forma¸c˜ao
As altera¸c˜oes na popula¸c˜ao de fˆonons devido as deforma¸c˜oes foram calculadas a partir da rela¸c˜ao de ocupa¸c˜ao
∆n(ω) = 1 + Rω
0 V DOSdef ormado(dω 0)dω0
1 +R0ωV DOSrelaxado(dω0)dω0
− 1 . (4.6) Nas Fig.4.13, 4.14 e 4.15, exibimos as altera¸c˜oes na popula¸c˜ao de fˆonons devido as de- forma¸c˜oes para o NHG. Em geral, para as deforma¸c˜oes biaxial e uniaxial na dire¸c˜ao armchair, os nossos c´alculos mostram que em baixas frequˆencias entre 0 THZ `a ∼ 1,0 THz h´a um esgo- tamento do modo ZA, devido a lineariza¸c˜ao na rela¸c˜ao de dispers˜ao (como mostra a Fig.4.3), sendo similar ao grafeno. Devido ao esgotamento do modo ZA, h´a uma diminui¸c˜ao no n´umero de fˆonons na c´elula de simula¸c˜ao, diminuindo o n´umero de colis˜oes e aumentando o valor do livre caminho m´edio, que consequentemente ocorre um aumento na condutividade t´ermica.
-0,1 0 0,1
∆
n
-0,1 0 0,1 ZA/ZO -0,1 0 0,1∆
n
LA/LO -0,1 0 0,1 Total 50 0,1 1 10Frequência (THz)
-0,1 0 0,1∆
n
TA/TO 50 0,1 1 10Frequência (THz)
-0,1 0 0,1 deformação = 2% deformação = 2% deformação = 4% deformação = 4% deformação = 6% deformação = 6%a)
b)
C
N
Figura 4.13: Altera¸c˜oes na popula¸c˜ao de fˆonons no NHG sob tra¸c˜ao biaxial. ´Atomos de a) carbono e b) nitrogˆenio.
-0,1 0 0,1
∆
n
-0,1 0 0,1 -0,1 0 0,1∆
n
-0,1 0 0,1 50 1 10Frequência (THz)
-0,1 0 0,1∆
n
50 1 10Frequência (THz)
-0,1 0 0,1 deformação = 2% deformação = 2% deformação = 4% deformação = 4% deformação = 6% deformação = 6%a)
b)
C
N
Figura 4.14: Altera¸c˜oes na popula¸c˜ao de fˆonons no NHG sob tra¸c˜ao uniaxial na dire¸c˜ao armchair. ´Atomos de a) carbono e b) nitrogˆenio.
Cap´ıtulo 4. Resultados e Discuss˜oes 59 -0,1 0 0,1
∆
n
-0,1 0 0,1 -0,1 0 0,1∆
n
-0,1 0 0,1 50 1 10Frequência (THz)
-0,1 0 0,1∆
n
50 1 10Frequência (THz)
-0,1 0 0,1 deformação = 2% deformação = 2% deformação = 4% deformação = 4% deformação = 6% deformação = 6%a)
b)
C
N
Figura 4.15: Altera¸c˜oes na popula¸c˜ao de fˆonons no NHG sob tra¸c˜ao uniaxial na dire¸c˜ao zigzag. ´Atomos de a) carbono e b) nitrogˆenio.
CONCLUS ˜OES
Em resumo, estudamos as respostas mecˆanicas e a condutividade t´ermica do NHG. Implementamos simula¸c˜oes atom´ısticas cl´assicas usando os m´etodos MD e NEMD, as liga¸c˜oes dos ´atomos nas estruturas foram descritas pelo potencial Tersoff parametrizado para os parˆametros B, N, C e h´ıbrido BN-C adequada a nanoestruturas semelhantes ao grafeno. Em todas as simula¸c˜oes foi utilizado um passo de simula¸c˜ao de 1,0 fs. A rela¸c˜ao de dispers˜ao dos fˆonons mostrou que o potencial descreve com precis˜ao a estrutura, e que ´a um endureci- mento do modo ZA sob deforma¸c˜oes biaxial. Para investigar as propriedades mecˆanicas, n´os realizamos simula¸c˜oes aplicando deforma¸c˜oes biaxial e uniaxial sob as c´elulas de simula¸c˜ao. Modificamos o raio de corte do potencial Tersoff de 0,19 nm para 0,22 nm para obter re- sultados f´ısicos consistentes ao longo dos processos de deforma¸c˜oes das estruturas do NHG e encontramos um m´odulo de elasticidade de 439 ± 2 GPa e 319 ± 3 GPa para sistemas sob tra¸c˜ao biaxial e uniaxial ao longo da dire¸c˜ao armchair, respectivamente, a temperatura ambiente. Tamb´em calculamos os m´odulos de elasticidade para diferentes temperaturas, e se notou que o m´odulo de elasticidade diminui `a medida que a temperatura aumenta. Obser- vamos a dependˆencia da condutividade t´ermica em fun¸c˜ao dos comprimentos das c´elulas de simula¸c˜ao e que a condutividade t´ermica aumenta linearmente para amostras com compri-
Cap´ıtulo 5. Conclus˜oes 61 mentos menores que o livre caminho m´edio e em seguida converge para um valor fixo. Para o sistema relaxado computamos uma condutividade t´ermica de 67,23 W/m·K e 70,15 W/m·K e um livre caminho m´edio efetivo de 16,84 nm e 22,55 nm ao longo da dire¸c˜ao armchair e zigzag no NHG, respectivamente. Comparado ao grafeno, que possui uma condutividade t´ermica de ≈ 1689 ± 100 W/m·K e um livre caminho m´edio efetivo de ≈ 5 µm, ambas quantidades s˜ao duas ordens de magnitude maior, a temperatura ambiente. Para manipular o valor da condutividade t´ermica aplicamos tra¸c˜oes biaxial e uniaxial, e averiguamos que se pode obter uma condutividade t´ermica no intervalo de 67,23 a 131,38 W/m·K, sendo a tra¸c˜ao biaxial e uniaxial na dire¸c˜ao zigzag a que mais e menos, respectivamente, refletem a altera¸c˜ao sob a condutividade t´ermica ao longo da dire¸c˜ao armchair, e a tra¸c˜ao uniaxial na dire¸c˜ao armchair apresentando valores intermedi´arios. Constatamos que a condutividade t´ermica diminue a medida que a temperatura aumenta, e mesmo com a presen¸ca de duas esp´ecies atˆomicas e de buracos na estrutura do NHG o espalhamento fˆonon-fˆonon prevalece sobre a resistˆencia t´ermica, e deste modo a condutividade t´ermica ´e influˆencia pela temperatura, uma vez que, κ ∼ T−0,70. Para elucidar os mecanismos f´ısicos sobre a condutividade t´ermica calculamos a densidade de estado vibracional e a altera¸c˜ao na popula¸c˜ao de fˆonons, os resultados mostra- ram que em baixas frequˆencias h´a um esgotamento da popula¸c˜ao de fˆonons, sendo o modo ZA o respons´avel pela modifica¸c˜ao no transporte t´ermico do NHG `a medida que a deforma¸c˜ao aumenta.
Perspectivas para trabalhos futuros:
• Utilizar outros m´etodos para prever a condutividade t´ermica: Muller-Plathe, Green- Kubo, Monte Carlo, dinˆamica de rede anarmonica.
• Incorporar disordem no sistema para construir um modelo mais real´ıstico e prever a condutividade t´ermica.
• Construir super-redes revezando periodicamente dom´ınios de C2N com outras estrutu-
ras semelhantes, como o C2P e C2As.
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