is determined as 6.1 plus or minus 0.4 x 10(exp -13) erg/molecule or 15 plus or minus 1 k(sub B)T at 22 C.

Gorti, Sridhar↗