The Fe3O4 particles with size in the range of 20–200 nm are uniformly aligned along the axial direction of the CNTs. The composite exhibits exceptionally high wave absorption capacity even at a very low thickness. Minimum reflection loss of −44.7 dB and absorbing bandwidth of 4.7 GHz at −10 dB are achieved in composites with one-layer graphene in six-layer CNT film-Fe3O4 prepared from 0.04 M FeCl3. Microstructural and theoretical studies of the wave-absorbing mechanism reveal a unique Debye dipolar relaxation with an Eddy current effect in the absorbing bandwidth.Graphene has sparked extensive research interest for its excellent physical properties and its unique potential for application in absorption of electromagnetic waves. However, the processing of stable large-scale graphene and magnetic particles on a micrometer-thick conductive support is a formidable challenge for achieving high reflection loss and impedance matching between the absorber and free space. Herein, a novel and simple approach for the processing of a CNT film-Fe EM waves consist of a time-varying electric and magnetic field, and EM wave absorption is achieved by the attenuation of EM wave energy through dielectric loss and magnetic loss as well as electromagnetic impedance match, which can minimize the reflection of the incident EM wave4. Therefore, dielectric loss and magnetic loss are the main factors determining absorption capability. The dielectric tangent loss (tan δε = ε″/ε′) is proportional to the dielectric loss, and it describes the dissipation of energy supplied by an external electric field as motion and heat5. Magnetic tangent loss (tan δμ = μ″/μ′) is known as magnetic loss factor or power factor; it is a measure of the energy loss inside a magnetic material due to the phase delay between the applied and induced magnetic fields.The rapid development of modern electronic equipment and wireless devices has resulted in severe electromagnetic (EM) radiation pollution, which has implications in human health and the normal functioning of electronics. Thus, the design and exploration of effective EM wave absorption materials is of basic scientific importance6Good impedance matching between the specimen and free space is necessary for enhancing EM wave absorption capability. The impedance matching coefficient |ZinZ0-1| can be expressed as0 is the characteristic impedance of free space (377 Ω)7. εr = ε′ − jε″ and μr = μ′ − jμ″ are, respectively, the complex permittivity and permeability of the absorber, c is the velocity of the EM wave in free space, f is the frequency of the EM wave, and d denotes the absorber thickness.And the reflection loss (RL) value is calculated according to the transmission line theory by Equation :2\docume8, the carrier mobility and current carrying capacity of CNTs is up to 105 cm2 V−1 s−1 and 109 A cm−1, respectively9. Most of the research effort to date has focused on CNTs decorated with magnetic metal or metal oxide particles for enhancing magnetic attenuation. However, the anticipated improvement in EM wave absorption performance has often been hindered by the poor dispersion of CNTs and their impedance mismatch with free space10. CNT films, on the other hand, not only retain the high permittivity of individual CNTs in an isotropic network structure but also greatly facilitate the dispersion of CNTs in the matrix11. Furthermore, the dispersion of Fe3O4 nanoparticles on the surface of CNTs can effectively improve permeability and impedance matching12. Thus, the CNT film-Fe3O4 absorber provides a highly desirable combination to enhance dielectric and magnetic loss and impedance matching as well as facilitate ease in composites processing.Carbon nanotubes (CNTs) offer the unique potential to be excellent EM wave absorbents. Besides their superior mechanical and thermal properties15. Graphene can support current densities greater than 108 A cm−2 16, its carrier mobility can exceed 15,000 cm2 V−1 s−1 even under ambient conditions17, and its real and imaginary parts of the theoretical permittivity exceed 104 at frequency less than 400 GHz18. Theoretical studies of large-scale graphene layers have shown strong EM wave absorption for normal incident wave. The maximum absorption reaches 50 percent at six layers of graphene and one-third of the incident EM energy is dissipated at a graphene-polymer interface20. Although large-scale multilayer graphene/methyl methacrylate for EM wave absorption has been suggested theoretically and realized in numerical simulations20, large-scale graphene absorption has never been demonstrated experimentally. This is due to the fact that large-scale graphene suffers from statistical fluctuations in strength and toughness as well as impedance mismatch with free space due to the high permittivity and negligible permeability21. Consequently, almost all published work so far on graphene-related EM-absorbing materials has focused on graphene powder; little research has been devoted to the EM wave-absorbing performance of large-scale graphene. Moreover, in order to enhance impedance matching and absorption of both electric and magnetic fields in graphene, the improved decoration and blend of magnetic metal or metal oxide particles have become effective approaches for researchers. Some reports demonstrated that the combination of Fe3O4 25, TiO226 and NiFe2O427 magnetic nanoparticles with reduced graphene oxide powders improved the EM wave-absorbing property. However, the magnetic nanoparticles supported on graphene particles are generally aggregated, resulting in uneven distribution25. Therefore, the design and processing of high-performance EM-absorbing materials based on CNT and graphene remain a formidable challenge.The other focus of this research is on graphene, which is well known for its excellent electronic, chemical and physical properties3O4 composites by the solvothermal method. The Fe3O4 nanoparticles on the surface of CNTs not only improved permeability but also enhanced impedance matching of the CNT film-Fe3O4-graphene composite. Then, the CNT film-Fe3O4 was used as a support substrate to prepare a large-scale graphene (LSG)-CNT film-Fe3O4 composite, which not only retained the dielectric performance of CNT and graphene but also avoided their aggregation.Here, a novel and simple approach was adopted to fabricate CNT film-Fe−3) with randomly oriented CNTs coated by Fe3O4 nanoparticles were used as absorbing layers, the single chemical vapor deposition graphene were laid on the surface of CNT-Fe3O4 film as blocking layer  was impedance matching layer. A schematic illustration of the fabrication process for constructing CNT film-Fe3O4-graphene-epoxy composites can be found as Supplementary Fig. To enhance the ability of EM wave absorption, highly conductive films , and the seven peaks at 18.17°, 30.07°, 35.48°, 43.01°, 53.42°, 57.04° and 62.55° are associated with the (111), (220), (311), (400), (422), (511) and (440) crystal planes of Fe3O4, respectively. No additional peaks belonging to other phases are observed, indicating the good crystallinity and high purity of the Fe3O4 nanoparticles. The energy dispersive spectroscopy (EDS) as shown in Fig. 3O4–0.05 M composite is mainly composed of C, O, and Fe elements.Figure ern Fig. , which i3O4 nanoparticles are calculated for the strongest peak (311) by the Debye–Scherrer formula. The nanocrystal sizes from the data of Fig. 3O4 composites prepared from 0.01, 0.02, 0.03, 0.04, 0.05 and 0.10 M FeCl3, respectively; this implies that the nanocrystal size increases significantly with increasing concentration of FeCl3. The saturation magnetization and relaxation values are directly related to the size of the nanocrystal size, and with the increase of Fe3O4 nanocrystal size, both the saturation magnetization and relaxation rate increase29.The average sizes of nanocrystals in the Fe3O4 composites at room temperature are shown in Fig. 3O4 composites  and remnant magnetization (Mr) of the CNT film-Fe3O4-0.01 M and 0.02 M remain nearly the same as those of the CNT film. At FeCl3 concentrations higher than 0.02 M, the Ms and Mr values increase rapidly, as shown in Fig. c) with FeCl3 concentration is shown in Fig. r and anisotropy energy, which are related to the values of Ms and Hc, affect the EM wave absorption capacities30.The magnetic properties of the CNT film-Fetes Fig. . The sat3O4-0.05 M composites with various numbers of layers were fabricated. The values of tan δε and tan δμ, impedance matching coefficient |Zin/Z0| and reflection loss of composites consisting of one to seven CNT film-Fe3O4-0.05 M layers were deduced from the measured data of relative complex permittivity εr, permeability μr and thickness d. The effect of the number of layers on the composite EM wave-absorbing properties was studied. The results of Fig. ε appear when the frequency is higher than 6 GHz. The locations of peaks shift toward lower frequencies with an increase in the number of layers of CNT film-Fe3O4 composite. The peak intensity varies with the number of layers and reaches a maximum value of 1.72 at four layers. Figure μ of the CNT film-Fe3O4 composites with frequency and number of layers. Strong peaks of tan δμ can be seen in the frequency range of 10–17 GHz, and the peak location also shifts toward lower frequencies with increasing number of layers. The peak intensity of tan δμ decreases from a maximum value of 0.58 at one layer to a minimum value of 0.08 at four layers. It should be noted that the values of tan δμ become negative in some frequency ranges, indicating that the magnetic energy radiated out from the composites due to the high carrier mobility of CNTs7. Overall, the above results demonstrate the dependence of the dielectric and magnetic responses on the number of layers of CNT film-Fe3O4 composite. In addition, the values of tan δε are larger than those of tan δε for almost the entire frequency range, suggesting that dielectric loss plays a major role in the intrinsic EM wave absorption.Based on the above magnetic property data and morphology observations, CNT film-Fein/Z0| and RL calculated from the relative permittivity and permeability data are given in Fig. in/Z0| is close to unity, most of the EM waves can effectively enter the composite and then dissipate as heat. Figure in/Z0| of the CNT film-Fe3O4 composites increases and reaches a maximum value of 1.73 at six layers and then decreases to 0.80 at seven layers. Only the values of |Zin/Z0| of the CNT film-Fe3O4 composites with five and six layers are close to unity in the frequency range of 10–17 GHz. Figure 3O4 composite with five layers, the minimum value of reflection loss is −19.3 dB, and the frequency bandwidth at −10 dB is 3.6 GHz. For the CNT film-Fe3O4 composite with six layers, the minimum value of reflection loss is −26.6 dB, and the frequency bandwidth at −10 dB is 2.9 GHz. However, although the CNT film-Fe3O4 composites with one, two, three, four and seven layers have higher dielectric loss, the frequency bandwidth at −10 dB and the magnitude of minimum reflection loss are far less than those of five- and six-layer composites.Results of |Z3O4 composites with different layers, CNT film-Fe3O4 composites of six layers with different FeCl3 concentrations were prepared. As shown in Fig. ε of the CNT film-Fe3O4 composites of 0.02–0.05 M are all less than that of the CNT film-Fe3O4–0.01 M composite, and the values of tan δμ are all higher than that of the CNT film-Fe3O4-0.01 M composite. It is interesting that tan δε of the CNT film-Fe3O4-0.10 M increases almost monotonically with frequency. The tan δμ value of the CNT film-Fe3O4-0.10 M is negative and shows a decreasing trend at frequencies higher than 8.5 GHz , and each semicircle is correlated with one Debye relaxation process6. The eddy current loss contribution to the imaginary part of permeability is related to the permeability of vacuum (μ0), thickness (d) and electrical conductivity (σ) of the composite as μ″ = 2πμ0(μ′)2σd2f/3. If the magnetic loss results from the eddy current effect, μ″(μ′)−2f−1 should be constant when the frequency varies. It is shown in Fig. −2f−1 drastically fluctuate in the frequency range of 2.0–8.0 GHz. However, when f >8.0 GHz, the values of μ″(μ′)−2f−1 remain essentially constant. Thus, it can be concluded that the magnetic loss at 2.0–8.0 GHz is caused by natural resonance, and the other peaks at 8.0–18.0 GHz are ascribed to the eddy current effect.In the microwave frequency band, magnetic loss mainly comes from the eddy current effect, along with natural and exchange resonance2O4 and CNT-La(NO3)3 absorbers 3 absorbers at 0.9, 1 and 1.4 mm, respectively, and the GO-Fe3O4 absorber also at 1.5 mm. However, the maximum reflection loss of this work is 1.2–2.5 times the values of the above five absorbers CNT-Ni, -Ag -CoFe2O4 and -La(NO3)3, GO-Fe3O4 . Ethanol, ferrocene, and thiophene were used as carbon source, catalyst precursor, and promotor, respectively. CNTs were synthesized and entangled in the hot zone forming a stocking-like aerogel. The CNT aerogel was then blown out continuously from the reactor and collected layer-by-layer by a wheel rotating perpendicularly to the gas flow, which formed macroscopic CNT film  with randomly oriented CNTs33. This CNT film was further densified by spraying ethanol onto it to enhance its mechanical and physical properties.CNT film was fabricated by floating catalyst chemical vapor deposition (FCCVD) method2 flow. Subsequently, a 20 sccm CH4 flow was introduced for graphene growth at 30 mTorr for 0.5 h. Then, the furnace was quickly cooled to room temperature under He flow, and the single-layer graphene on Cu foil was obtained34. The size of the graphen was 25 mm × 20 mm.The single-layer graphene films were synthesized on a Cu substrate using the CVD method. A Cu foil was annealed at 1000 °C for 1.5 h in a quartz tube with a 2 sccm H3O4 composites were prepared in a solvothermal system by the reduction reaction between FeCl3 and ethylene glycol in the presence of CNT film. FeCl3·6H2O was dissolved into 50 mL ethylene glycol followed by the addition of 3.0 NaAc (protective agent) and 10 mL ethylene diamine (EDA) to form a homogeneous solution with magnetic stirring. The mixture was then transferred to a 100 mL Teflon-lined stainless steel autoclave, and 30 cm2 CNT film was completely immersed in the solution for solvothermal reaction at 200 °C for 10 h , curing agent (DETDA) and ethyl acetate in the ratio of 10:1:100, followed by degassing in a vacuum oven for 30 min. Next, a CNT film-Fe3O4-graphene-epoxy composite was prepared by laminating the as fabricated films by spin coating Resin 862 and DETDA in the ratio of 10:1, followed by curing at 100 °C for 1 h. The thickness of one layer of CNT film-Fe3O4-epoxy composite was about 0.25 mm.The individual CNT-FeX-ray diffraction (XRD) patterns of the composites were measured on a Bruker D8 advance diffractometer using a Cu Kα source (λ = 0.154056 nm). Scanning electron microscopy (SEM) and transmission electron microscope (TEM) images were performed on the Auriga 60 and TEM Talos F200C, respectively. A magnetic study was performed by a vibrating sample magnetometer . The electromagnetic parameters of the samples were measured using a vector network analyzer (Agilent 8722ES) in the range of 1-18 GHz after a full two-port calibration .Superb electromagnetic wave-absorbing composites based on large-scale graphene and carbon nanotube films


The aim of this study is contribute to clinical practice of bilinguals around the globe, as well as to add to our understanding of bilingual aphasia processing, by analysing confrontation naming data from four Afrikaans/English bilingual individuals with acquired aphasia due to a left hemisphere stroke.This is a case series analysis of four Afrikaans/English bilingual aphasic individuals following a left cerebrovascular accident. Error analysis of confrontation naming data in both languages was performed. Research questions were directed toward the between language differences in lexical retrieval abilities, types of errors produced and degree of cognate overlap.Three of the four participants showed significantly higher naming accuracy in first acquired language (L1) relative to the second acquired language (L2) and the largest proportion of error type for those three participants in both L1 and L2 was omission. One of the four participants  showed no between language accuracy difference. Regarding cognate overlap, there was a trend for higher accuracy for higher cognate words (compared to low).This study showed that naming performance in these four individuals was reflective of their relative language proficiency and use patterns prior to their stroke. These findings are consistent with the hierarchical model, in normal bilingual speakers and with persons with bilingual aphasia. Aphasia is a chronic, pervasive and often debilitating impairment of language that is most often a consequence of stroke in the left cerebral hemisphere. Speech-language pathologists strive to provide effective clinical rehabilitative services to remediate language impairments in persons with aphasia (PWA); with increasing prevalence of bilingualism in the world, special consideration to bilingual aphasia is imperative. Bilingual aphasia is a complex topic largely because of the heterogeneity within and across bilingual speakers due to varying manners of acquisition, patterns of use and relative abilities across languages , a lexical layer   and typological characteristics of each language . Further, characteristics inherent to bilingual speakers that can influence production are related to patterns and relative use across languages  is a structural element of language that has also been shown to impact word processing in bilinguals  of persons with relatively balanced abilities across languages  who work in Pretoria hospitals, clinics and rehabilitation centres. Data were collected by two speech pathology students (third and fourth authors).Inclusion criteria included the presence of a left hemisphere stroke, the presence of aphasia determined by a clinical SLP, bilingual speaker of English/Afrikaans with one language indicated by the participant as the predominant language and adequate hearing thresholds to conduct all tasks. The participants had to be capable of using full sentences or phrases in L1 during communication to ensure adequate verbal ability to perform the task. Exclusion criteria included severe aphasia, severely compromised receptive language ability, psychiatric illness, degenerative neurological disease, chronic medical illness, severe impairment in vision or hearing and knowledge or use of a third language.The four participants were on average 73 years of age (SD 11.7) and ranged between four years and two months post stroke onset. There were two men and two women, all were right-handed and were bilingual in Afrikaans and English see .Participant 1 (P1), male, age 72 was three months post stroke onset, had a university education and worked premorbidly as a university lecturer. He stated that he was fully bilingual since an early age, with acquisition of Afrikaans first (L1) and English later (L2) at the age of three. He was exposed to English through family and school and predominately spoke English in his occupational setting.Participant 2 (P2), female, age 84 was two months post stroke onset, completed Grade 12 and worked as a homemaker. She stated that she learned English first in the home (L1) and was exposed to Afrikaans from the age of four years (L2). She indicated that she was exposed to both English and Afrikaans in both the community and school and reported to have mastered both languages equally. For approximately 20 years pre-onset she was mainly exposed to English (L1) and used only English at home.Participant 3 (P3), male, age 57 was three months post stroke onset, had a four-year university degree and worked as an engineer. He stated that his first language was Afrikaans (L1) and that his second language, English (L2), was acquired at approximately eight years, predominately through formal classes in school and by watching the television. He regarded himself as quite proficient in both languages, using English and Afrikaans interchangeably at work.Participant 4 (P4), female, age 76 was three years and five months post stroke onset, had a Grade 12 education and worked as a homemaker. She stated that her first and most used language was Afrikaans (L1) and that she was exposed to English (L2) at age eight from formal lessons at school. She stated that she had a good English vocabulary prior to her stroke; however, she did not use English as much as Afrikaans in her daily life.http://www.wordcount.org . This cognate scale indexes four different features: initial sound, number of syllables, percentage of overlapping consonants and percentage of overlapping vowels. A specific rating scale is employed to further describe each of the four features. Initial sound is scored between 0 and 3 points . Number of syllables was scored between 0 and 2 points . Consonants were scored between 0 and 3 points . Finally, vowels were scored between 0 and 2 points . All scores for each word were tallied. For the purposes of this study, we deemed that a word was judged to have high overlap if it was between 8 and 10, medium overlap between 5 and 7, low overlap between 1 and 4 and no overlap if 0. See Participants were seated in a quiet room and stimulus cards were randomised and presented one at a time without any cues. The participants were requested to first name all objects in the set of 40 pictures in L1. After completion of the set of pictures in L1 they were again presented with the pictures, which were again randomised, and asked to name the pictures in L2. L1 was consistently probed first to control the possible influence of uncertainty or higher demands in L2. Instructions were provided in both languages (English for the English naming and Afrikaans for the Afrikaans naming). Participant responses were not constrained with a time limit. Participant responses were audio recorded and later scored for overall accuracy, total number of phonemes correctly produced and error type by three members from the motor speech laboratory at the University of Pretoria .The first research question addressed confrontation picture naming whole word accuracy. The second question addressed total number of phonemes correct and types of errors made. The final question looked at naming accuracy as a function of high, medium and low overlapping cognate status. Methods and procedures for each of these outcome measures are described below.Digital recordings of participant responses were scored, by consensus, by three trained SLPs (first and last two authors), two of whom are proficient Afrikaans/English bilingual speakers. The English speaking only SLP scored just the English responses. Only the participants’ first responses were coded. Correct response included the correct lexical item only. Fillers such as ‘um’ and ‘I don't know’ were not counted. Incorrect responses were coded for error type using five categories:phonologic (P) – substitutions, additions, transpositions, omissions.semantic (S) – related within language (SR-w: ‘child’ for ‘girl’), unrelated within language (SU–w: ‘grape’ for ‘house’), related across language , unrelated across language .mixed (M) – real words with a phonologic relationship to the target.omission (O) – includes circumlocutions and non-responses.neologism (N) – nonwords that were not phonologically related to the target.Direct translations were coded (T), as well as translations with phonologic errors (Tp).To answer research question 1, paired-samples unequal variance t tests comparing confrontation naming accuracy between L1 and L2 were performed. For the error analysis questions, paired-samples t tests compared L1 and L2 for raw number of each error type and error type proportions . For the cognate question, percentage accuracy was documented for high, medium and low overlap cognate words and paired-samples t tests were used to compare L1 and L2 differences.Consensus reliability on 25% of the corpus resulted in 98% point-to-point reliability on accuracy scores and 83% reliability on error type coding.p = 0.209). Results for P2 were 58% (L1) and 28% (L2), showing a significant between language difference (p = 0.038). Results for P3 were 38% (L1) and 20% (L2) accurate, showing statistical significance (p = 0.047). Finally, results for P4 were 23% (L1) and 2.5% (L2) accurate, which was significantly different (p = 0.047) (see The first research question asked if there was a significant difference in confrontation naming abilities between L1 and L2 as measured by accuracy. Results for P1 showed 75% (L1) and 83% (L2) accuracy, resulting in no difference (047) see .The second research question asked if there was a significant difference for each participant between L1 and L2 in the number and types of errors produced as measured by raw number and proportion of errors. Results for each participant, for L1 and L2, are described and are shown in P1 (L1) had 10 raw errors (out of 40 words). Nine errors were semantic and one mixed. The L1 semantic errors were further subdivided into eight within language-related errors and one within language-unrelated error. Proportion of errors were 0.90 semantic and 0.10 mixed. In L2, he had seven total errors (out of 40 words). Four errors were semantic, two phonologic and one omission. The L2 semantic errors were further subdivided into three within language-related errors and one within language-unrelated error. Proportion of errors was 0.29 phonologic, 0.57 semantic and 0.14 omission.P2 (L1) had 17 raw errors (out of 40 words). Seven errors were semantic, 1 phonologic, 7 omission, 1 translation and 1 neologism. The L1 semantic errors were further subdivided into 5 within language-related, 1 within language-unrelated and 1 across language-related error categories. Proportion of errors was 0.41 semantic, 0.06 mixed, 0.06 translation and 0.06 neologism. In L2, she had 29 errors (out of 40 words). Ten errors were semantic, 18 omission and 1 translation. The L2 semantic errors were further subdivided into 7 within language related, 2 within language unrelated and 1 across language related categories. Proportion of errors was 0.34 semantic, 0.62 omission and 0.03 translation.P3 (L1) had 25 raw errors (out of 40 words). Eight errors were semantic, two phonologic, 10 omission, two translation and three neologism. The L1 semantic errors were further subdivided into two across language-unrelated, three within language-unrelated, one across language-related and two within language-related categories. Proportion of errors were 0.08 phonologic, 0.32 semantic, 0.40 omission, 0.08 translation and 0.12 neologism. In L2, he had 32 errors (out of 40 words). Ten errors were semantic, one phonologic, one mixed, 14 omission, three translation and three neologism. The L2 semantic errors were further subdivided into two across language-unrelated, four within language-related, one across language-related and one within language-related categories. Proportion of errors was 0.31 semantic, 0.03 phonologic, 0.03 mixed, 0.43 omission, 0.09 translation and 0.09 neologism.P4 (L1) had 31 raw errors (out of 40 words). Two errors were semantic, six phonologic, two mixed, 16 omission and five neologism. The L1 semantic errors were further subdivided into one within language-unrelated and one within language-related categories. Proportion of errors was 0.19 phonologic, 0.06 semantic, 0.07 mixed, 0.48 omission and 0.16 neologism. In L2, she had 39 errors (out of 40 words). Four errors were semantic, two phonologic, 14 omission, 17 translation and two neologism. The L2 semantic errors were further subdivided into one within language-unrelated and three across language-related categories. Proportion of errors was 0.14 semantic, 0.07 phonologic, 0.48 omission, 0.59 translation and 0.07 neologism.The third research question asked if any differences were observed in spoken word accuracy between L1 and L2 for high, medium and low overlapping cognates. As a reminder, out of 40 words there were 17 with high overlap, 9 with medium overlap and 14 low-overlapping cognate words. Data are displayed in p = 0.22). P2 was higher in L1 (65%) than L2 (35%) (p = 0.09). P3 was slightly higher in L1 (47%) than L2 (33%) (p = 0.30). P4 was more accurate in L1 (47%) than in L2 (29%) (p = 0.30).In regard to naming accuracy for the high overlap words, P1 showed similar performance between L1 (71%) and L2 (88%) (p = 1.0). P2 was higher in L1 (67%) than L2 (33%) (p = 0.18). P3 performed slightly higher in L1 (33%) than L2 (0%) (p = 0.08). P4 was slightly more accurate in L1 (33%) than in L2 (0%) (p = 0.08).Naming accuracy for the medium overlap words for P1 showed equivocal performance between L1 (89%) and L2 (89%) (p = 1.0). P2 was higher in L1 (43%) than L2 (14%) (p = 0.10). P3 performed higher in L1 (29%) than L2 (21%) (p = 0.68). P4 was slightly more accurate in L1 (29%) than in L2 (21%) (p = 0.68).Naming accuracy for the low overlap words for P1 showed similar performance for L1 (71%) and L2 (71%)  individuals with aphasia with the goal of elucidating psycholinguistic mechanisms involved in bilingual word production. Overall, this study showed that whilst all participants had a diagnosis of aphasia, their naming impairments were reflective of their reported relative use patterns prior to their stroke. These findings are consistent with the hierarchical model  appeared to be relatively balanced in use and proficiency in both languages and he is the only participant who did not show significant differences in accuracy across languages. On the other hand, although P2, P3 and P4 acquired both languages relatively young (≤10 years old) and demonstrated the most severe naming impairments of the group, they showed significant differences in accuracy between L1 and L2. The lower performance of these three participants, then, could be interpreted from the perspective of premorbid use patterns  as opposed to severity of aphasia. Although the amount of detail we have regarding the participants’ premorbid language use is limited, our findings are consistent with Pitre’s  L2 lexical representations see . Converset al., The second research question explored if there were any differences in the types of errors produced in L1 versus L2. The results revealed that the proportion of semantic, phonological and mixed, omission, cross-linguistic and neologistic errors was essentially the same, regardless if the words were being spoken in L1 or in L2 (excepting P1’s semantic errors and P4’s cross-linguistic errors). From the perspective of bilingual word processing, the linguistic system is shared between languages and, as such, a linguistic impairment would evidence similarly in both languages. So, if there is a decrease in activation of the semantic system, the spread of activation is target language nonspecific, resulting in similar errors in both languages Costa, . Thus, tOmission errors were evidenced by P2, P3 and P4, who exhibited a more severe form of anomia. The higher proportion of omission errors (relative to other error types as well as relative to milder P1) could be attributed to the combined effect of lower proficiency or usage and an overall decrease of lexical or semantic activation. Finally, P4 showed more cross-linguistic errors in L2 versus L1 . A cross-linguistic error is not a true omission (lack of activation in both languages); rather, it may evidence that she was relying on L1 when she was unable to produce a word in L2.With respect to the phonological errors, P1, the only participant to show more phonological errors in L2, had the highest accuracy overall and was closer to the target in general across all attempts. Further, his phonological errors occurred in the low overlap items, suggesting that these words might be most sensitive in L2, even for relatively balanced bilinguals. P4 showed more phonologic errors in L1 (six), compared to L2 (two) which may indicate that since a phonologic error is a ‘smart’ error, it would occur in L1 and not L2 (which is the less accurate or proficient language).et al., The third research question explored L1 and L2 differences as a function of cognate status. This issue was important, as degree of phonological and orthographic overlap between languages has been shown to impact word processing in bilinguals  compared to L1 (71%). Although not statistically significant, this trend is consistent with Roberts and Deslauriers , who shoet al. , thereby facilitating production. The converse is true as well. A trend of lower accuracy observed with the low overlap words spoken with the least proficient language supports this notion as well.Finally, phonological overlap may indeed be a good way to characterise words for bilinguals in addition to more conventional, psycholinguistic terms, such as frequency  on patterns of recovery should be addressed in future research studies. Finally, it is important to note that parallels to other African languages are limited as the results will be person-specific and may depend on the classification of the languages that are compared. Both languages in the current study were Germanic languages. The clinical implications for this study are that the clinician needs to gather necessary information during the assessment period on level of proficiency and use. Also, if possible, the clinician should evaluate the word retrieval impairment across languages to provide additional information regarding severity.Characterising phonological word equivalents across languages in word evaluations (i.e. translations) in evaluations of lexical retrieval in aphasia may provide additional insight into the interactions between premorbid proficiency and use, level of impairment and degree of phonological overlap across languages.


We present a new universal method to accelerate calculations of transmission function and electrical conductance of 2D materials, the supercell of which may contain hundreds or thousands of atoms. The verification of the proposed method is carried out by exemplarily calculating the electrical characteristics of graphene and graphane films. For the first time, we calculated the transmission function and electrical conductance of pillared graphene, composite film of carbon nanotubes (CNTs)/graphene. The electrical conductance of different models of this material was calculated in two mutually perpendicular directions. Regularities in resistance values were found. The development of technologies for the synthesis of graphene nanomaterials has led to an expansion of the scope of their application. One of the graphene composites that have been actively studied in the last few years is pillared graphene . It is aT(E). The dependence of the transmission function on the energy of the electron in the system is characteristic for each point of the reciprocal lattice. The final form of T(E) depends on the number of k-points in the reciprocal lattice, because T(E) average over these lattice points. Using the convergent transmission function it is possible to find the electrical conductance of the nanostructure. However, in order to obtain a converged form of the averaged transmission function, it may be necessary to calculate it in a set of points in the reciprocal lattice, which is unattainable for a large number of atoms in the considered system. In this connection, the development of methods for accelerating the calculation of the transmission function without a significant loss in the accuracy of calculations has particular relevance and significance for research of the electrical conductive properties of new composite materials. At present, such accelerating techniques are practically absent. We found only one work [The non-equilibrium Green function (NEGF) method with density functional tight-binding (DFTB) scheme or density functional theory (DFT) scheme is used to calculate the electrical conductance of molecular structures consisting of atoms of various elements with high accuracy . Within one work  in whichIn order to calculate the electrical conductance we use the Green–Keldysh functions and the Landauer–Büttiker formalism . The calT(E) is the transmission function characterizing the quantum mechanical transparency of the conducting channel as a function of the energy of the electron moving along it, μ is the Fermi energy of the electrode, e is the charge of the electron, and h is the Planck constant. The thermal broadening function FT(E) is calculated by the formula:where kB is the Boltzmann constant, and T is the temperature. The transmission function is given by:where  and  are, respectively, the advanced and retarded Green matrices (describing the contact with the electrodes), ΓS(E) and ΓD(E) are, respectively, the level broadening matrices for source and drain. The function T(E) is found by summation over the entire Brillouin zone (BZ) and N is the number of points in the reciprocal space. The accuracy of calculating T(E) is determined by the segmentation of the reciprocal space and the considered number of energies values. The calculation will be reliable when the function T(E) does not change with decreasing pitch of the change in the wave number k. For example, for finitely segmented BZ with limits a and b, the function T(E) converges to its true form for N ≥ 103. For materials in which the cell contains of the order of several hundreds or thousands of atoms, the calculation of T(E) at a single point (for a fixed k) takes a rather long time, thus making 103 calculations impossible. For example, for a 2D crystal cell with 472 atoms, the calculation of the transmission function averaged over 288 points of the reciprocal space takes almost four days for the parallel calculation in 24 processes (Intel® Xeon® CPU E5-2660 v2 with a frequency of 2.2 GHz). If the BZ is not a segment, but a 2D or 3D figure, the number N increases by orders of magnitude. In the next section, a method will be described to reduce the number of reciprocal space points and energy values for which a transmission function calculation is required, without substantially losing accuracy of the shape of T(E).where T(E) for two different N by using the example of a graphene monolayer. Figure la shows the considered system, that is, the unit cell connected to the electrodes. Since we calculated the conductance of this material (graphene), the same cells act as electrodes. Electrodes are translated to infinity along the Y-direction, and they are semi-infinite along X. The central cell is also translated to infinity over Y. Thus, the wave number ky varies within , where ay is the unit cell size along the Y-direction (as shown in T(E) from Equations 1–3 with different values of N are shown in k = 0.1 1/Å (N = 15), the function has a step-like form. When the step of the decomposition is reduced to dk = 0.0015 1/Å (N = 984), the curve takes the correct well-known form for a graphene monolayer. The transmission function is represented in conductance quanta e2/h.Let us demonstrate the proposed method for calculating T(E) function is additionally processed. The values of T(E) near the transition area between the steps are refined to make them more abrupt. In many cases, this procedure allows us to eliminate the need for a more detailed decomposition of the energy interval. For this, within transmission-function calculations we used an interval-halving technique, which allows one to obtain a 16-times more accurate boundary value between the steps for four iterations. Each iteration reduces the difference between the energies E1 and E2 by a factor of two , E2 is the first energy value for the same k-point at which T = T(E2) and T(E2) ≠ T(E1)), since the value of the transmission function at the midpoint E3 = 0.5(E1 + E2), which is either T(E1) or T(E2), is determined. Then, the interval  is considered if T(E3) = T(E2), or the interval  if T(E3) = T(E1). Therefore, four similar iterations yield a 16-fold reduction of the energy difference between two adjacent steps of the transmission function.For each point of the reciprocal lattice, the calculated T(E) between two neighbouring points of the reciprocal lattice. T(E) for three different numbers ky. In general, independently of ky, interpolation for each point of the polygonal chain determines the nearest points with energy having the same value of the function T(E) and belonging to the neighbouring polyline. The picture of the distribution of points in this case has the form shown in T(E) = 2 is fixed. Thus, all the points of neighbouring polygonal lines having the same value of T(E) are first found, and then the nearest ones are selected from the energy difference. If a polyline has two adjacent lines, then each point of this polyline can have no more than one near point on each of them. Similarly, in the case of a single neighbouring polyline, there will not be more than one near point for each point on the polygonal chain. If the difference in the values of the transmission function exceeds one, additional points are added. For example, if for some value of ky the transmission function undergoes a jump on passing from a point with energy Ei to a point with energy Ei+1, with Ti+1 − Ti = 2, then an additional point will be added to this polygonal chain. This point is characterized by an energy value of 0.5 (Ei+1 + Ei) and the transmission function at this point is equal to Ti +1. This is necessary in order to find the nearest point with the value of the transmission function Ti + 1.To eliminate the step-like form of the averaged transmission function, we interpolate the function T(E) as the nearest points. The number of points added depends on the length of the segment connecting the nearest points on different polygonal chains. The longer the lengths of the segment, the more additional points are added. If an additional point has not been used to form the connecting segment, it is not used to construct an interpolating function. The starting points and the remaining added points are used to construct the interpolating function.Next, the nearest points found are used to add additional points between them, lying on the segment connecting these points. All additional points have the same value of T1 makes it possible to realize a detailed decomposition over ky values, ensuring smoothing of the initial roughness. T(E): T1. The step-like behaviour of the function T(E) has disappeared everywhere, except for the region near the Fermi level (0.0 eV here). Indeed, there may exist “special regions” for which the original partitioning by ky was too coarse. Special regions are determined by the researcher in the gradient of the image. Areas of smooth colour change indicate the lack of partitioning for this area. Calculations with a more particular partition are additionally carried out for this area, but already in a narrow range of values: from 0 to 0.2 1/Å for ky, and from −0.3 to 0.3 eV for E. The next step is the construction of a new interpolating function T2. T2, T(E) averaged over all ky. The solid curve shows the calculation with the distance between two neighbouring points in reciprocal lattice of 0.0015 1/Å, the dotted line shows the result of applying the developed method. The norm of the difference between the interpolated and the converged values is 0.68%. Time taken to obtain the average transmission function  varies: 34 minutes, 2 seconds per accurate calculation and 2 minutes, 22 seconds to obtain the final values of the interpolated graph. Note that, in general, the time taken to add points depends on the amount of input data, and not on the number of atoms in the considered structure.The interpolating two-dimensional function The proposed method for calculating the transmission function was also tested with the example of graphane. The results of solving the test problems show that the transmission function calculations were accelerated by factor of 14.38 for graphene and of 19.92 for graphane by using the method developed here. Nevertheless, the speed of calculations is limited by the complexity of the dependence of the transmission function on energy and the considered point of the reciprocal lattice. The higher the rate of change in the transmission function, the more detailed calculations are needed.k. The test problems solved for graphene and graphane show that the discrepancy between the values of the transmission function calculated without the developed method and with its application was about 1–2%.The accuracy of the results of the transmission function calculations obtained using the proposed method depends on the size of the unit cell and the chosen reciprocal lattice vector X-axis and 2.13 nm along the Y-axis for each unit cell. X- and Y-directions, as in the case of the graphene monolayer, a central supercell and supercell electrodes are separated  in the left figure, and along Y  in the right figure. In this case the supercell consists of 580 atoms with a distance between the graphene layers of 2.4 nm. The conductance was calculated using the developed method because of the large number of atoms. The plots of the function T(E) averaged over all k in the case of electron transport in the X-and Y-directions are shown in Using the developed method for calculating the transmission function we investigated the transmission functions and electrical conductance of 2D graphene/CNT composites. The investigated film was modelled by two layers of graphene connected by single-layer armchair tubes  with a diameter of 1.23 nm . The distance between the tubes was equal to 2.1 nm, the length of the tubes  ranged from 1.1 to 2.4 nm. The graphene sheet had a length of 2.45 nm along the ated see . The conT(E) were calculated for all models of supercells of a composite on the basis of CNT  at the same distance between tubes of 2.1 nm. The conductance and resistance of the pillared graphene film were calculated based on the calculated T(E). Y-direction for single-layer composites, and around a value of 90 kΩ in the X-direction only with larger amplitude.Similarly, the transmission functions X-axis and 4.12 nm along the Y-axis for each unit cell.Similar investigations were carried out for two-layer pillared graphene . The graY-direction and 29.32 kΩ in the X-direction. The difference between the resistance in the X- and Y-directions is significantly lower for two-layer composite in comparison with single-layer composite. The conductivity in the Y-direction has increased for all the considered situations  varies insignificantly and does not depend on the distance between the graphene layers. For a two-layer composite, the average resistance depends on the axis direction. This can be explained by the high electrical conductance of graphene nanostructures with a zigzag edge. The conductance of these ribbons does not depend on the width of the ribbon and weakly depends on its topology. In the direction of the X-axis (armchair edge of graphene sheet), the electrical conductance of single- and two-layer composites depends significantly on the topology of the film. The resistance changes drastically with the increase in the CNT length.Based on obtained results, we can conclude that for the single-layer pillared graphene film, the resistance in the direction of the k-point sampling or a too coarse energy sampling will lead unrealistic results, in spite of any post-processing scheme.We created a new universal method for calculating the electron-transmission function and electrical conductance at quantum transport in composite nanomaterials. This method allows us to investigate the electrophysical properties of atomic structures, which contain hundreds and thousands of atoms in the transmitted supercell. By the example of monolayer graphene and graphane it was shown that the developed method significantly reduces the calculation time of the transmission function. The error of the calculation was equal to 0.68% and 1.79% for graphene and graphane, respectively. A number of competitive advantages of the proposed approach compared to other methods in the literature are: Our approach does not use the Dijkstra method used in [Using developed method we obtained new knowledge about the electrical conductive properties of a new composite material, namely pillared graphene. The calculated electrical conductance and resistance of the pillared graphene film showed that the current flow is more preferable along the zigzag edge of the graphene sheet both for single-layer and two-layer composites. The average resistance value in this direction was 12 kΩ for the single-layer composite. This value is close to the resistance value of an ideal nanotube. For the two-layer composite, the average resistance was 10.2–29.3 kΩ depending on the direction. This can be explained by the high electrical conductance of graphene nanostructures with a zigzag edge. The conductance of these ribbons does not depend on the width of the ribbon and weakly depends on its topology. In the direction of the armchair edge of the graphene sheet, the electrical conductance depends significantly on the topology of the film. The resistance changes drastically with the increase in CNT length. Using the analogy with graphene nanoribbons, it can be seen that the regularities in the electronic transport along the armchair edge are determined by the width of the ribbon and its morphology. In summary, we can conclude that the pillared graphene films with nanotubes having a diameter of 1.23 nm are characterized by a relatively high electrical conductivity. Due to high strength and conductivity, these films, provided a developed surface and pores for filling with the necessary connections, could be successfully applied in electronic devices and as electrodes of storage batteries.


On the other hand, the BP-based humidity sensor is less repeatable due to the instability of BP with water molecules and the stability of the sensor is reduced. In this study, this limitation of the BP-based humidity sensor was overcome by preparing a BP/graphene hybrid as a novel humidity sensing nanostructure. The BP/graphene interface improved the stability of the humidity sensor after a few weeks with a linear response within the relative humidity (RH) range of 15–70%. The sensor’s response/recovery speed of the humidity sensor was extremely fast within few seconds. The response (S) of the humidity sensor based on the BP/graphene hybrid is 43.4% at RH = 70%. The estimated response and recovery time of the sensor is only 9 and 30 seconds at RH = 70% at room temperature. The experimental investigation reveals that the BP/graphene hybrid not only improves the reversibility and hysteresis factors but also enhances the stability of the humidity sensor.Black phosphorus (BP) materials have attracted considerable attention owing to their ultra-sensitive humidity sensing characteristics because of the natural absorption of water (H Various humidity sensor technologies have been developed, such as those based on resistive1, semiconductor1, optical2, and surface acoustic wave technologies3. Among these devices, resistive sensors have several advantages compare with other types such as simple structure, high sensitivity, rapid response, low cost and low power consumption1. Popular humidity sensing materials include polymers4, semiconducting metal oxides1, and carbon-based materials (carbon nanotube and graphene oxide)5. These conventional materials with a range of nanostructures offer many advantages for use in humidity sensing. On the other hand, humidity sensors from these conventional nanomaterials still exhibit a slow response/recovery time and in some cases require heating temperatures for operation5. Recently, new two dimension (2D) nanomaterials have demonstrated many advantages in the sensing area with a planar crystallite structure, large surface-to-volume, and low electronic noise6. The unique properties of new 2D materials, such as graphene7, black phosphorus (BP)10, and tin disulfide (SnS2)11, provided superior sensing factors including single molecules agents, ultra-fast super sensitivity and low power consumption.Humidity sensing techniques have been investigated in many areas such as the industrial processing, environment, food, agricultural, and indoor applications13. In particular, BP is a new excellent humidity sensing material with ultra-sensitivity and a rapid response12. However, BP has low stability and reacts naturally with water molecules, limiting its long-term stability in humid environment12. To overcome this limitation, there have been some attempts to passivate the surface of BP14, encapsulate it with graphene15, or use a composite/hybrid with other materials18. In particular, chemical bonding between phosphorus and carbon (P-C) has been reported to play a significant role in stabilizing BP/graphene composites/hybrids for practical applications17. On the other hand, the conventional composites/hybrids are usually limited due to defect formation at the interface, leading to lower stability of the electronic device. Graphene-based heterojunction presents an interesting alternative way to overcome this limitation because of excellent properties of graphene as a support material. In addition, the combination of these new 2D materials on graphene to form heterojunctions between 2D materials has advantages in 2D electronic device such as low electronic noise, low power consumption, and good stability at the interfaces15. The new 2D material and graphene heterojunction control provides the latest advantages of 2D electronics, such as low electronic noise, low power consumption and excellent stability interfaces.BP has been reported as a novel material for gas and humidity sensing with excellent properties13. However, to take advantage of unique characteristics of scalable technologies, it is essential to establish a mass production process for 2D materials synthesis and sensor device fabrication. This very exciting challenge will be addressed in the current work. In this study, a large quantity of BP materials was synthesized in powder form  with a novel technique of high energy ball milling (HEBM). The BP powder was exfoliated by a mild ultrasonication process and BP/graphene heterojunction was formed on the graphene surface using an electrospray system for humidity sensor. The humidity sensing performances of the sensors prepared with a pure BP and BP-graphene heterojunction were investigated and compared in terms of the sensitivity, reversibility, and stability. The role of graphene and the interface between BP/graphene for humidity sensors was investigated in detail.To date, exfoliated 2D layers, particularly BP, could only be transferred in small sizes onto substrates in basic and proof-of-concept studies2/Si with wafer-level. Then, the platform of humidity sensor chip comprise patterned graphene between two gold (Au) electrode. The BP powder was synthesized by a HEBM method and deposited on the patterned graphene by electro-spray (see in Supplementary data for more detail). Figure g1, B2g, and Ag2 peaks of BP are clearly visible at 359, 432, and 462 cm−1, respectively19. The Ag1 and Ag2 peaks of the pure BP sample were observed at 356 and 459 cm−1, respectively. The Raman spectrum of single layer graphene consisted of two major sharp peaks (G and 2D peaks) at 1584 and 2674 cm−1. The major peaks (G and 2D peaks) originated from the doubly degenerate zone center E2g mode and the second order zone boundary phonons, respectively20. The D peak at 1350 cm−1 is related to the defects present20. The features of those peaks are indicators of the quality of graphene, such as doping and strain. The G and 2D peaks in BP/graphene were 1590 and 2689 cm−1, respectively. No obvious increase in the D peak in the Raman spectra before and after depositing BP powder on graphene was observed. The as-synthesized single layer graphene has Raman spectra with 2D/G ratio > 1. However, the 2D/G ratio value was reduced (2D/G < 1) after the sensor fabrication process  when the sensor is exposed to a given humidity. The recovery time is defined as the time needed to recover to 90% of the initial baseline after turning-off the humidity. The responses S (%) of the humidity sensor based on BP-graphene heterojunction calculating from Fig. 21 and 5/5 seconds12. Meanwhile, the response/recovery time of our humidity sensor using pure BP was 24/72 seconds. The results showed that the humidity sensor using BP/graphene heterojunction is better than that using pure BP with a 2-fold faster response time. Moreover, the humidity sensor using pure BP without a passivation method showed large degradation after a few cycles (within 2 hours)21. Fig. 2O) molecules withdraw a free electron from the BP flakes and increase the hole density in BP. The BP exhibits a p-type semiconductor behavior15. Therefore, the increasing hole density in p-type BP leads to decreasing resistance in the humidity sensor of the pure BP sample  is defined as the percentage resistance change of the resistivity sensor by exposure to humidity:12, the BP-graphene heterojunction humidity sensor in this study has the advantageous features of a fast response/recovery time, linearity and mass production process of sensor. The degradation of the BP only sensor was caused by lower stability of the surface of the BP flake in moisture and humidity14. In this case, pure BP played a role both as a humidity sensing material and conducting patch between the Au electrodes in the sensor device, leading to higher noise and degradation during humidity absorption/desorption. The sensing mechanism of BP/graphene heterojunction involves charge transfer at the interface between BP/graphene and graphene playing a role as a stable conducting path. In addition, due to the good stability at the BP/graphene interface17, the humidity sensor could show better stability and reversibility, compared to the sensor using the BP only sample. Passivation of BP surface is essential for sensing applications22, and electronic devices15 based on BP materials. This is the greatest challenge for applying BP as a sensing material because the passivated BP process reduced the sensitivity of the BP surface, leading to the complicated fabrication of the sensor. However, the sensor based on passivated BP showed a long-term stability up to one month22 or three months12. In this study, the BP/graphene heterojunction humidity sensor showed high sensitivity, fast/response recovery owing to BP without a passivation process and acceptable stability for up to two-weeks, which is better than that of the sensor using the pure exfoliated BP material with stability for only a few hours.Figure A humidity sensor based on BP/graphene heterojunction was developed using a large scale fabrication technique. The role of graphene in the heterojunction of the humidity sensor was investigated by comparing the sensor performance of the BP and BP/graphene sample. The BP-only samples showed good sensitivity to humidity with the advantages of a strong response and rapid response/recovery time, but were less stable, non-linear and reversible. On the other hand, the BP/graphene heterojunction-based humidity sensor overcomes these limitations and has excellent sensing properties with a response of 43.4% and a response/recovery time of 9/30 seconds with a RH of 70%. In addition, the humidity sensor has good repeatability, low hysteresis and long-term stability over two weeks by forming a BP-graphene heterojunction. Moreover, it solves the instability of the BP-only sensor.23. The wafer-scale of single layer graphene was synthesized by chemical vapor deposition (CVD)20. The sensor chip (graphene chip) with patterned graphene between the two gold (Au)-electrodes (distance of 100 µm) was fabricated in wafer-scale level by a dry-etching technique and conventional MEMS process (see the Supplementary data). The BP powder dispersed in dimethyl sulphonate  by an ultrasonic treatment was deposited on a graphene chip to fabricate a humidity sensor via an electrospray system. DMSO was used as the solvent for BP in the electrospray experiment, where BP was deposited on the patterned graphene surface. The water flow rate was controlled precisely by a syringe pump . The electric potential was adjusted using a power supply  connected to the metal capillary. The metal capillary was used as an electrospray emitter with an inner diameter of 250 μm. The nozzle tip- to-substrate distance was fixed to 10 mm. For rapid evaporation of the solvent, the surface temperature of the substrate was adjusted using a hot plate . For comparison, the humidity sensor using pure BP powder was fabricated but without graphene between the Au electrodes. Humidity sensors using pure BP powder for comparison were fabricated under the same conditions but without graphene between the Au electrodes. In the wire-bonding process, the humidity sensor was mounted on the TO-39 chip to finish the sensor fabrication process.The BP powder was synthesized using the HEBM technique at ambient temperature and pressure. The detail experimental conditions for the synthesis of BP powder by HEBM can be found elsewhere (see the Supplementary data)The surfaces of the BP/graphene hybrid were characterized by field emission scanning electron microscope . Transmission electron microscopy (TEM) and high resolution TEM (HRTEM) images of the BP were captured using an ultra-high resolution field emission electron microscope (JEOL JEM-2100). The crystalline characteristics of the BP were investigated by X-ray diffraction . Raman spectroscopy was performed in a back scattering configuration using a 532 nm laser source and holographic grating of 1200 grooves/mm.2 gas. A computerized mass flow controller  was used to change the humidity and concentration of N2 gas. The relative humidity (RH%) was varied from 15 to 70%. N2 gas with different humidity level was delivered to the chamber at a constant flow rate of 100 standard cubic centimeters per minute (sccm). The gas chamber was purged with N2 gas between each humidity pulse, allowing the surfaces of the sensors to return to the standby state.The sensors were mounted inside an enclosed environmental chamber and a multi-meter (Fluke 8846 A) connected to the computer was used to record the resistance of the sensors. The humidity in gas chamber was generated using a water bubble controller and introduced into the chamber by NSupplementary Info


Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of uncertainty and other effects that are particularly manifest in cognitive processes, which makes it well suited for the study of decision making. QDT describes a decision maker’s choice as a stochastic event occurring with a probability that is the sum of an objective utility factor and a subjective attraction factor. QDT offers a prediction for the average effect of subjectivity on decision makers, the quarter law. We examine individual and aggregated (group) data, and find that the results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. This article revisits the formalism of QDT along a concrete example and offers a practical guide to researchers who are interested in applying QDT to a dataset of binary lotteries in the domain of gains. For example, a typical question could be to choose between the following options: “option 1: get CHF 50 with a 40% chance (or nothing with a 60% chance); option 2: get CHF 10 for sure.” Our dataset includes the 200 decisions performed by each of 27 subjects with various values of p and x.In this article, we apply quantum decision theory (QDT) to a dataset of choices between a certain and a risky lottery, both in the domain of gains. Each decision task consists in a choice between (1) a risky option in which the decision maker can win a fixed amount, here QDT offers a quantitative prediction, the so-called quarter law, which concerns the average effect of subjectivity on people’s decisions. In the present case, the quarter law allows us to predict the frequency with which either of two options will be chosen.With this article, our aim is to provide a practical how-to guide for QDT in its present state, not to resolve paradoxes of human decision making (as has been done in QDT articles –3) or exAnother contribution is to offer a practical illustration of how to apply QDT to a dataset of binary lotteries in the domain of gains, so as to test the quarter law at the level of individuals and groups when each subject is faced with a number of different decisions. Previous QDT publications, e.g. , 3, typiWe examine individual and aggregated (group) results, and find that our results are in good agreement with the quarter law at the level of groups. At the individual level, it appears that the quarter law could be refined in order to reflect individual characteristics. We use gender to distribute subjects into two groups and apply QDT to compare these groups and test the quarter law within each group. Gender is a convenient variable on which to test the aggregation of individual data. Indeed, it is a readily available individual characteristics that splits the sample in two sets of almost equal size. Moreover, there is a vast literature on gender-specific risk-taking behavior –17. The Let us stress that QDT does not suppose that the brain is a quantum object. The mathematical formalism of quantum mechanics, rigorously developed by von Neumann , is thatWe thus use the same mathematical formalism as that of quantum mechanics, but do not claim that neurological processes are quantum in nature. For clarity, let us give a parallel example. Newton (1642-1726/7) was interested in planetary motion and developed calculus to establish the laws of movement and gravitation. That does not mean that there is anything fundamentally planetary to calculus. This formalism very generally allows the study of change. In the case of planetary motion, calculus describes the change of position and speed along physical trajectories in space and time. Meanwhile, calculus has been used in every scientific domain concerned with change. In the same way, the mathematical framework of Hilbert spaces is known in physics for its application to quantum mechanics, but it can be said to generally apply to the study of uncertainty, and this is what motivates us to make use of it for decision making processes.Others have recently followed a similar path, most notably Busemeyer and collaborators e.g. –24); see; see24])j) is characterized by a set of outcomes and their probability of occurrence, and is written aspj is a probability measure over the set of payoffs {xn} and thus belongs to the interval  and is normalized to one.Let us now give a few elements of decision theory that help understand how QDT relates to classical theories of that field that are well known in the fields of psychology and behavioral economics. For this review, we consider how classical theories evaluate simple gambles. Simple gambles, as Kahneman  (p.269) In experimental settings, it is common for decision makers to have to choose between two simple gambles or between a gamble and a sure thing, as in “would you rather have a 20% chance to win CHF 50 (with an 80% chance to get nothing), or get CHF 10 for sure?”. We call this a “decision task” . We write the former example asIn decision theory, such decision tasks serve as simple models for the more complex decisions we face in everyday life. In real situations, outcomes are often not expressed in monetary terms, and their probabilities are unknown. For instance, we are unable to assign a probability to the event that our happiness will increase if we get a new job and move, nor do we assign an exclusively quantitative value to this change of happiness. Nevertheless, it is the consensus of the field that simple choice problems such as the above elicit risk preferences, and we will focus on lotteries of that form.A few risk elicitation methods are reviewed by . The metIn accordance with probability theory, Pascal  expresseu transforming values in u(x) = ln(x), such as to reflect that we become more indifferent to changes of wealth as the initial amount of wealth increases. For example, an increase of wealth from 1 to 4 million has a higher psychological value than an increase from 4 to 7 million.Later on, Bernoulli  examinedu(x)) remained dominant for a very long time. Von Neumann and Morgenstern  .Hence, we identify the probability that the lottery p(Lj)  is to be understood as the theoretical frequency of the prospect Lj being chosen over a large number of times. Two types of setups can be put in place. The first setup involves a number of agents; in that case p(Lj) gives the fraction of agents expected to choose Lj. In the second setup, a single decision maker is faced with a number of decision tasks, among which the same decision task appears several times. This setup is designed such that each repetition of the same decision task can be assumed to be independent of previous occurrences. That is, we assume negligible memory and influence of previous decisions. In this second setup, the option Lj is chosen a fraction p(Lj) of the time by the same decision maker. QDT treats similarly these two setups.The probability ψ|πj〉|2 in terms of the coefficients given in Eqs ψ|πj〉|2 iutility factor,The classical terms become the so-called f(Lj) remains in p(Lj). When q(Lj) = 0, the standard classical correspondence principle , q(Lj) lies in the interval . These two conditions are called in QDT the alternation conditions:Since q equal to L (the number of prospects in each decision task) multiplied by the number of choices made. Let us introduce φ(q), the normalized distribution of q, and writeArising from interference effects between prospects in the mind of the decision maker, the attraction factor can be seen as a random quantity varying across decision makers and over time for a single decision maker. Thus, the choices made by different individuals or by the same person at different times constitute a number of realizations of L = 2 prospects, the distribution of q is symmetrical around zero and the mean of q is zero:Because of the alternation conditions Let us define the quantitiesFrom the alternation conditions q is equiprobable, i.e. the distribution φ(q) is uniform. From In the absence of any information, the variable L1 is the most attractive prospect, we haveL2 is the most attractive prospect. In QDT, this is called the quarter law and constitutes a quantitative prediction on the average value of the attraction factors in any given experiment, under the assumption of no additional prior information.Applied to a binary lottery choice, this yields the prediction that, when φ(q) yield the same average value of 1/4 for the attraction factor, which makes this result quite general, as pointed out by Yukalov and Sornette in , with α > 0 and Γ(α) the gamma function. The beta distribution is employed in many applications, for example in Bayesian inference as a prior probability distribution. The quarter law also follows from several other distributions normalized on the interval , such as the symmetric quadratic distribution,Several families of distributions nette in . For exaTypical values of the attraction factors are derived by Yukalov and Sornette in  in the gA rule has been expressed by Yukalov and Sornette in  (p.1162)This rule considers two lotteriesThe maximal and minimal gains are denoted asg(L1) of the first prospect, the risk factor r(L2) of choosing the second prospect, and the quantity α(L1) are then defined as follows:The gain factor q(L1), is defined by the ruleUsing these quantities, the sign of the first prospect attraction factor, L1, is risky: subjects can win either CHF 50, with a probability p, or nothing, with a probability 1-p. In the other lottery L2, subjects get the sure amount x in CHF . This can be seen as a “certain lottery.” The condition 0 < x < 50 is always ensured, otherwise there would be no point in choosing the risky lottery. The two lotteries are writtenx < y and in the experiment, y = 50 CHF.In the dataset we are analyzing, subjects have to choose between one of two lotteries. One lotteries, L1 as p, x with probability 0 and y with probability p. Similarly, writing L2 as x with probability 1 and y with probability 0. This way of expressing the two prospects captures the fact that decision makers compare the two lotteries as they are making up their mind.Note that the same amounts appear in both prospects. Writing p (the probability of winning the fixed amount CHF 50 in the risky lottery L1) and x (the guaranteed payoff in the certain lottery L2). In the experiment that generated the dataset, pairs of  values were randomly generated and the corresponding decision tasks  were submitted to subjects.In this dataset, a decision task is characterized by the values of the two parameters p was varied between 0.05 and 0.9 by steps of 0.05, and the sure amount x between 0 and 49 by steps of 1. At most 900 different  pairs could thus be generated.Each of 27 participants was given 200 randomly generated decision tasks, in 4 runs of 50 questions each. This amounts to 5,400 data points. Overall, the probability The detailed method of the experiment in given in  (chap. 7The mean age of participants was 25.8 ± 3.6 years. Thirteen women (mean age 25 ± 3.3 years) and fourteen men (mean age 27 ± 3.7 years) were included in the study. The decisions were contextualized, in the sense that participants were asked to imagine a bank investment. Each decision was equally important, as participants were promised to receive, at the end of the experiment, the amount resulting from one randomly chosen decision task. The Ethics Committee of the Canton of Zurich approved the study. All participants provided written, informed consent and were compensated for their participation.We now present how QDT specifically applies to the empirical dataset under study. The theoretical correspondence was carried out in the section that follows the introduction. Indeed, this section considers a decision problem whose structure corresponds to that of the decision tasks generating the dataset.As stated earlier, we equate prospect utilities with expected values given by Then, according to p(Lj). As is the case of other datasets available to researchers, the present dataset was not generated with QDT in mind. We suggest in the discussion how to design decision tasks more suitable for testing QDT. There are several ways to aggregate the decision tasks, of which the following:Since QDT is a probabilistic theory, a decision task must be offered several times in order to obtain an empirical choice frequency approximating (i)p, x) values, i.e. the same utilities U(L1), U(L2).Only aggregate decisions presenting the same ((ii)p, x) values. For example,  and  present the same value of p and close values of x, and could be considered so similar as to represent the same decision task.Aggregate decisions with close ((iii)f(L1), f(L2). For instance, the  pairs A, B and C give respectively f(L1) = 0.1.Aggregate decisions presenting the same utility factors p, x) pairs (option (i)) is that the available empirical dataset does not always present a sufficient number of realizations of each  pair to perform a meaningful probabilistic analysis. For instance, in our dataset, 10.7% of all  pairs were offered only once; 11.5% were offered twice; 30.4% were offered three times or less. At most, one  pair was offered 126 times. Ignoring decision tasks with less than a minimum number of realizations is possible, but means giving up a substantial amount of data.The issue with only aggregating identical (f(L1) to the lowest 0.01, no decision task characterized by its utility factor f(L1) was offered less than three times, and only 1.3% of all values of f(L1) were submitted exactly three times. At most, a given value of f(L1) was submitted 274 times. The number of decision tasks given per value of f(L1) is shown in Aggregating by utility factor (option (iii)) partly resolves this issue. When rounding p and x from different  pairs have to be in order to aggregate the pairs. This option can bring an intermediate result between options (i) and (iii). In this analysis, we use option (iii).In option (ii), one has to decide how close values of Nj a prospect was chosen by one or several decision makers over the N times the same decision task was offered. Since the probabilities, utility factors and attraction factors for the two prospects  are related by Eqs  an anNj a pd by Eqs , the entp(L1). In what follows, we identify pexp(L1) with p(L1).The empirical frequency is given byX such that, at the k-th realization of a given decision task,p(L1) is thus the Bernoulli distribution of X.Let us introduce a random variable retract function, which retracts a variable z into an interval :Let us additionally introduce the p(L1), the utility factor f(L1) and the attraction factor q(L1):p(L1) lies in .Empirically, based on p(L1)<1, because of the retract function in p(L1) = 0 and p(L1) = 1, q(L1) can have taken any value such that f(L1) + q(L1)≤0 or f(L1) + q(L1)≥1, respectively. Hence, the exact value of q(L1) that guided the decision maker(s) cannot be retrieved in these two cases; applying q(L1).The attraction factor can be deduced from experimental results asf(L1) in . In order to visualize to which extent empirical data conforms to the quarter law through p(L1) as a function of f(L1). Then q(L1) is given by the difference between p(L1) and the lower left to upper right diagonal of the graph (p(L1) = f(L1)), as long as 0 < p(L1)<1. The absolute value of this distance is predicted by the quarter law to be equal to 0.25, on average. The dataset consists in decision tasks with various values of r(L2) = 0, α(L1) = −1 and sgn q(L1) = −1. In other words, at and around f(L1) = f(L2) = 0.5, the risky prospect’s attraction factor should be negative and the certain prospect should be preferred, in accordance with the principle of risk aversion.The rule for the sign of the attraction factor in the case of close utility factors given by For clarity, we summarize here the few steps necessary to obtain the attraction factors and test the quarter law in a dataset of choices between two lotteries in the domain of gains.f(Lj) ∈  ∀j = 1, 2.Choose a form for the utility factors satisfying Decide on an aggregation of decision tasks .Lj being chosen, p(Lj).For each aggregate, compute the frequency of a lottery p(Lj) in , compute for each aggregate the attraction factor q(Lj) = p(Lj) − f(Lj).For p(Lj) as a function of f(Lj).Represent f(Lj), or averaged over intervals of f(Lj)), |q(Lj)|, to the value 1/4 predicted by the quarter law.Compare the absolute value of the attraction factor , as a function of the utility factor of this prospect, f(L1). In the left panel, each point comprises the results of decision tasks presenting the same  values. The area of the markers is proportional to the number of decision tasks per point, which varies between 1 and 4. It is apparent in this panel that the majority of decision tasks were given only once, based on markers area as well as the fact that most points are situated at p(L1) = 0 or p(L1) = 1.f(L1), the same individual may not consistently choose the same prospect, especially at intermediary values of f(L1). Yet, at low and high values of f(L1), decisions tend to be consistent, as may be expected.The left panel of p(L1)) as a function of a quantity depending on the question’s parameters, which in our case is f(L1). To these data points is then typically fitted a logistic (S-shaped) function whose parameter can be interpreted as partly characterizing a decision maker’s risk behavior . Th. Thp(L1)p(L1) as a function of f(L1) for the same individual, but here we aggregated  values yielding the same f(L1) value rounded to the lowest 0.01. As noted in the methods, there are thus more decision tasks per point, which motivates us to continue the analysis based on this aggregation. In contrast to aforementioned fitting approaches, we are interested in examining whether these data points follow the QDT prediction given by the quarter law, expressed by p(L1) is situated at f(L1) ± 0.25 on average.The right panel of It is instructive to take a closer look at individual results. f(L1). The participant from the bottom left panel shows a strong preference for the certain prospect until high values of f(L1). In the bottom right panel, a relatively large number of choices seem to be random, although there is overall a transition from the certain to the risky prospect. Second, it appears that individuals behave quite differently from one another. For example, the participant in the top left panel appears to have calculated the expected values of each prospect and consistently chosen the one with the highest expected value. By contrast, in the top right panel, the transition from the certain to the risky prospect is noisier and takes place along a longer interval of In this section, we carry out an aggregation of individual results by gender and examine whether the quarter law holds at this level and whether gender differences can be observed in our sample. We use gender out of convenience, because it is a readily available characteristics of subjects that splits the sample in two sets of almost equal size. Moreover, it is common to observe gender differences in risk-taking behavior –17, as bpW(L1)) and men (pM(L1)) separately, as functions of the utility factor f(L1).qW(L1) (for women) and qM(L1) (for men). We use the SciPy script scipy.stats.ks_2samp  for men, as compared to f(L1) ∈  for women. Namely,f(L1) than men, andwomen (as a group) transition from the certain to the risky prospect at a higher value of f(L1) than men.women (as a group) transition over a longer interval of f(L1) = 0.5 and the preference transition to the risky prospect reflects the population’s average risk aversion. The larger distance for women suggests that women in the sample show a stronger risk aversion than men, on average. However, let us stress that the sample size of thirteen women and fourteen men is too small to generalize these results to genders in general. We come back to this point in the discussion.The distance between the risk-neutral value The interval length, for its part, can have two different interpretations.f(L1) (homogeneous population), a longer interval reflects that decision makers show little discrimination between different values of f(L1) along that interval, and are inconsistent in their choices, leading to intermediary values of p(L1).If individual transitions all start and end at roughly the same values of Alternatively, if individual transitions occur at different points or along intervals of different length (heterogeneous population), averaging over individuals will yield a broad transition at the level of the group. In that case, the transitional interval length at the group level reflects inter-individual variability.The analysis performed in the next section suggests that inter-individual variability is higher among women than men and is likely to contribute to the longer transition observed in q(L1). This yields one p-value per pair of individuals. Small p-values indicate that individuals in a pair make significantly different decisions.We now compare the distributions of attraction factors in pairs of individuals, separating between same-gender and cross-gender pairs. We thus make three types of pairings, man-man, woman-woman and woman-man. For each pair, we perform a Kolmogorov-Smirnov test on the individual distributions of attraction factors p = 0.025) and from the woman-woman distribution (p = 0.05), but the woman-woman distribution is quite similar to the woman-man distribution (p = 0.68).We also compare these distributions of p-values, using again Kolmogorov-Smirnov tests, and find that the man-man distribution is very different from the man-woman distribution | over all decision tasks for women and men separately. Let us recall that one has to exclude from the analysis the decision tasks with p(L1) = 0 or p(L1) = 1, as explained in the methods.In this section, we test the validity of the quarter law at the level of each gender. According to QDT, the absolute value of the attraction factor of either option in a binary lottery should be equal to 1/4 on average. We thus compute the average of |q(L1)| at the level of a group, as well as two different measures of variability. For completeness, we present all of these computations, as each gives a different perspective on the empirical results.We may use two different aggregations of individual results to obtain the mean of |Ns subjects to illustrate the different computations. Say that overall Nf different values of f(L1) were offered to this sample. Each value of f(L1) is associated with the choices made by different individuals. These choices can be aggregated to get one value of q(L1) per value of f(L1), without differentiating between individuals. This amounts to interpreting the sample as a set of homogeneous individuals, or equivalently as a single entity. We then average these Nf values of |q(L1)| . The standard deviation measures the variation of |q(L1)| across all decisions and sample subjects aggregated.Let us consider a sample of q(L1)| over the different values of f(L1) submitted to this subject alone. We thus get Ns values of Another approach is to first isolate each individual’s choices so as to obtain the subject’s average value of |Nf or Ns) whose variability is being measured and thus depends on the chosen aggregation.An alternative measure of variability to the standard deviation is the standard error of the mean (SEM). The SEM (that can only be estimated here) measures the variation between same-size samples compared to the full population from which the sample is drawn. Here, the “full population” is not the world human population. It is the comparable population in terms of age, gender (if the sample is restricted to one gender), socio-economic situation, education level, and culture. It may be qualified as WEIRD , as coined by . The estThese approaches yield the following attraction factors, standard deviations and SEM (in brackets), for women (W) and men (M). Without differentiating between subjects, we getWith a single value of q(L1)| is reasonably close to the value of 0.25 predicted by the quarter law, and this is formally evaluated by the standard deviation or SEM. When we consider each aggregate as an entity and use the standard deviation, the results for both genders are in agreement with the quarter law prediction of 0.25 on average. We interpret in the discussion the relatively large standard deviations found in this case.In all cases, the mean value of |When we average over each subject first and thus get a single value of With both approaches, the SEM does not cover the difference between the empirical and the theoretical value. This can be expected because, as noted above, the sampled population is biased and thus does not satisfy the no prior information hypothesis at the basis of the quarter law. We briefly come back to this point in the discussion.q(L1)| and the theoretical value of 0.25. However, the sample is overall biased. It could be the case that a larger sample would bring the mean absolute of the attraction factor nearer to 0.25 so that the SEM would cover the difference. This would occur if the bias of the mean decreases faster than the SEM as the sample size increases. Yet this is rather unlikely, as more of the same “kind” of subjects  would still constitute a biased sample.Overall, these results indicate that individual choices vary sufficiently to span the difference between the empirical value of |In this section, we aggregate individual results with the aim to test the quarter law at the population level.f(L1) = 0.5, we find the following attraction factor, based on 224 decision tasks:f(L1) = 0.5, expressed by . A rounding of f(Lj) should be chosen such as to allow this repetition over the N decision tasks and have the distribution of f(Lj) cover the interval . The lotteries should be generated beforehand and the distribution of games should be controlled to reflect the desired distribution. The order in which  games are presented to subjects should be randomized so that participants are unlikely to answer very similar questions consecutively.One of the practical challenges we encountered was to choose an adequate aggregation of decision tasks in order to carry out a meaningful probabilistic analysis guided by QDT, given the empirical distribution of . As a comparison, prospect theory founders Kahneman and Tversky typically ran experiments on 50 to 300 subjects , 63, 64.We offer in this work a guide and illustration of how to apply quantum decision theory (QDT) to an empirical dataset of binary lotteries in which decision makers had to choose between a certain and a risky option involving gains. Through this, we hope to promote the empirical investigation of QDT, in order to test its current claims, but also challenge it and indicate new research directions. One such direction could be to calibrate the attraction factor and characterize individual decision makers in terms of type of strategy and degree of predictability.S1 FileEach row in the dataset represents a decision task and includes an individual identifier (1 to 27), the gender of the participant (F or M), the probability with which the amount CHF 50 would be obtained in the risky option, the amount guaranteed by the certain option, and the decision made by the participant . There are 200 decision tasks per participant, resulting in 5,400 data rows.(CSV)Click here for additional data file.


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