Empirically Estimated Electron Lifetimes in the Earth's Radiation Belts: Van Allen Probe Observations

We use measurements from NASA's Van Allen Probes to calculate the decay time constants for electrons over a wide range of energies (30 keV to 4 MeV) and L values ( L = 1.3-6.0) in the Earth's radiation belts. Using an automated routine to identify flux decay events, we construct a large database of lifetimes for near-equatorially mirroring electrons over a 5-year interval. We provide the first accurate estimates of the long decay timescales in the inner zone ( ∼ 100 days), which are highly resolved in energy and free from proton contamination. In the slot region and outer zone, we compare our lifetime calculations with prior empirical estimates and find good quantitative agreement (lifetimes ∼ 1-20 days). The comparisons suggest that some prior estimates may overestimate electron lifetimes between L ≈ 2.5-4.5 due to instrumental effects and/or background contamination. Previously reported two-stage decays are explicitly demonstrated to be a consequence of using integral fluxes.

Empirically Estimated Electron Lifetimes in the Earth's Radiation Belts: Comparison With Theory

We compute quasilinear diffusion rates due to pitch angle scattering by various mechanisms in the Earth's electron radiation belts. The calculated theoretical lifetimes are compared with observed decay rates, and we find excellent qualitative agreement between the two. The overall structure of the observed lifetime profiles as a function of energy and L is largely due to plasmaspheric hiss and Coulomb scattering. The results also reveal a local minimum in lifetimes in the inner zone at lower energy ( ∼ 50 keV), attributed to enhanced scattering via ground-based very low frequency transmitters, and a reduction in lifetimes at higher L and energy ( > 1 MeV), attributed to enhanced electromagnetic ion cyclotron wave scattering. In addition, we find significant quantitative disagreement at L < 3 . 5 , where the theoretical lifetimes are typically a factor of ∼ 10 larger than the observed, pointing to an additional loss process that is missing from current models. We discuss potential factors that could contribute to this disagreement.

Microalgae Filtration Using an Electrochemically Reactive Ceramic Membrane: Filtration Performances, Fouling Kinetics, and Foulant Layer Characteristics

Electrochemical membrane filtration has proven to be successful for microbial removal and separation from water. In addition, membrane fouling could be mitigated by electrochemical reactions and electrostatic repulsion on a reactive membrane surface. This study assessed the filtration performances and fouling characteristics of electrochemically reactive ceramic membranes (a Magneli phase suboxide of TiO₂) when filtering algal suspension under different dc currents to achieve anodic or cathodic polarization. The critical flux results indicate that when applying positive or negative dc currents (e.g., 1.25-2.5 mA·cm^-2) to the membrane, both significantly mitigated membrane fouling and thus maintained higher critical fluxes (up to 14.6 × 10^-5·m³·m^-2·s^-1 or 526 LMH) compared to the critical flux without dc currents. Moreover, applying dc currents also enhanced membrane defouling processes and recovered high permeate flux better than hydraulic and chemical backwash methods. Moreover, fouling kinetics and the cake layer formation were further analyzed with a resistance-in-series model that revealed many important but underexamined parameters (e.g., cake layer resistance and cake layer thickness). The cake layer structures (e.g., compressibility) were shown to vary with the electrochemical activity, which provide new insight into the biofouling mechanisms. Finally, the algogenic odor, geosmin, was shown to be effectively removed by this reactive membrane under positive dc currents (2.5 mA·cm^-2), which highlights the multifunctional capabilities of electrochemically reactive membrane filtration in biomass separation, fouling prevention, and pollutant degradation.

Effect of TiO2-nanoparticles on copper toxicity to bacteria: role of bacterial surface

The impact of titanium dioxide nanoparticles (nano-TiO₂) on the aquatic environment is an important issue due to their increasing application. Although nano-TiO₂ was reported to show an effect on heavy metal toxicity to aquatic organisms, the underlying mechanism is not well understood. In this study, two bacterial species (Bacillus thuringiensis (B. thuringiensis) and Bacillus megaterium (B. megaterium)) from sediment were selected to study the effects of nano-TiO₂ on copper toxicity. Nano-TiO₂ was found to inhibit the growth of B. thuringiensis and enhance the oxidative stress damage caused by copper, whereas these effects were not observed for B. megaterium. Transmission electron microscopy and flow cytometry showed that B. thuringiensis has stronger association ability to nano-TiO₂ than B. megaterium. The existence of the S-layer on the surface of B. thuringiensis might be the possible reason, leading to the difference in copper toxicity. This indicates that the characteristics of bacterial surfaces might be important to the toxicity responses of nanoparticles.

Different surface characteristics of bacteria, for example, S-layer or exopolysaccharides, might lead to different effects of nanomaterials on metal toxicity.

Leucine and isoleucine have similar effects on reducing lipid accumulation, improving insulin sensitivity and increasing the browning of WAT in high-fat diet-induced obese mice

Leucine (Leu) and isoleucine (Ile) have similar effects in the management of obesity and related disorders.

[Related factors of frailty in the elderly male patients with chronic kidney disease]

Objective: To investigate the characteristics of frailty in the elderly male patients with chronic kidney disease (CKD) and the effects of renal function on the incidence of frailty. Methods: A total of 105 non-dialysis CKD patients aged ≥65 years who were admitted to the Chinese PLA General Hospital between October 1, 2018 and January 30, 2019 were included in this study. Their clinical data and laboratory indicators were collected. Frailty was defined according to Fried frailty criteria. According to the frailty scores, the participants were categorized as non-frail (n=37), intermediately frail (n=37) and frail (n=31). The association of frailty and the level of estimated glomerular filtration rate (eGFR) in the patients was analyzed using the model of multivariate Logistic regression. Results: Among the 105 patients, the mean age was 74 (68, 77) years old. The incidence of frail and intermediate frail was 35.2% (37/105) and 29.5% (31/105), respectively. Multivariate logistic analysis showed statistically significant associations of frailty with age (OR=1.14, 95%CI:1.08-1.20, P<0.001), body mass index (OR=0.87, 95%CI:0.79-0.95, P=0.001) and the level of eGFR (OR=0.98, 95%CI:0.96-0.99, P=0.003) in those patients. The incidence of frail in patients with eGFR<45 ml·min(-1)·(1.73 m(2))(-1) and 45-59 ml·min(-1)·(1.73 m(2))(-1) was 1.02 (OR=2.02, 95%CI: 1.06~3.87) and 0.84 (OR=1.84, 95%CI: 1.05-3.22) times higher than that of eGFR≥60 ml·min(-1)·(1.73 m(2))(-1), respectively. Conclusion: The incidence of frailty in the elderly patients with CKD is affected by many factors, such as age, body mass index and renal function, and increases with decreased renal function.

[Phosphatase and tensin homolog deleted on chromosome ten deficiency sensitizes tumor cells to lithium chloride treatment]

Objective: To identify the therapeutic efficacy of lithium chloride (LiCl) on phosphatase and tensin homolog deleted on chromosome ten (PTEN)-deficient tumors. Methods: First, the Catalogue of Somatic Mutations in Cancer for mutation spectrum of human endometrial carcinoma samples was analyzed. Second, the relationship between PTEN abundance and LiCl inhibition of endometrial cancer cell lines using Pten(+/+) and Pten(-/-) mouse embryonic fibroblast (MEF) lines was investigated. Moreover, potential alterations of mammalian target of rapamycin (mTOR) signaling pathway after treatment with LiCl were checked.Last,LiCl's efficacy on PTEN null tumors was studied. Results: PTEN was mutated in 39% of endometrial carcinomas. LiCl preferentially inhibited the proliferation of PTEN-deficient endometrial carcinoma cells and MEFs. Furthermore, LiCl blocked PTEN-deficient tumor development. Mechanistically, LiCl down-regulated mTOR signaling. Conclusions: PTEN is the most frequently mutated gene in endometrial carcinoma.By targeting mTOR signaling pathway,LiCl is a promising regimen for the treatment of tumors with PTEN deficiency.

Network Analysis of Y-STR in Six Ethnic Populations in Guangxi and Its Forensic Significances

Abstract

Objective To explore the distribution of genetic structure of Y-SNP and Y-STR genetic markers in different ethnic groups and its application in forensic science. Methods SNaPshot minisequencing was used to detect the polymorphisms of 12 Y-SNP loci in 439 males from 6 ethnic groups, including Guangxi Han, Guangxi Jing, Guangxi Miao, Guangxi Yao, Guangxi Zhuang and Guangxi Dong. DNATyperTM Y26 kit was used to multiplex-amplify 26 Y-STR loci. The PCR products were analyzed by 3130xl genetic analyzer. The network analysis of Y-STR haplotype under the same Y-SNP haplogroup was analyzed by Network 5.0 software. Results Six haplogroups defined by 12 Y-SNP loci were detected in 6 ethnic groups, and 362 haplotypes were detected in 26 Y-STR loci. The haplotype diversity was 0.996 6. In the C haplogroup, the samples from Guangxi Yao, Guangxi Zhuang and Guangxi Dong were clustered on different branches; in the O1 haplogroup, those from Guangxi Zhuang, Guangxi Miao and Guangxi Jing were relatively independent and clustered separately; in the O2 haplogroup, some samples from Guangxi Miao and Guangxi Yao were gathered in a cluster. Conclusion Based on the Y-STR network analysis of samples with identical haplogroup of Y-SNP, some ethnic groups can be preliminarily distinguished, which could be used to infer male suspects' ethnic group through detecting their genetic markers left in the crime scene.

Genetic Polymorphism of Y Chromosome Haplogroup D-M174 in East Asian Populations

Abstract

Objective To explore the genetic polymorphism of Y chromosome D-M174 haplogroup and sub-haplogroups in East Asia. Methods The samples of 1 426 unrelated male individuals from East Asia were collected, and then 7 Y chromosome haplogroup D-M174 and the Y-SNP of its sub-haplogroups were detected with mini-sequencing. The 22 Y-STR genotypes were detected with DNA Typer™ Y26 kit. The haplogroup was analyzed using direct counting method, heatmap, phylogenetic cluster and network graph cluster, and then distribution of genetic polymorphism and the clustering relation between populations and samples of Y chromosome D haplogroup were discussed. Results Haplogroup D-M174 were distributed mostly among Tibetans （40.96%）and Japanese （35.71%）, while less or none were distributed among the surrounding areas of Tibet and other areas. Conclusion The geographical distribution of Y chromosome D-M174 haplogroup in East Asian populations has significant characteristics.

[Risk factors of cervical anastomotic leakage after thoracoscopic-lapacoscopic esophagectomy in patients with esophageal carcinoma]

Objective: To analyze the risk factors of cervical anastomotic leakage after thoracoscopic-lapacoscopic esophagectomy. Methods: 530 patients with esophageal cancer underwent thoracoscopic-lapacoscopic esophagectomy at the Cancer Hospital, Chinese Academy of Medical Sciences from Jan 2011 to Dec 2015. The demographic, surgical and clinical data of patients were retrospectively analyzed. Multivariate logistic regression was used to evaluate risk factors of cervical anastomotic leakage in these patients. Results: A total of 530 patients undergoing thoracoscopic-lapacoscopic esophagectomy were enrolled in this study. There were 421 males and 109 females. The mean age was (59.40±8.08) years old, and 91 patients with cervical anastomotic leakage. Sigle factor analysis revealed that the risk grading by American Society of Aneshesiologists, previous history of chest surgery, respiratory comorbidity, diffusion capacity for carbon monoxide of the lung, operation time, anastomosis, average days of postoperative hospitalization, death within 30 days after surgery, respiratory complications, pleural effusion or empyema, and poor healing of the incision were statistically associated with cervical anastomotic leakage (all P<0.05). Multivariate analysis showed that previous history of chest surgery, hepatic insufficiency, manual anastomosis, prolonged postoperative hospitalization, and poor healing of the incision were independent risk factors for cervical anastomotic leakage after thoracoscopic-lapacoscopic esophagectomy (all P<0.05). Conclusions: Previous history of chest surgery, hepatic insufficiency, poor healing of the incision, manual anastomosis and prolonged postoperative hospitalization were significantly associated with cervical anastomotic leakage after thoracoscopic-lapacoscopic esophagectomy. It's important to strengthen perioperative nursing and surgical techniques to prevent anastomotic leakage after thoracoscopic-lapacoscopic esophagectomy.

[The expressions and diagnostic values of miR-18a and miR-21 in esophageal cancer]

Objective: To investigate the expressional levels and diagnostic values of miR-18a and miR-21 in esophageal carcinoma. Methods: The expressions of miR-18a and miR-21 in esophageal cancer tissues and adjacent tissues from 45 esophageal cancer patients, peripheral blood from 45 esophageal cancer patients and 50 healthy donors respectively were detected by RT-PCR. The expressions of miR-18a and miR-21 in normal esophageal epithelial cell HET-1A, esophageal cancer cell lines including ECA109, KYSE150 and TE1 were also detected. Chemiluminescence immunoassay was used to quantitatively detect the concentrations of carcinoembryonic antigen (CEA), squamous cell carcinoma antigen (SCC), CYRFA21-1 and TPA (tissue polypeptide antigen) in peripheral blood serum from esophageal cancer patients and healthy controls. Meanwhile, the diagnostic effects of miR-18a and miR-21 on esophageal cancer were compared with those of tumor markers in serum. Results: The expression levels of miR-18a and miR-21 in esophageal cancer cells ECA109, KYSE150 and TE1 were 1.64±0.17, 1.62±0.19, 1.46±0.12 and 20.52±1.48, 6.73±0.73, 1.43±0.19, respectively, higher than those in normal esophageal epithelial cells (both P<0.01). The expressions of miR-18a and miR-21 in esophageal cancer tissues were 32.48±28.62 and 8.67±11.98, respectively, significantly higher than those in adjacent tissues (all P<0.001). The expression levels of miR-18a and miR-21 in peripheral blood of patients with esophageal cancer were 12.66±11.92 and 9.15±8.14, respectively, significantly higher than those in the normal control group (both P<0.001). The receiver operating characteristic (ROC) curve analysis showed that the area under the curve of miR-18a and miR-21 for diagnosis of esophageal cancer were 0.948 and 0.913 5, respectively. Compared with traditional esophageal tumor markers, the expressions of miR-18a and miR-21 were more sensitive in the diagnosis of esophageal cancer. The sensitivity and accuracy of the expressions of miR-18a and miR-21 combined with traditional esophageal tumor markers in diagnosis of esophageal cancer can be further improved to 97.8% and 68.4%, respectively. Conclusion: Our study reveals that the expressions of miR-18a and miR-21 play important roles in the diagnosis of esophageal cancer and may be potentially novel biomarkers.

Thermodynamic signatures of quantum criticality in cuprate superconductors

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*-at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram¹. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range² that includes p*. As a function of doping, we find that C_el/T is strongly peaked at p* (where C_el is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point^3-5, as observed in heavy-fermion⁶ and iron-based⁷ superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.

[Analysis of psychological status and relevant factors of patients with esophageal and gastric cardia precancerous lesions in Linzhou of Henan]

Objective: To explore the psychological status and related factors in patients with precancerous of esophageal and gastric cardia in Linzhou of Henan. Methods: Clinical psycho-rating scale of Social Support Rating Scale (SSRS), Self-Rating Anxiety Scale (SAS, score ≥50 points with symptoms of anxiety) and Self-Rating Depression Scale (SDS, score ≥53 points with the symptoms of depression) were applied to survey life events and psychological status of subjects who aged 40-69 years old and participated in"The Early diagnosis and Early Treatment"program in Linzhou cancer hospital from July 2015 to Jan 2016. Patients with lower intraepithelial neoplasia or high-grade intraepithelial neoplasia were selected as precancerous lesions (n=118), and patients with normal grade were selected as healthy controls (n=210). Compare the differences of the scores between the two groups, and the logistic regression model was used to analyze the related factors of precancerous lesions and psychological status of the study subjects. Results: Precancerous lesions included esophageal (72 cases), gastric cardia (40 cases), esophageal and cardia dual source (6 cases); Precancerous lesions and healthy controls aged (57.17±7.71) and (53.12±7.99) years old, the difference was statistically significant (P<0.001). The anxiety and depression scale showed that the scores of SAS and SDS scores in the precancerous lesions were (37.18±10.01), (40.44±8.37) points, and (34.02±6.63), (38.49±8.73) points in control group, the difference was statistically significant (P=0.002, 0.032). While the social support total score (38.26±5.26), and subjective support score (24.08±3.83) and objective support score (7.50±1.89) in control group were all higher than those of precancerous group (36.80±6.18, 23.01±3.93, 6.93±1.57), and the difference were statistically significant (P=0.024, 0.016, 0.004). In addition, the Logistic analysis showed that subjects with low objective social support, subjective social support and anxiety symptoms were more likely to develop precancerous lesions, and the OR were 0.81, 0.72 and 1.05, respectively (P=0.028, 0.005, 0.009). Conclusion: Social support, anxiety and depression status may be related to the occurrence and development of esophageal and gastric cardia precancerous lesions.

[HSP90 inhibitor 17-AAG plays an important role in JAK3/STAT5 signaling pathways in HTLV-1 infection cell line HUT-102]

Objective: To analyze whether heat-shock protein 90 (HSP90) be involved in a permanently abnormal activated JAK/STAT signaling in ATL cells in vitro. Methods: The effect of 17-AAG on proliferation of ATL cell lines HUT-102 was assessed using CCK8 at different time points. Cell apoptosis was measured by flow cytometry. The specific proteins HSP90, STAT5, p-STAT5 and JAK3 were detected by Western blotting. Results: Overexpression of HSP90 in HUT-102 cell lines was disclosed (P<0.05) , and constitutive activation of JAK3/STAT5 signaling was observed in HTLV-1-infected T-cell lines but not in normal PBMCs; Treatment of ATL cell lines with 17-AAG led to reduced cell proliferation, but there was no significant change in terms of cell proliferation when the concentration of 17-AAG between 2 000-8 000 nmol/L (P>0.05) . 17-AAG induced cell apoptosis in different time-points and concentrations. 17-AAG don't affect the expression of JAK3 gene. Conclusion: This study indicated that JAK3 as HSP90 client protein was aberrantly activated in HTLV-1-infected T-cell lines, leading to constitutive activation of p-STAT5 in JAK/STAT signal pathway, which demonstrated that HSP90-inhibitors 17-AAG inhibited the growth of HTLV-1-infected T-cell lines by reducing cell proliferation and inducing cell apoptosis.

[Study on the application of dexmedetomidine combined with remifentanil in dressing change of conscious patients with non-intubation in burn intensive care unit]

Objective: To observe the analgesic and sedative effect and safety of application of dexmedetomidine combined with remifentanil in dressing change of conscious patients with non-intubation in burn intensive care unit. Methods: Forty patients conforming to the study criteria hospitalized in our burn intensive care unit from April 2015 to April 2017 were selected. Prospective, randomized, and double-blind method was used for the design. Patients were divided into dexmedetomidine group and dexmedetomidine+ remifentanil group according to the random number table, with 20 cases in each group. Patients in the two groups were respectively given corresponding drugs during dressing change. The frequency and time of dressing change, Verbal Rating Scale (VRS) score of patients during dressing change (at drug administration for 25 minutes) and after dressing change (25 min after dressing change), Ramsay Sedation Score (RSS) during dressing change, satisfaction level for anesthesia of the patients and physicians after dressing change, dosage of remifentanil, and various adverse effects during and after dressing change were recorded. The heart rate, mean arterial blood pressure (MAP), respiratory rate, and pulse oxygen saturation (SpO₂) before drug administration and at 10, 15, and 25 minutes after drug administration were also recorded. Data were processed with analysis of variance for repeated measurement, t test, chi-square test, and Fisher's exact probability test. Results: (1) Totally 38 patients completed the trial. There were no statistically significant differences between patients in two groups in gender, American Association of Anesthesiologist Grading, age, weight, and total burn area (χ²=0.230, 0.146, t=0.224, 0.351, 0.367, P>0.05). (2) The frequency of dressing change of patients in two groups were both 48 times. The time of dressing change and VRS scores during dressing change of patients in two groups were similar (t=0.821, 1.522, P>0.05). The VRS score of patients in dexmedetomidine+ remifentanil group after dressing change was (3.1±0.4) points, obviously lower than (3.8±0.8) points in remifentanil group (t=2.213, P<0.05). The RSS, satisfaction level scores for anesthesia of the patients and physicians after dressing change in dexmedetomidine+ remifentanil group were (3.13±0.32), (3.44±0.41), and (3.13±0.25) points, respectively, obviously better than (1.82±0.24), (2.71±0.23), (2.53±0.41) points in remifentanil group (t=2.226, 2.684, 7.702, P<0.01). The dosage of remifentanil of patients in dexmedetomidine+ remifentanil group was (282±19) μg, obviously less than (340±31) μg in remifentanil group (t=9.896, P<0.01). There were no statistically significant differences between patients in two groups in rates of respiratory inhibition and hypotension (χ²=0.211, 0.154, P>0.05). Compared with those in remifentanil group, the rates of nausea, vomiting, and other gastrointestinal symptoms of patients in dexmedetomidine+ remifentanil group were obviously reduced (P<0.05), but the rate of bradycardia was obviously increased (χ²=6.008, P<0.05). (3) There were no statistically significant differences between patients in two groups in heart rate, MAP, respiratory frequency, and SpO₂ before drug administration (t=0.444, 0.892, 1.059, 1.039, P>0.05). The heart rates of patients in dexmedetomidine+ remifentanil group at 10, 15, and 25 minutes after drug administration were (83±11), (78±10), and (82±14) times per minute, respectively, significantly lower than (95±10), (87±12), and (89±12) times per minute in remifentanil group (t=5.592, 3.992, 2.630, P<0.05 or P<0.01). The MAP of patients in dexmedetomidine+ remifentanil group at 15 and 25 minutes after drug administration were (69.4±3.1) and (73.8±2.2) mmHg (1 mmHg=0.133 kPa), respectively, significantly lower than (75.4±3.0) and (78.1±3.5) mmHg in remifentanil group (t=9.181, 7.206, P<0.01). There were no statistically significant differences between patients in two groups in respiratory frequency at each time point after drug administration (t=1.489, 1.862, 1.963, P>0.05). The SpO₂ of patients in dexmedetomidine+ remifentanil group at 15 minutes after drug administration was 0.972±0.018, obviously lower than 0.979±0.015 in remifentanil group (t=2.070, P<0.05). Conclusions: Application of remifentanil with small dosage has effective analgesia for conscious burn patients with non-intubation during dressing changes, however, adverse effects such as nausea and vomiting are likely to occur. Remifentanil combined with dexmedetomidine not only guarantee the analgesic effect, but also reduce the dosage of analgesics, improve the sedative effect and satisfaction of the patients for anesthesia, and reduce various adverse effects. However, it will increase the incidence of bradycardia and has some inhibition effect on circulation at the same time.

Adsorption of reactive dyes onto chitosan/montmorillonite intercalated composite: multi-response optimization, kinetic, isotherm and thermodynamic study

Chitosan/montmorillonite intercalated composite (CTS/MMT) was used as an effective adsorbent for removal of reactive dyes, i.e. Reactive Black 5 (RB5), Reactive Red 136 (RR136), Reactive Yellow 145 (RY145) and Reactive Blue 222 (RB222). Taguchi method attached grey relational analysis was applied to determine the optimal adsorption conditions, including pH, initial concentration of dye, temperature, adsorbent dosage and contact time, for achieving simultaneous maximization of removal percentage and adsorption capacity. The percentage contribution of each adsorption condition was determined in the analysis of variance and showed that the most effective parameter in removal of RB5, RY145 and RB222 is the dye solution pH, whereas the initial concentration was the determining factor for optimum efficiency for the dye RR136. Under respective optimal condition, the removal percentages and adsorption capacity of four reactive dyes onto CTS/MMT were both found in the following order: RR136 > RY145 > RB5 > RB222. The maximum removal percentages of 78.8 and 49.5%, and the adsorption capacity of 315.20 and 123.75 mg/g were obtained for RR136 and RB222, respectively. The adsorption behaviors showed that the adsorption kinetics and isotherms were in best agreement with Avrami fractionary order model and the Toth isotherm, respectively.